TSTP Solution File: SYO330^5 by cocATP---0.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SYO330^5 : TPTP v7.5.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Tue Mar 29 00:51:10 EDT 2022
% Result : Timeout 287.22s 287.64s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SYO330^5 : TPTP v7.5.0. Released v4.0.0.
% 0.03/0.12 % Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.33 % Computer : n012.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPUModel : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % RAMPerCPU : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % DateTime : Sat Mar 12 04:15:05 EST 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27'
% 0.12/0.34 Python 2.7.5
% 2.37/2.62 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox2/benchmark/', '/export/starexec/sandbox2/benchmark/']
% 2.37/2.62 FOF formula (<kernel.Constant object at 0x2aecac397998>, <kernel.DependentProduct object at 0x2aecac397fc8>) of role type named cNUMBER
% 2.37/2.62 Using role type
% 2.37/2.62 Declaring cNUMBER:(fofType->Prop)
% 2.37/2.62 FOF formula (<kernel.Constant object at 0x2352d40>, <kernel.DependentProduct object at 0x2aecac3973b0>) of role type named cODD
% 2.37/2.62 Using role type
% 2.37/2.62 Declaring cODD:(fofType->Prop)
% 2.37/2.62 FOF formula (<kernel.Constant object at 0x2aecac397998>, <kernel.DependentProduct object at 0x2aecac397f80>) of role type named cEVEN
% 2.37/2.62 Using role type
% 2.37/2.62 Declaring cEVEN:(fofType->Prop)
% 2.37/2.62 FOF formula (<kernel.Constant object at 0x2aecac3973b0>, <kernel.DependentProduct object at 0x2aecac397170>) of role type named cS
% 2.37/2.62 Using role type
% 2.37/2.62 Declaring cS:(fofType->fofType)
% 2.37/2.62 FOF formula (<kernel.Constant object at 0x2aecac397f80>, <kernel.Single object at 0x2aecac397998>) of role type named c0
% 2.37/2.62 Using role type
% 2.37/2.62 Declaring c0:fofType
% 2.37/2.62 FOF formula (((and ((and ((and ((and ((and (cEVEN c0)) (forall (Xn:fofType), ((cEVEN Xn)->(cEVEN (cS (cS Xn))))))) (cODD (cS c0)))) (forall (Xn:fofType), ((cODD Xn)->(cODD (cS (cS Xn))))))) (forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))) (forall (Xn:fofType), ((iff (cNUMBER Xn)) ((or (cEVEN Xn)) (cODD Xn)))))->(forall (Xn:fofType), (cNUMBER Xn))) of role conjecture named cEVEN_ODD_4
% 2.37/2.62 Conjecture to prove = (((and ((and ((and ((and ((and (cEVEN c0)) (forall (Xn:fofType), ((cEVEN Xn)->(cEVEN (cS (cS Xn))))))) (cODD (cS c0)))) (forall (Xn:fofType), ((cODD Xn)->(cODD (cS (cS Xn))))))) (forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))) (forall (Xn:fofType), ((iff (cNUMBER Xn)) ((or (cEVEN Xn)) (cODD Xn)))))->(forall (Xn:fofType), (cNUMBER Xn))):Prop
% 2.37/2.62 We need to prove ['(((and ((and ((and ((and ((and (cEVEN c0)) (forall (Xn:fofType), ((cEVEN Xn)->(cEVEN (cS (cS Xn))))))) (cODD (cS c0)))) (forall (Xn:fofType), ((cODD Xn)->(cODD (cS (cS Xn))))))) (forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))) (forall (Xn:fofType), ((iff (cNUMBER Xn)) ((or (cEVEN Xn)) (cODD Xn)))))->(forall (Xn:fofType), (cNUMBER Xn)))']
% 2.37/2.62 Parameter fofType:Type.
% 2.37/2.62 Parameter cNUMBER:(fofType->Prop).
% 2.37/2.62 Parameter cODD:(fofType->Prop).
% 2.37/2.62 Parameter cEVEN:(fofType->Prop).
% 2.37/2.62 Parameter cS:(fofType->fofType).
% 2.37/2.62 Parameter c0:fofType.
% 2.37/2.62 Trying to prove (((and ((and ((and ((and ((and (cEVEN c0)) (forall (Xn:fofType), ((cEVEN Xn)->(cEVEN (cS (cS Xn))))))) (cODD (cS c0)))) (forall (Xn:fofType), ((cODD Xn)->(cODD (cS (cS Xn))))))) (forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))) (forall (Xn:fofType), ((iff (cNUMBER Xn)) ((or (cEVEN Xn)) (cODD Xn)))))->(forall (Xn:fofType), (cNUMBER Xn)))
% 2.37/2.62 Found x30:(cNUMBER Xn0)
% 2.37/2.62 Instantiate: Xn0:=Xn:fofType
% 2.37/2.62 Found x30 as proof of (cNUMBER Xn)
% 2.37/2.62 Found x30:=(x3 x20):(cNUMBER Xn0)
% 2.37/2.62 Instantiate: Xn0:=Xn:fofType
% 2.37/2.62 Found (x3 x20) as proof of (cNUMBER Xn)
% 2.37/2.62 Found (x3 x20) as proof of (cNUMBER Xn)
% 2.37/2.62 Found x30:=(x3 x20):(cNUMBER Xn0)
% 2.37/2.62 Instantiate: Xn0:=Xn:fofType
% 2.37/2.62 Found (x3 x20) as proof of (cNUMBER Xn)
% 2.37/2.62 Found (fun (x3:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 2.37/2.62 Found (fun (x3:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x3 x20)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 2.37/2.62 Found x30:=(x3 x20):(cNUMBER Xn0)
% 2.37/2.62 Found (x3 x20) as proof of (cNUMBER Xn)
% 2.37/2.62 Found (x3 x20) as proof of (cNUMBER Xn)
% 2.37/2.62 Found (x3 x20) as proof of (cNUMBER Xn)
% 2.37/2.62 Found x30:=(x3 x20):(cNUMBER Xn0)
% 2.37/2.62 Found (x3 x20) as proof of (cNUMBER Xn)
% 4.56/4.75 Found (x3 x20) as proof of (cNUMBER Xn)
% 4.56/4.75 Found (fun (x3:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 4.56/4.75 Found (fun (x3:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x3 x20)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 4.56/4.75 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 4.56/4.75 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 4.56/4.75 Found (x3 x20) as proof of (cNUMBER Xn)
% 4.56/4.75 Found (x3 x20) as proof of (cNUMBER Xn)
% 4.56/4.75 Found (x3 x20) as proof of (cNUMBER Xn)
% 4.56/4.75 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 4.56/4.75 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 4.56/4.75 Found (x3 x20) as proof of (cNUMBER Xn)
% 4.56/4.75 Found (x3 x20) as proof of (cNUMBER Xn)
% 4.56/4.75 Found (fun (x3:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 4.56/4.75 Found (fun (x3:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x3 x20)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 4.56/4.75 Found x50:(cNUMBER Xn0)
% 4.56/4.75 Instantiate: Xn0:=Xn:fofType
% 4.56/4.75 Found x50 as proof of (cNUMBER Xn)
% 4.56/4.75 Found x30:(cNUMBER Xn0)
% 4.56/4.75 Instantiate: Xn0:=Xn:fofType
% 4.56/4.75 Found x30 as proof of (cNUMBER Xn)
% 4.56/4.75 Found x30:(cNUMBER Xn0)
% 4.56/4.75 Instantiate: Xn0:=Xn:fofType
% 4.56/4.75 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30) as proof of (cNUMBER Xn)
% 4.56/4.75 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 4.56/4.75 Found x50:=(x5 x40):(cNUMBER Xn0)
% 4.56/4.75 Instantiate: Xn0:=Xn:fofType
% 4.56/4.75 Found (x5 x40) as proof of (cNUMBER Xn)
% 4.56/4.75 Found (x5 x40) as proof of (cNUMBER Xn)
% 4.56/4.75 Found x30:(cNUMBER Xn0)
% 4.56/4.75 Instantiate: Xn0:=Xn:fofType
% 4.56/4.75 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30) as proof of (cNUMBER Xn)
% 4.56/4.75 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 4.56/4.75 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn)))
% 4.56/4.75 Found x30:=(x3 x20):(cNUMBER Xn0)
% 4.56/4.75 Instantiate: Xn0:=Xn:fofType
% 4.56/4.75 Found (x3 x20) as proof of (cNUMBER Xn)
% 4.56/4.75 Found (x3 x20) as proof of (cNUMBER Xn)
% 4.56/4.75 Found x50:=(x5 x40):(cNUMBER Xn0)
% 4.56/4.75 Instantiate: Xn0:=Xn:fofType
% 4.56/4.75 Found (x5 x40) as proof of (cNUMBER Xn)
% 4.56/4.75 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 5.45/5.68 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x5 x40)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 5.45/5.68 Found x30:=(x3 x20):(cNUMBER Xn0)
% 5.45/5.68 Instantiate: Xn0:=Xn:fofType
% 5.45/5.68 Found (x3 x20) as proof of (cNUMBER Xn)
% 5.45/5.68 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 5.45/5.68 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 5.45/5.68 Found x50:=(x5 x40):(cNUMBER Xn0)
% 5.45/5.68 Found (x5 x40) as proof of (cNUMBER Xn)
% 5.45/5.68 Found (x5 x40) as proof of (cNUMBER Xn)
% 5.45/5.68 Found (x5 x40) as proof of (cNUMBER Xn)
% 5.45/5.68 Found x30:=(x3 x20):(cNUMBER Xn0)
% 5.45/5.68 Instantiate: Xn0:=Xn:fofType
% 5.45/5.68 Found (x3 x20) as proof of (cNUMBER Xn)
% 5.45/5.68 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 5.45/5.68 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 5.45/5.68 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn)))
% 5.45/5.68 Found x30:=(x3 x20):(cNUMBER Xn0)
% 5.45/5.68 Found (x3 x20) as proof of (cNUMBER Xn)
% 5.45/5.68 Found (x3 x20) as proof of (cNUMBER Xn)
% 5.45/5.68 Found (x3 x20) as proof of (cNUMBER Xn)
% 5.45/5.68 Found x50:=(x5 x40):(cNUMBER Xn0)
% 5.45/5.68 Found (x5 x40) as proof of (cNUMBER Xn)
% 5.45/5.68 Found (x5 x40) as proof of (cNUMBER Xn)
% 5.45/5.68 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 5.45/5.68 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x5 x40)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 5.45/5.68 Found x30:=(x3 x20):(cNUMBER Xn0)
% 5.45/5.68 Found (x3 x20) as proof of (cNUMBER Xn)
% 5.45/5.68 Found (x3 x20) as proof of (cNUMBER Xn)
% 5.45/5.68 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 5.45/5.68 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 7.40/7.59 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 7.40/7.59 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 7.40/7.59 Found (x5 x40) as proof of (cNUMBER Xn)
% 7.40/7.59 Found (x5 x40) as proof of (cNUMBER Xn)
% 7.40/7.59 Found (x5 x40) as proof of (cNUMBER Xn)
% 7.40/7.59 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 7.40/7.59 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 7.40/7.59 Found (x3 x20) as proof of (cNUMBER Xn)
% 7.40/7.59 Found (x3 x20) as proof of (cNUMBER Xn)
% 7.40/7.59 Found (x3 x20) as proof of (cNUMBER Xn)
% 7.40/7.59 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 7.40/7.59 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 7.40/7.59 Found (x5 x40) as proof of (cNUMBER Xn)
% 7.40/7.59 Found (x5 x40) as proof of (cNUMBER Xn)
% 7.40/7.59 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 7.40/7.59 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x5 x40)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 7.40/7.59 Found x30:=(x3 x20):(cNUMBER Xn0)
% 7.40/7.59 Found (x3 x20) as proof of (cNUMBER Xn)
% 7.40/7.59 Found (x3 x20) as proof of (cNUMBER Xn)
% 7.40/7.59 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 7.40/7.59 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 7.40/7.59 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn)))
% 7.40/7.59 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 7.40/7.59 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 7.40/7.59 Found (x3 x20) as proof of (cNUMBER Xn)
% 7.40/7.59 Found (x3 x20) as proof of (cNUMBER Xn)
% 7.40/7.59 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 7.40/7.59 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 7.40/7.59 Found x30:(cNUMBER Xn0)
% 7.40/7.59 Instantiate: Xn0:=Xn:fofType
% 7.40/7.59 Found x30 as proof of (cNUMBER Xn)
% 7.40/7.59 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 7.40/7.59 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 7.40/7.59 Found (x3 x20) as proof of (cNUMBER Xn)
% 8.75/8.95 Found (x3 x20) as proof of (cNUMBER Xn)
% 8.75/8.95 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 8.75/8.95 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 8.75/8.95 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn)))
% 8.75/8.95 Found x30:(cNUMBER Xn0)
% 8.75/8.95 Instantiate: Xn0:=Xn:fofType
% 8.75/8.95 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of (cNUMBER Xn)
% 8.75/8.95 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))
% 8.75/8.95 Found x70:(cNUMBER Xn0)
% 8.75/8.95 Instantiate: Xn0:=Xn:fofType
% 8.75/8.95 Found x70 as proof of (cNUMBER Xn)
% 8.75/8.95 Found x50:(cNUMBER Xn0)
% 8.75/8.95 Instantiate: Xn0:=Xn:fofType
% 8.75/8.95 Found x50 as proof of (cNUMBER Xn)
% 8.75/8.95 Found x30:(cNUMBER Xn0)
% 8.75/8.95 Instantiate: Xn0:=Xn:fofType
% 8.75/8.95 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of (cNUMBER Xn)
% 8.75/8.95 Found (fun (x6:((and ((and (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))
% 8.75/8.95 Found (fun (x6:((and ((and (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 (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)))
% 8.75/8.95 Found x30:=(x3 x20):(cNUMBER Xn0)
% 8.75/8.95 Instantiate: Xn0:=Xn:fofType
% 8.75/8.95 Found (x3 x20) as proof of (cNUMBER Xn)
% 8.75/8.95 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 8.75/8.95 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 8.75/8.95 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn)))
% 8.75/8.95 Found (and_rect20 (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 8.75/8.95 Found ((and_rect2 (cNUMBER Xn)) (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 8.75/8.95 Found (((fun (P:Type) (x4:(((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->P)))=> (((((and_rect ((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))) P) x4) x0)) (cNUMBER Xn)) (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 8.75/8.95 Found (((fun (P:Type) (x4:(((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->P)))=> (((((and_rect ((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))) P) x4) x0)) (cNUMBER Xn)) (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 9.67/9.87 Found x30:=(x3 x20):(cNUMBER Xn0)
% 9.67/9.87 Instantiate: Xn0:=Xn:fofType
% 9.67/9.87 Found (x3 x20) as proof of (cNUMBER Xn)
% 9.67/9.87 Found (x3 x20) as proof of (cNUMBER Xn)
% 9.67/9.87 Found x50:(cNUMBER Xn0)
% 9.67/9.87 Instantiate: Xn0:=Xn:fofType
% 9.67/9.87 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of (cNUMBER Xn)
% 9.67/9.87 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))
% 9.67/9.87 Found x30:=(x3 x20):(cNUMBER Xn0)
% 9.67/9.87 Instantiate: Xn0:=Xn:fofType
% 9.67/9.87 Found (x3 x20) as proof of (cNUMBER Xn)
% 9.67/9.87 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 9.67/9.87 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 9.67/9.87 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn)))
% 9.67/9.87 Found (and_rect20 (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 9.67/9.87 Found ((and_rect2 (cNUMBER Xn)) (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 9.67/9.87 Found (((fun (P:Type) (x4:(((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->P)))=> (((((and_rect ((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))) P) x4) x0)) (cNUMBER Xn)) (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 10.15/10.41 Found (fun (x3:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (((fun (P:Type) (x4:(((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->P)))=> (((((and_rect ((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))) P) x4) x0)) (cNUMBER Xn)) (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)))) as proof of (cNUMBER Xn)
% 10.15/10.41 Found (fun (x3:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (((fun (P:Type) (x4:(((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->P)))=> (((((and_rect ((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))) P) x4) x0)) (cNUMBER Xn)) (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)))) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 10.15/10.41 Found x30:=(x3 x20):(cNUMBER Xn0)
% 10.15/10.41 Instantiate: Xn0:=Xn:fofType
% 10.15/10.41 Found (x3 x20) as proof of (cNUMBER Xn)
% 10.15/10.41 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 10.15/10.41 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))
% 10.15/10.41 Found x50:(cNUMBER Xn0)
% 10.15/10.41 Instantiate: Xn0:=Xn:fofType
% 10.15/10.41 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of (cNUMBER Xn)
% 10.15/10.41 Found (fun (x6:((and ((and (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))
% 10.15/10.41 Found (fun (x6:((and ((and (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 (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)))
% 11.98/12.23 Found x70:=(x7 x60):(cNUMBER Xn0)
% 11.98/12.23 Instantiate: Xn0:=Xn:fofType
% 11.98/12.23 Found (x7 x60) as proof of (cNUMBER Xn)
% 11.98/12.23 Found (x7 x60) as proof of (cNUMBER Xn)
% 11.98/12.23 Found x50:=(x5 x40):(cNUMBER Xn0)
% 11.98/12.23 Instantiate: Xn0:=Xn:fofType
% 11.98/12.23 Found (x5 x40) as proof of (cNUMBER Xn)
% 11.98/12.23 Found (x5 x40) as proof of (cNUMBER Xn)
% 11.98/12.23 Found x30:=(x3 x20):(cNUMBER Xn0)
% 11.98/12.23 Instantiate: Xn0:=Xn:fofType
% 11.98/12.23 Found (x3 x20) as proof of (cNUMBER Xn)
% 11.98/12.23 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 11.98/12.23 Found (fun (x6:((and ((and (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))
% 11.98/12.23 Found (fun (x6:((and ((and (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 (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)))
% 11.98/12.23 Found x30:=(x3 x20):(cNUMBER Xn0)
% 11.98/12.23 Found (x3 x20) as proof of (cNUMBER Xn)
% 11.98/12.23 Found (x3 x20) as proof of (cNUMBER Xn)
% 11.98/12.23 Found (x3 x20) as proof of (cNUMBER Xn)
% 11.98/12.23 Found x70:=(x7 x60):(cNUMBER Xn0)
% 11.98/12.23 Instantiate: Xn0:=Xn:fofType
% 11.98/12.23 Found (x7 x60) as proof of (cNUMBER Xn)
% 11.98/12.23 Found (fun (x7:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x7 x60)) as proof of (cNUMBER Xn)
% 11.98/12.23 Found (fun (x7:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x7 x60)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 11.98/12.23 Found x50:=(x5 x40):(cNUMBER Xn0)
% 11.98/12.23 Instantiate: Xn0:=Xn:fofType
% 11.98/12.23 Found (x5 x40) as proof of (cNUMBER Xn)
% 11.98/12.23 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 11.98/12.23 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))
% 11.98/12.23 Found x30:=(x3 x20):(cNUMBER Xn0)
% 11.98/12.23 Found (x3 x20) as proof of (cNUMBER Xn)
% 11.98/12.23 Found (x3 x20) as proof of (cNUMBER Xn)
% 11.98/12.23 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 11.98/12.23 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))
% 11.98/12.23 Found x70:=(x7 x60):(cNUMBER Xn0)
% 11.98/12.23 Found (x7 x60) as proof of (cNUMBER Xn)
% 11.98/12.23 Found (x7 x60) as proof of (cNUMBER Xn)
% 11.98/12.23 Found (x7 x60) as proof of (cNUMBER Xn)
% 11.98/12.23 Found x50:=(x5 x40):(cNUMBER Xn0)
% 11.98/12.23 Instantiate: Xn0:=Xn:fofType
% 11.98/12.23 Found (x5 x40) as proof of (cNUMBER Xn)
% 11.98/12.23 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 11.98/12.23 Found (fun (x6:((and ((and (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))
% 11.98/12.23 Found (fun (x6:((and ((and (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 (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)))
% 11.98/12.23 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 11.98/12.23 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 11.98/12.23 Found (x3 x20) as proof of (cNUMBER Xn)
% 11.98/12.23 Found (x3 x20) as proof of (cNUMBER Xn)
% 11.98/12.23 Found (x3 x20) as proof of (cNUMBER Xn)
% 14.50/14.69 Found x50:=(x5 x40):(cNUMBER Xn0)
% 14.50/14.69 Found (x5 x40) as proof of (cNUMBER Xn)
% 14.50/14.69 Found (x5 x40) as proof of (cNUMBER Xn)
% 14.50/14.69 Found (x5 x40) as proof of (cNUMBER Xn)
% 14.50/14.69 Found x30:=(x3 x20):(cNUMBER Xn0)
% 14.50/14.69 Found (x3 x20) as proof of (cNUMBER Xn)
% 14.50/14.69 Found (x3 x20) as proof of (cNUMBER Xn)
% 14.50/14.69 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 14.50/14.69 Found (fun (x6:((and ((and (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))
% 14.50/14.69 Found (fun (x6:((and ((and (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 (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)))
% 14.50/14.69 Found x70:=(x7 x60):(cNUMBER Xn0)
% 14.50/14.69 Found (x7 x60) as proof of (cNUMBER Xn)
% 14.50/14.69 Found (x7 x60) as proof of (cNUMBER Xn)
% 14.50/14.69 Found (fun (x7:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x7 x60)) as proof of (cNUMBER Xn)
% 14.50/14.69 Found (fun (x7:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x7 x60)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 14.50/14.69 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 14.50/14.69 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 14.50/14.69 Found (x3 x20) as proof of (cNUMBER Xn)
% 14.50/14.69 Found (x3 x20) as proof of (cNUMBER Xn)
% 14.50/14.69 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 14.50/14.69 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))
% 14.50/14.69 Found x50:=(x5 x40):(cNUMBER Xn0)
% 14.50/14.69 Found (x5 x40) as proof of (cNUMBER Xn)
% 14.50/14.69 Found (x5 x40) as proof of (cNUMBER Xn)
% 14.50/14.69 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 14.50/14.69 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))
% 14.50/14.69 Found x60:((or (cEVEN Xn0)) (cODD Xn0))
% 14.50/14.69 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 14.50/14.69 Found (x7 x60) as proof of (cNUMBER Xn)
% 14.50/14.69 Found (x7 x60) as proof of (cNUMBER Xn)
% 14.50/14.69 Found (x7 x60) as proof of (cNUMBER Xn)
% 14.50/14.69 Found x30:(cNUMBER Xn0)
% 14.50/14.69 Instantiate: Xn0:=Xn:fofType
% 14.50/14.69 Found x30 as proof of (cNUMBER Xn)
% 14.50/14.69 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 14.50/14.69 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 14.50/14.69 Found (x5 x40) as proof of (cNUMBER Xn)
% 14.50/14.69 Found (x5 x40) as proof of (cNUMBER Xn)
% 14.50/14.69 Found (x5 x40) as proof of (cNUMBER Xn)
% 14.50/14.69 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 14.50/14.69 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 14.50/14.69 Found (x3 x20) as proof of (cNUMBER Xn)
% 14.50/14.69 Found (x3 x20) as proof of (cNUMBER Xn)
% 14.50/14.69 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 14.50/14.69 Found (fun (x6:((and ((and (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))
% 14.50/14.69 Found (fun (x6:((and ((and (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 (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)))
% 14.50/14.69 Found x50:=(x5 x40):(cNUMBER Xn0)
% 14.50/14.69 Found (x5 x40) as proof of (cNUMBER Xn)
% 14.50/14.69 Found (x5 x40) as proof of (cNUMBER Xn)
% 14.50/14.69 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 14.50/14.69 Found (fun (x6:((and ((and (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))
% 15.66/15.85 Found (fun (x6:((and ((and (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 (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)))
% 15.66/15.85 Found x60:((or (cEVEN Xn0)) (cODD Xn0))
% 15.66/15.85 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 15.66/15.85 Found (x7 x60) as proof of (cNUMBER Xn)
% 15.66/15.85 Found (x7 x60) as proof of (cNUMBER Xn)
% 15.66/15.85 Found (fun (x7:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x7 x60)) as proof of (cNUMBER Xn)
% 15.66/15.85 Found (fun (x7:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x7 x60)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 15.66/15.85 Found x30:=(x3 x20):(cNUMBER Xn0)
% 15.66/15.85 Found (x3 x20) as proof of (cNUMBER Xn0)
% 15.66/15.85 Found (x3 x20) as proof of (cNUMBER Xn0)
% 15.66/15.85 Found x30:=(x3 x21):(cNUMBER Xn0)
% 15.66/15.85 Instantiate: Xn0:=Xn:fofType
% 15.66/15.85 Found (x3 x21) as proof of (cNUMBER Xn)
% 15.66/15.85 Found (x3 x21) as proof of (cNUMBER Xn)
% 15.66/15.85 Found x30:=(x3 x21):(cNUMBER Xn0)
% 15.66/15.85 Found (x3 x21) as proof of (cNUMBER Xn)
% 15.66/15.85 Found (x3 x21) as proof of (cNUMBER Xn)
% 15.66/15.85 Found (x3 x21) as proof of (cNUMBER Xn)
% 15.66/15.85 Found x21:((or (cEVEN Xn0)) (cODD Xn0))
% 15.66/15.85 Found x21 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 15.66/15.85 Found (x3 x21) as proof of (cNUMBER Xn)
% 15.66/15.85 Found (x3 x21) as proof of (cNUMBER Xn)
% 15.66/15.85 Found (x3 x21) as proof of (cNUMBER Xn)
% 15.66/15.85 Found x30:(cNUMBER Xn0)
% 15.66/15.85 Instantiate: Xn0:=Xn:fofType
% 15.66/15.85 Found (fun (x9:(cODD (cS c0)))=> x30) as proof of (cNUMBER Xn)
% 15.66/15.85 Found (fun (x9:(cODD (cS c0)))=> x30) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 15.66/15.85 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 15.66/15.85 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 15.66/15.85 Found (x5 x40) as proof of (cNUMBER Xn)
% 15.66/15.85 Found (x5 x40) as proof of (cNUMBER Xn)
% 15.66/15.85 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 15.66/15.85 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))
% 15.66/15.85 Found x30:=(x3 x20):(cNUMBER Xn0)
% 15.66/15.85 Instantiate: Xn0:=Xn:fofType
% 15.66/15.85 Found (x3 x20) as proof of (cNUMBER Xn)
% 15.66/15.85 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 15.66/15.85 Found (fun (x6:((and ((and (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))
% 15.66/15.85 Found (fun (x6:((and ((and (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 (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)))
% 15.66/15.85 Found (and_rect30 (fun (x6:((and ((and (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)
% 15.66/15.85 Found ((and_rect3 (cNUMBER Xn)) (fun (x6:((and ((and (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)
% 15.66/15.85 Found (((fun (P:Type) (x6:(((and ((and (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 (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) x4)) (cNUMBER Xn)) (fun (x6:((and ((and (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)
% 17.19/17.37 Found (((fun (P:Type) (x6:(((and ((and (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 (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) x4)) (cNUMBER Xn)) (fun (x6:((and ((and (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)
% 17.19/17.37 Found x30:=(x3 x20):(cNUMBER Xn0)
% 17.19/17.37 Found (x3 x20) as proof of (cNUMBER Xn0)
% 17.19/17.37 Found (x3 x20) as proof of (cNUMBER Xn0)
% 17.19/17.37 Found x30:=(x3 x21):(cNUMBER Xn0)
% 17.19/17.37 Instantiate: Xn0:=Xn:fofType
% 17.19/17.37 Found (x3 x21) as proof of (cNUMBER Xn)
% 17.19/17.37 Found (x3 x21) as proof of (cNUMBER Xn)
% 17.19/17.37 Found x30:=(x3 x21):(cNUMBER Xn0)
% 17.19/17.37 Found (x3 x21) as proof of (cNUMBER Xn)
% 17.19/17.37 Found (x3 x21) as proof of (cNUMBER Xn)
% 17.19/17.37 Found (x3 x21) as proof of (cNUMBER Xn)
% 17.19/17.37 Found x21:((or (cEVEN Xn0)) (cODD Xn0))
% 17.19/17.37 Found x21 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 17.19/17.37 Found (x3 x21) as proof of (cNUMBER Xn)
% 17.19/17.37 Found (x3 x21) as proof of (cNUMBER Xn)
% 17.19/17.37 Found (x3 x21) as proof of (cNUMBER Xn)
% 17.19/17.37 Found x50:(cNUMBER Xn0)
% 17.19/17.37 Instantiate: Xn0:=Xn:fofType
% 17.19/17.37 Found x50 as proof of (cNUMBER Xn)
% 17.19/17.37 Found x30:(cNUMBER Xn0)
% 17.19/17.37 Instantiate: Xn0:=Xn:fofType
% 17.19/17.37 Found (fun (x9:(cODD (cS c0)))=> x30) as proof of (cNUMBER Xn)
% 17.19/17.37 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> x30) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 17.19/17.37 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> x30) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 17.19/17.37 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 17.19/17.37 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 17.19/17.37 Found (x5 x40) as proof of (cNUMBER Xn)
% 17.19/17.37 Found (x5 x40) as proof of (cNUMBER Xn)
% 17.19/17.37 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 17.19/17.37 Found (fun (x6:((and ((and (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))
% 17.19/17.37 Found (fun (x6:((and ((and (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 (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)))
% 17.19/17.37 Found x30:=(x3 x20):(cNUMBER Xn0)
% 17.19/17.37 Instantiate: Xn0:=Xn:fofType
% 17.19/17.37 Found (x3 x20) as proof of (cNUMBER Xn)
% 17.19/17.37 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 17.19/17.37 Found (fun (x6:((and ((and (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))
% 17.19/17.37 Found (fun (x6:((and ((and (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 (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)))
% 17.19/17.37 Found (and_rect30 (fun (x6:((and ((and (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)
% 17.19/17.37 Found ((and_rect3 (cNUMBER Xn)) (fun (x6:((and ((and (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)
% 17.65/17.89 Found (((fun (P:Type) (x6:(((and ((and (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 (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) x4)) (cNUMBER Xn)) (fun (x6:((and ((and (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)
% 17.65/17.89 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (((fun (P:Type) (x6:(((and ((and (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 (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) x4)) (cNUMBER Xn)) (fun (x6:((and ((and (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)
% 17.65/17.89 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (((fun (P:Type) (x6:(((and ((and (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 (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) x4)) (cNUMBER Xn)) (fun (x6:((and ((and (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 (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 17.65/17.89 Found x30:=(x3 x20):(cNUMBER Xn0)
% 17.65/17.89 Instantiate: Xn0:=Xn:fofType
% 17.65/17.89 Found (x3 x20) as proof of (cNUMBER Xn)
% 17.65/17.89 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 17.65/17.89 Found (fun (x6:((and ((and (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))
% 17.65/17.89 Found (fun (x6:((and ((and (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 (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)))
% 17.65/17.89 Found (and_rect30 (fun (x6:((and ((and (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)
% 17.65/17.89 Found ((and_rect3 (cNUMBER Xn)) (fun (x6:((and ((and (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)
% 17.65/17.89 Found (((fun (P:Type) (x6:(((and ((and (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 (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) x4)) (cNUMBER Xn)) (fun (x6:((and ((and (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)
% 17.80/18.01 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (((fun (P:Type) (x6:(((and ((and (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 (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) x4)) (cNUMBER Xn)) (fun (x6:((and ((and (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)
% 17.80/18.01 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (((fun (P:Type) (x6:(((and ((and (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 (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) x4)) (cNUMBER Xn)) (fun (x6:((and ((and (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 (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 17.80/18.01 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (((fun (P:Type) (x6:(((and ((and (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 (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) x4)) (cNUMBER Xn)) (fun (x6:((and ((and (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 (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn)))
% 17.80/18.01 Found x30:=(x3 x21):(cNUMBER Xn0)
% 19.87/20.05 Instantiate: Xn0:=Xn:fofType
% 19.87/20.05 Found (x3 x21) as proof of (cNUMBER Xn)
% 19.87/20.05 Found (fun (x3:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x3 x21)) as proof of (cNUMBER Xn)
% 19.87/20.05 Found (fun (x3:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x3 x21)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 19.87/20.05 Found x50:(cNUMBER Xn0)
% 19.87/20.05 Instantiate: Xn0:=Xn:fofType
% 19.87/20.05 Found (fun (x9:(cODD (cS c0)))=> x50) as proof of (cNUMBER Xn)
% 19.87/20.05 Found (fun (x9:(cODD (cS c0)))=> x50) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 19.87/20.05 Found x30:=(x3 x20):(cNUMBER Xn0)
% 19.87/20.05 Instantiate: Xn0:=Xn:fofType
% 19.87/20.05 Found (x3 x20) as proof of (cNUMBER Xn)
% 19.87/20.05 Found (x3 x20) as proof of (cNUMBER Xn)
% 19.87/20.05 Found x50:=(x5 x40):(cNUMBER Xn0)
% 19.87/20.05 Instantiate: Xn0:=Xn:fofType
% 19.87/20.05 Found (x5 x40) as proof of (cNUMBER Xn)
% 19.87/20.05 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 19.87/20.05 Found (fun (x6:((and ((and (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))
% 19.87/20.05 Found (fun (x6:((and ((and (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 (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)))
% 19.87/20.05 Found (and_rect30 (fun (x6:((and ((and (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)
% 19.87/20.05 Found ((and_rect3 (cNUMBER Xn)) (fun (x6:((and ((and (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)
% 19.87/20.05 Found (((fun (P:Type) (x6:(((and ((and (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 (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) x2)) (cNUMBER Xn)) (fun (x6:((and ((and (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)
% 19.87/20.05 Found (((fun (P:Type) (x6:(((and ((and (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 (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) x2)) (cNUMBER Xn)) (fun (x6:((and ((and (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)
% 19.87/20.05 Found x90:(cNUMBER Xn0)
% 19.87/20.05 Instantiate: Xn0:=Xn:fofType
% 19.87/20.05 Found x90 as proof of (cNUMBER Xn)
% 19.87/20.05 Found x70:(cNUMBER Xn0)
% 19.87/20.05 Instantiate: Xn0:=Xn:fofType
% 19.87/20.05 Found x70 as proof of (cNUMBER Xn)
% 19.87/20.05 Found x50:(cNUMBER Xn0)
% 19.87/20.05 Instantiate: Xn0:=Xn:fofType
% 19.87/20.05 Found (fun (x9:(cODD (cS c0)))=> x50) as proof of (cNUMBER Xn)
% 19.87/20.05 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> x50) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 19.87/20.05 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> x50) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 19.87/20.05 Found x30:=(x3 x20):(cNUMBER Xn0)
% 19.87/20.05 Instantiate: Xn0:=Xn:fofType
% 19.87/20.05 Found (x3 x20) as proof of (cNUMBER Xn)
% 19.87/20.05 Found (fun (x9:(cODD (cS c0)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 21.49/21.74 Found (fun (x9:(cODD (cS c0)))=> (x3 x20)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 21.49/21.74 Found x50:=(x5 x40):(cNUMBER Xn0)
% 21.49/21.74 Instantiate: Xn0:=Xn:fofType
% 21.49/21.74 Found (x5 x40) as proof of (cNUMBER Xn)
% 21.49/21.74 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 21.49/21.74 Found (fun (x6:((and ((and (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))
% 21.49/21.74 Found (fun (x6:((and ((and (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 (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)))
% 21.49/21.74 Found (and_rect30 (fun (x6:((and ((and (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)
% 21.49/21.74 Found ((and_rect3 (cNUMBER Xn)) (fun (x6:((and ((and (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)
% 21.49/21.74 Found (((fun (P:Type) (x6:(((and ((and (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 (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) x2)) (cNUMBER Xn)) (fun (x6:((and ((and (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)
% 21.49/21.74 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (((fun (P:Type) (x6:(((and ((and (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 (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) x2)) (cNUMBER Xn)) (fun (x6:((and ((and (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)
% 21.49/21.74 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (((fun (P:Type) (x6:(((and ((and (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 (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) x2)) (cNUMBER Xn)) (fun (x6:((and ((and (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 Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 21.49/21.74 Found x70:(cNUMBER Xn0)
% 21.49/21.74 Instantiate: Xn0:=Xn:fofType
% 21.49/21.74 Found (fun (x9:(cODD (cS c0)))=> x70) as proof of (cNUMBER Xn)
% 21.49/21.74 Found (fun (x9:(cODD (cS c0)))=> x70) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 21.49/21.74 Found x50:=(x5 x40):(cNUMBER Xn0)
% 21.49/21.74 Instantiate: Xn0:=Xn:fofType
% 21.49/21.74 Found (x5 x40) as proof of (cNUMBER Xn)
% 21.49/21.74 Found (x5 x40) as proof of (cNUMBER Xn)
% 21.49/21.74 Found x30:=(x3 x20):(cNUMBER Xn0)
% 21.49/21.74 Instantiate: Xn0:=Xn:fofType
% 21.49/21.74 Found (x3 x20) as proof of (cNUMBER Xn)
% 21.49/21.74 Found (fun (x9:(cODD (cS c0)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 21.49/21.74 Found (fun (x8:((and (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))
% 23.76/24.02 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x20)) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 23.76/24.02 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 23.76/24.02 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 23.76/24.02 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 23.76/24.02 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 23.76/24.02 Found (fun (x7:((and (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)))
% 23.76/24.02 Found (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0))))
% 23.76/24.02 Found (and_rect40 (fun (x7:((and (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))
% 23.76/24.02 Found ((and_rect4 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (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))
% 23.76/24.02 Found (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (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 (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))
% 23.76/24.02 Found (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (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 (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))
% 23.76/24.02 Found x30:=(x3 x20):(cNUMBER Xn0)
% 23.76/24.02 Found (x3 x20) as proof of (cNUMBER Xn)
% 23.76/24.02 Found (x3 x20) as proof of (cNUMBER Xn)
% 23.76/24.02 Found (x3 x20) as proof of (cNUMBER Xn)
% 23.76/24.02 Found x30:=(x3 x21):(cNUMBER Xn0)
% 23.76/24.02 Found (x3 x21) as proof of (cNUMBER Xn)
% 23.76/24.02 Found (x3 x21) as proof of (cNUMBER Xn)
% 23.76/24.02 Found (fun (x3:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x3 x21)) as proof of (cNUMBER Xn)
% 23.76/24.02 Found (fun (x3:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x3 x21)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 23.76/24.03 Found x70:(cNUMBER Xn0)
% 23.76/24.03 Instantiate: Xn0:=Xn:fofType
% 23.76/24.03 Found (fun (x9:(cODD (cS c0)))=> x70) as proof of (cNUMBER Xn)
% 23.76/24.03 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> x70) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 23.76/24.03 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> x70) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 23.76/24.03 Found x50:=(x5 x40):(cNUMBER Xn0)
% 23.76/24.03 Instantiate: Xn0:=Xn:fofType
% 23.76/24.03 Found (x5 x40) as proof of (cNUMBER Xn)
% 23.76/24.03 Found (fun (x9:(cODD (cS c0)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 23.76/24.03 Found (fun (x9:(cODD (cS c0)))=> (x5 x40)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 23.76/24.03 Found x90:=(x9 x80):(cNUMBER Xn0)
% 23.76/24.03 Instantiate: Xn0:=Xn:fofType
% 23.76/24.03 Found (x9 x80) as proof of (cNUMBER Xn)
% 23.76/24.03 Found (x9 x80) as proof of (cNUMBER Xn)
% 23.76/24.03 Found x30:=(x3 x20):(cNUMBER Xn0)
% 25.27/25.45 Found (x3 x20) as proof of (cNUMBER Xn)
% 25.27/25.45 Found (x3 x20) as proof of (cNUMBER Xn)
% 25.27/25.45 Found (fun (x9:(cODD (cS c0)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 25.27/25.45 Found (fun (x9:(cODD (cS c0)))=> (x3 x20)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 25.27/25.45 Found x70:=(x7 x60):(cNUMBER Xn0)
% 25.27/25.45 Instantiate: Xn0:=Xn:fofType
% 25.27/25.45 Found (x7 x60) as proof of (cNUMBER Xn)
% 25.27/25.45 Found (x7 x60) as proof of (cNUMBER Xn)
% 25.27/25.45 Found x50:=(x5 x40):(cNUMBER Xn0)
% 25.27/25.45 Instantiate: Xn0:=Xn:fofType
% 25.27/25.45 Found (x5 x40) as proof of (cNUMBER Xn)
% 25.27/25.45 Found (fun (x9:(cODD (cS c0)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 25.27/25.45 Found (fun (x8:((and (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))
% 25.27/25.45 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x40)) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 25.27/25.45 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 25.27/25.45 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 25.27/25.45 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 25.27/25.45 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 25.27/25.45 Found (fun (x8:((and (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)))
% 25.27/25.45 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0))))
% 25.27/25.45 Found (and_rect40 (fun (x8:((and (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))
% 25.27/25.45 Found ((and_rect4 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (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))
% 25.27/25.45 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (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 (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))
% 25.27/25.45 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (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 (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))
% 25.27/25.45 Found x90:=(x9 x80):(cNUMBER Xn0)
% 25.27/25.45 Instantiate: Xn0:=Xn:fofType
% 25.27/25.45 Found (x9 x80) as proof of (cNUMBER Xn)
% 25.27/25.45 Found (fun (x9:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x9 x80)) as proof of (cNUMBER Xn)
% 25.27/25.45 Found (fun (x9:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x9 x80)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 25.27/25.45 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 25.27/25.45 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 25.27/25.45 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 25.27/25.45 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 25.27/25.45 Found (fun (x7:((and (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)))
% 26.15/26.33 Found (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0))))
% 26.15/26.33 Found (and_rect40 (fun (x7:((and (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))
% 26.15/26.33 Found ((and_rect4 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (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))
% 26.15/26.33 Found (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (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 (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))
% 26.15/26.33 Found (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (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 (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))
% 26.15/26.33 Found x50:=(x5 x40):(cNUMBER Xn0)
% 26.15/26.33 Found (x5 x40) as proof of (cNUMBER Xn)
% 26.15/26.33 Found (x5 x40) as proof of (cNUMBER Xn)
% 26.15/26.33 Found (x5 x40) as proof of (cNUMBER Xn)
% 26.15/26.33 Found x30:=(x3 x20):(cNUMBER Xn0)
% 26.15/26.33 Found (x3 x20) as proof of (cNUMBER Xn)
% 26.15/26.33 Found (x3 x20) as proof of (cNUMBER Xn)
% 26.15/26.33 Found (fun (x9:(cODD (cS c0)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 26.15/26.33 Found (fun (x8:((and (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))
% 26.15/26.33 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x20)) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 26.15/26.33 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 26.15/26.33 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 26.15/26.33 Found (x3 x20) as proof of (cNUMBER Xn)
% 26.15/26.33 Found (x3 x20) as proof of (cNUMBER Xn)
% 26.15/26.33 Found (x3 x20) as proof of (cNUMBER Xn)
% 26.15/26.33 Found x30:=(x3 x20):(cNUMBER Xn0)
% 26.15/26.33 Found (x3 x20) as proof of (cNUMBER Xn0)
% 26.15/26.33 Found (x3 x20) as proof of (cNUMBER Xn0)
% 26.15/26.33 Found x70:=(x7 x60):(cNUMBER Xn0)
% 26.15/26.33 Instantiate: Xn0:=Xn:fofType
% 26.15/26.33 Found (x7 x60) as proof of (cNUMBER Xn)
% 26.15/26.33 Found (fun (x9:(cODD (cS c0)))=> (x7 x60)) as proof of (cNUMBER Xn)
% 26.15/26.33 Found (fun (x9:(cODD (cS c0)))=> (x7 x60)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 26.15/26.33 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 26.15/26.33 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 26.15/26.33 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 26.15/26.33 Found x31:(cNUMBER Xn0)
% 26.15/26.33 Instantiate: Xn0:=Xn:fofType
% 26.15/26.33 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x31) as proof of (cNUMBER Xn)
% 26.15/26.33 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x31) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 27.25/27.47 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x31) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn)))
% 27.25/27.47 Found x21:((or (cEVEN Xn0)) (cODD Xn0))
% 27.25/27.47 Found x21 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 27.25/27.47 Found (x3 x21) as proof of (cNUMBER Xn)
% 27.25/27.47 Found (x3 x21) as proof of (cNUMBER Xn)
% 27.25/27.47 Found (fun (x3:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x3 x21)) as proof of (cNUMBER Xn)
% 27.25/27.47 Found (fun (x3:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x3 x21)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 27.25/27.47 Found x31:(cNUMBER Xn0)
% 27.25/27.47 Instantiate: Xn0:=Xn:fofType
% 27.25/27.47 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x31) as proof of (cNUMBER Xn)
% 27.25/27.47 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x31) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 27.25/27.47 Found x50:=(x5 x40):(cNUMBER Xn0)
% 27.25/27.47 Found (x5 x40) as proof of (cNUMBER Xn)
% 27.25/27.47 Found (x5 x40) as proof of (cNUMBER Xn)
% 27.25/27.47 Found (fun (x9:(cODD (cS c0)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 27.25/27.47 Found (fun (x9:(cODD (cS c0)))=> (x5 x40)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 27.25/27.47 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 27.25/27.47 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 27.25/27.47 Found (x3 x20) as proof of (cNUMBER Xn)
% 27.25/27.47 Found (x3 x20) as proof of (cNUMBER Xn)
% 27.25/27.47 Found (fun (x9:(cODD (cS c0)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 27.25/27.47 Found (fun (x9:(cODD (cS c0)))=> (x3 x20)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 27.25/27.47 Found x90:=(x9 x80):(cNUMBER Xn0)
% 27.25/27.47 Found (x9 x80) as proof of (cNUMBER Xn)
% 27.25/27.47 Found (x9 x80) as proof of (cNUMBER Xn)
% 27.25/27.47 Found (x9 x80) as proof of (cNUMBER Xn)
% 27.25/27.47 Found x30:=(x3 x21):(cNUMBER Xn0)
% 27.25/27.47 Instantiate: Xn0:=Xn:fofType
% 27.25/27.47 Found (x3 x21) as proof of (cNUMBER Xn)
% 27.25/27.47 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x21)) as proof of (cNUMBER Xn)
% 27.25/27.47 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x21)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 27.25/27.47 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x21)) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn)))
% 27.99/28.26 Found x30:=(x3 x20):(cNUMBER Xn0)
% 27.99/28.26 Found (x3 x20) as proof of (cNUMBER Xn0)
% 27.99/28.26 Found (x3 x20) as proof of (cNUMBER Xn0)
% 27.99/28.26 Found x30:=(x3 x21):(cNUMBER Xn0)
% 27.99/28.26 Instantiate: Xn0:=Xn:fofType
% 27.99/28.26 Found (x3 x21) as proof of (cNUMBER Xn)
% 27.99/28.26 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x21)) as proof of (cNUMBER Xn)
% 27.99/28.26 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x21)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 27.99/28.26 Found x70:=(x7 x60):(cNUMBER Xn0)
% 27.99/28.26 Instantiate: Xn0:=Xn:fofType
% 27.99/28.26 Found (x7 x60) as proof of (cNUMBER Xn)
% 27.99/28.26 Found (fun (x9:(cODD (cS c0)))=> (x7 x60)) as proof of (cNUMBER Xn)
% 27.99/28.26 Found (fun (x8:((and (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))
% 27.99/28.26 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x7 x60)) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 27.99/28.26 Found x30:(cNUMBER Xn0)
% 27.99/28.26 Instantiate: Xn0:=Xn:fofType
% 27.99/28.26 Found x30 as proof of (cNUMBER Xn)
% 27.99/28.26 Found x50:(cNUMBER Xn00)
% 27.99/28.26 Instantiate: Xn00:=Xn:fofType
% 27.99/28.26 Found x50 as proof of (cNUMBER Xn)
% 27.99/28.26 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 27.99/28.26 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 27.99/28.26 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 27.99/28.26 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 27.99/28.26 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 27.99/28.26 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 27.99/28.26 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 27.99/28.26 Found (fun (x8:((and (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)))
% 27.99/28.26 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0))))
% 27.99/28.26 Found (and_rect40 (fun (x8:((and (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))
% 27.99/28.26 Found ((and_rect4 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (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))
% 27.99/28.26 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (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 (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))
% 29.47/29.70 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (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 (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))
% 29.47/29.70 Found x70:=(x7 x60):(cNUMBER Xn0)
% 29.47/29.70 Found (x7 x60) as proof of (cNUMBER Xn)
% 29.47/29.70 Found (x7 x60) as proof of (cNUMBER Xn)
% 29.47/29.70 Found (x7 x60) as proof of (cNUMBER Xn)
% 29.47/29.70 Found x31:(cNUMBER Xn0)
% 29.47/29.70 Instantiate: Xn0:=Xn:fofType
% 29.47/29.70 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x31) as proof of (cNUMBER Xn)
% 29.47/29.70 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x31) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 29.47/29.70 Found x50:=(x5 x40):(cNUMBER Xn0)
% 29.47/29.70 Found (x5 x40) as proof of (cNUMBER Xn0)
% 29.47/29.70 Found (x5 x40) as proof of (cNUMBER Xn0)
% 29.47/29.70 Found x50:=(x5 x41):(cNUMBER Xn0)
% 29.47/29.70 Instantiate: Xn0:=Xn:fofType
% 29.47/29.70 Found (x5 x41) as proof of (cNUMBER Xn)
% 29.47/29.70 Found (x5 x41) as proof of (cNUMBER Xn)
% 29.47/29.70 Found x50:=(x5 x40):(cNUMBER Xn0)
% 29.47/29.70 Found (x5 x40) as proof of (cNUMBER Xn)
% 29.47/29.70 Found (x5 x40) as proof of (cNUMBER Xn)
% 29.47/29.70 Found (x5 x40) as proof of (cNUMBER Xn)
% 29.47/29.70 Found x50:=(x5 x40):(cNUMBER Xn0)
% 29.47/29.70 Found (x5 x40) as proof of (cNUMBER Xn)
% 29.47/29.70 Found (x5 x40) as proof of (cNUMBER Xn)
% 29.47/29.70 Found (fun (x9:(cODD (cS c0)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 29.47/29.70 Found (fun (x8:((and (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))
% 29.47/29.70 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x40)) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 29.47/29.70 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 29.47/29.70 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 29.47/29.70 Found (x5 x40) as proof of (cNUMBER Xn)
% 29.47/29.70 Found (x5 x40) as proof of (cNUMBER Xn)
% 29.47/29.70 Found (x5 x40) as proof of (cNUMBER Xn)
% 29.47/29.70 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 29.47/29.70 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 29.47/29.70 Found (x3 x20) as proof of (cNUMBER Xn)
% 29.47/29.70 Found (x3 x20) as proof of (cNUMBER Xn)
% 29.47/29.70 Found (fun (x9:(cODD (cS c0)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 29.47/29.70 Found (fun (x8:((and (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))
% 29.47/29.70 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x20)) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 29.47/29.70 Found x90:=(x9 x80):(cNUMBER Xn0)
% 29.47/29.70 Found (x9 x80) as proof of (cNUMBER Xn)
% 29.47/29.70 Found (x9 x80) as proof of (cNUMBER Xn)
% 29.47/29.70 Found (fun (x9:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x9 x80)) as proof of (cNUMBER Xn)
% 29.47/29.70 Found (fun (x9:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x9 x80)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 29.47/29.70 Found x30:=(x3 x20):(cNUMBER Xn0)
% 29.47/29.70 Found (x3 x20) as proof of (cNUMBER Xn)
% 29.47/29.70 Found (x3 x20) as proof of (cNUMBER Xn)
% 29.47/29.70 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 30.27/30.50 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 30.27/30.50 Found x30:(cNUMBER Xn0)
% 30.27/30.50 Instantiate: Xn0:=Xn:fofType
% 30.27/30.50 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30) as proof of (cNUMBER Xn)
% 30.27/30.50 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 30.27/30.50 Found x30:=(x3 x20):(cNUMBER Xn0)
% 30.27/30.50 Found (x3 x20) as proof of (cNUMBER Xn0)
% 30.27/30.50 Found (x3 x20) as proof of (cNUMBER Xn0)
% 30.27/30.50 Found x30:=(x3 x21):(cNUMBER Xn0)
% 30.27/30.50 Instantiate: Xn0:=Xn:fofType
% 30.27/30.50 Found (x3 x21) as proof of (cNUMBER Xn)
% 30.27/30.50 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x21)) as proof of (cNUMBER Xn)
% 30.27/30.50 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x21)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 30.27/30.50 Found x30:(cNUMBER Xn0)
% 30.27/30.50 Instantiate: Xn0:=Xn:fofType
% 30.27/30.50 Found x30 as proof of (cNUMBER Xn)
% 30.27/30.50 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 30.27/30.50 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 30.27/30.50 Found (x5 x40) as proof of (cNUMBER Xn)
% 30.27/30.50 Found (x5 x40) as proof of (cNUMBER Xn)
% 30.27/30.50 Found (x5 x40) as proof of (cNUMBER Xn)
% 30.27/30.50 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 30.27/30.50 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 30.27/30.50 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 30.27/30.50 Found x30:=(x3 x20):(cNUMBER Xn0)
% 30.27/30.50 Found (x3 x20) as proof of (cNUMBER Xn0)
% 30.27/30.50 Found (x3 x20) as proof of (cNUMBER Xn0)
% 30.27/30.50 Found x30:=(x3 x21):(cNUMBER Xn0)
% 30.27/30.50 Instantiate: Xn0:=Xn:fofType
% 30.27/30.50 Found (x3 x21) as proof of (cNUMBER Xn)
% 30.27/30.50 Found (x3 x21) as proof of (cNUMBER Xn)
% 30.27/30.50 Found x30:=(x3 x20):(cNUMBER Xn0)
% 30.27/30.50 Found (x3 x20) as proof of (cNUMBER Xn)
% 30.27/30.50 Found (x3 x20) as proof of (cNUMBER Xn)
% 30.27/30.50 Found (x3 x20) as proof of (cNUMBER Xn)
% 30.27/30.50 Found x30:=(x3 x20):(cNUMBER Xn0)
% 30.27/30.50 Instantiate: Xn0:=Xn:fofType
% 30.27/30.50 Found (x3 x20) as proof of (cNUMBER Xn)
% 30.27/30.50 Found (fun (x9:(cODD (cS c0)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 30.27/30.50 Found (fun (x8:((and (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))
% 30.27/30.50 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x20)) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 30.27/30.50 Found (and_rect40 (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x20))) as proof of (cNUMBER Xn)
% 30.27/30.50 Found ((and_rect4 (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x20))) as proof of (cNUMBER Xn)
% 30.27/30.50 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x20))) as proof of (cNUMBER Xn)
% 31.25/31.46 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x20))) as proof of (cNUMBER Xn)
% 31.25/31.46 Found x70:=(x7 x60):(cNUMBER Xn0)
% 31.25/31.46 Found (x7 x60) as proof of (cNUMBER Xn)
% 31.25/31.46 Found (x7 x60) as proof of (cNUMBER Xn)
% 31.25/31.46 Found (fun (x9:(cODD (cS c0)))=> (x7 x60)) as proof of (cNUMBER Xn)
% 31.25/31.46 Found (fun (x9:(cODD (cS c0)))=> (x7 x60)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 31.25/31.46 Found x50:=(x5 x40):(cNUMBER Xn0)
% 31.25/31.46 Found (x5 x40) as proof of (cNUMBER Xn0)
% 31.25/31.46 Found (x5 x40) as proof of (cNUMBER Xn0)
% 31.25/31.46 Found x50:=(x5 x41):(cNUMBER Xn0)
% 31.25/31.46 Instantiate: Xn0:=Xn:fofType
% 31.25/31.46 Found (x5 x41) as proof of (cNUMBER Xn)
% 31.25/31.46 Found (x5 x41) as proof of (cNUMBER Xn)
% 31.25/31.46 Found x50:=(x5 x40):(cNUMBER Xn0)
% 31.25/31.46 Found (x5 x40) as proof of (cNUMBER Xn)
% 31.25/31.46 Found (x5 x40) as proof of (cNUMBER Xn)
% 31.25/31.46 Found (x5 x40) as proof of (cNUMBER Xn)
% 31.25/31.46 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 31.25/31.46 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 31.25/31.46 Found (x5 x40) as proof of (cNUMBER Xn)
% 31.25/31.46 Found (x5 x40) as proof of (cNUMBER Xn)
% 31.25/31.46 Found (fun (x9:(cODD (cS c0)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 31.25/31.46 Found (fun (x9:(cODD (cS c0)))=> (x5 x40)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 31.25/31.46 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 31.25/31.46 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 31.25/31.46 Found (x3 x20) as proof of (cNUMBER Xn)
% 31.25/31.46 Found (x3 x20) as proof of (cNUMBER Xn)
% 31.25/31.46 Found (x3 x20) as proof of (cNUMBER Xn)
% 31.25/31.46 Found x80:((or (cEVEN Xn0)) (cODD Xn0))
% 31.25/31.46 Found x80 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 31.25/31.46 Found (x9 x80) as proof of (cNUMBER Xn)
% 31.25/31.46 Found (x9 x80) as proof of (cNUMBER Xn)
% 31.25/31.46 Found (x9 x80) as proof of (cNUMBER Xn)
% 31.25/31.46 Found x30:=(x3 x20):(cNUMBER Xn0)
% 31.25/31.46 Found (x3 x20) as proof of (cNUMBER Xn)
% 31.25/31.46 Found (x3 x20) as proof of (cNUMBER Xn)
% 31.25/31.46 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 31.25/31.46 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 31.25/31.46 Found x30:(cNUMBER Xn0)
% 31.25/31.46 Instantiate: Xn0:=Xn:fofType
% 31.25/31.46 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30) as proof of (cNUMBER Xn)
% 31.25/31.46 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))
% 31.25/31.46 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)))
% 31.25/31.46 Found x30:=(x3 x20):(cNUMBER Xn0)
% 31.25/31.46 Found (x3 x20) as proof of (cNUMBER Xn)
% 31.25/31.46 Found (x3 x20) as proof of (cNUMBER Xn)
% 31.25/31.46 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 31.25/31.46 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 31.25/31.49 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn)))
% 31.25/31.49 Found x30:(cNUMBER Xn0)
% 31.25/31.49 Instantiate: Xn0:=Xn:fofType
% 31.25/31.49 Found (fun (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30) as proof of (cNUMBER Xn)
% 31.25/31.49 Found (fun (x5:(cODD Xn0)) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 31.25/31.49 Found (fun (x5:(cODD Xn0)) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30) as proof of ((cODD Xn0)->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn)))
% 31.25/31.49 Found x30:(cNUMBER Xn0)
% 31.25/31.49 Instantiate: Xn0:=Xn:fofType
% 31.25/31.49 Found (fun (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30) as proof of (cNUMBER Xn)
% 31.25/31.49 Found (fun (x5:(cEVEN Xn0)) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 31.25/31.49 Found (fun (x5:(cEVEN Xn0)) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30) as proof of ((cEVEN Xn0)->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn)))
% 31.25/31.49 Found ((or_ind00 (fun (x5:(cEVEN Xn0)) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30)) (fun (x5:(cODD Xn0)) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 31.25/31.50 Found (((or_ind0 ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))) (fun (x5:(cEVEN Xn0)) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30)) (fun (x5:(cODD Xn0)) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 31.25/31.50 Found ((((fun (P:Prop) (x5:((cEVEN Xn0)->P)) (x6:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x5) x6) x20)) ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))) (fun (x5:(cEVEN Xn0)) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30)) (fun (x5:(cODD Xn0)) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 31.25/31.50 Found ((((fun (P:Prop) (x5:((cEVEN Xn0)->P)) (x6:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x5) x6) (x2 x30))) ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))) (fun (x5:(cEVEN Xn0)) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30)) (fun (x5:(cODD Xn0)) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 31.25/31.50 Found ((((fun (P:Prop) (x5:((cEVEN Xn0)->P)) (x6:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x5) x6) (x2 x30))) ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))) (fun (x5:(cEVEN Xn0)) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30)) (fun (x5:(cODD Xn0)) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 31.51/31.73 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 31.51/31.73 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 31.51/31.73 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 31.51/31.73 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 31.51/31.73 Found (fun (x7:((and (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)))
% 31.51/31.73 Found (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0))))
% 31.51/31.73 Found (and_rect40 (fun (x7:((and (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))
% 31.51/31.73 Found ((and_rect4 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (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))
% 31.51/31.73 Found (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (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 (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))
% 31.51/31.73 Found (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (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 (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))
% 31.51/31.73 Found (x3 (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (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 (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of (cNUMBER Xn0)
% 31.51/31.73 Found (x3 (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (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 (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of (cNUMBER Xn0)
% 31.51/31.73 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 31.51/31.73 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 31.51/31.73 Found (x5 x40) as proof of (cNUMBER Xn)
% 31.51/31.73 Found (x5 x40) as proof of (cNUMBER Xn)
% 31.51/31.73 Found (x5 x40) as proof of (cNUMBER Xn)
% 31.51/31.73 Found x30:(cNUMBER Xn0)
% 31.51/31.73 Instantiate: Xn0:=Xn:fofType
% 31.51/31.73 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x30) as proof of (cNUMBER Xn)
% 31.51/31.73 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x30) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 31.51/31.73 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 31.99/32.18 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 31.99/32.18 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 31.99/32.18 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 31.99/32.18 Found (fun (x8:((and (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)))
% 31.99/32.18 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0))))
% 31.99/32.18 Found (and_rect40 (fun (x8:((and (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))
% 31.99/32.18 Found ((and_rect4 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (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))
% 31.99/32.18 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (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))
% 31.99/32.18 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (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))
% 31.99/32.18 Found x30:=(x3 x20):(cNUMBER Xn0)
% 31.99/32.18 Found (x3 x20) as proof of (cNUMBER Xn0)
% 31.99/32.18 Found (x3 x20) as proof of (cNUMBER Xn0)
% 31.99/32.18 Found x30:=(x3 x21):(cNUMBER Xn0)
% 31.99/32.18 Instantiate: Xn0:=Xn:fofType
% 31.99/32.18 Found (x3 x21) as proof of (cNUMBER Xn)
% 31.99/32.18 Found (x3 x21) as proof of (cNUMBER Xn)
% 31.99/32.18 Found x30:=(x3 x20):(cNUMBER Xn0)
% 31.99/32.18 Found (x3 x20) as proof of (cNUMBER Xn)
% 31.99/32.18 Found (x3 x20) as proof of (cNUMBER Xn)
% 31.99/32.18 Found (x3 x20) as proof of (cNUMBER Xn)
% 31.99/32.18 Found x30:=(x3 x20):(cNUMBER Xn0)
% 31.99/32.18 Instantiate: Xn0:=Xn:fofType
% 31.99/32.18 Found (x3 x20) as proof of (cNUMBER Xn)
% 31.99/32.18 Found (fun (x9:(cODD (cS c0)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 31.99/32.18 Found (fun (x8:((and (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))
% 31.99/32.18 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x20)) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 31.99/32.18 Found (and_rect40 (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x20))) as proof of (cNUMBER Xn)
% 31.99/32.18 Found ((and_rect4 (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x20))) as proof of (cNUMBER Xn)
% 31.99/32.18 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x20))) as proof of (cNUMBER Xn)
% 31.99/32.18 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x20)))) as proof of (cNUMBER Xn)
% 32.78/33.00 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x20)))) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 32.78/33.00 Found x70:=(x7 x60):(cNUMBER Xn0)
% 32.78/33.00 Found (x7 x60) as proof of (cNUMBER Xn)
% 32.78/33.00 Found (x7 x60) as proof of (cNUMBER Xn)
% 32.78/33.00 Found (fun (x9:(cODD (cS c0)))=> (x7 x60)) as proof of (cNUMBER Xn)
% 32.78/33.00 Found (fun (x8:((and (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))
% 32.78/33.00 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x7 x60)) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 32.78/33.00 Found x60:((or (cEVEN Xn0)) (cODD Xn0))
% 32.78/33.00 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 32.78/33.00 Found (x7 x60) as proof of (cNUMBER Xn)
% 32.78/33.00 Found (x7 x60) as proof of (cNUMBER Xn)
% 32.78/33.00 Found (x7 x60) as proof of (cNUMBER Xn)
% 32.78/33.00 Found x50:=(x5 x41):(cNUMBER Xn0)
% 32.78/33.00 Instantiate: Xn0:=Xn:fofType
% 32.78/33.00 Found (x5 x41) as proof of (cNUMBER Xn)
% 32.78/33.00 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x5 x41)) as proof of (cNUMBER Xn)
% 32.78/33.00 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x5 x41)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 32.78/33.00 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 32.78/33.00 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 32.78/33.00 Found (x5 x40) as proof of (cNUMBER Xn)
% 32.78/33.00 Found (x5 x40) as proof of (cNUMBER Xn)
% 32.78/33.00 Found (fun (x9:(cODD (cS c0)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 32.78/33.00 Found (fun (x8:((and (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))
% 32.78/33.00 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x40)) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 32.78/33.00 Found x30:=(x3 x20):(cNUMBER Xn0)
% 32.78/33.00 Instantiate: Xn0:=Xn:fofType
% 32.78/33.00 Found (x3 x20) as proof of (cNUMBER Xn)
% 32.78/33.00 Found (fun (x9:(cODD (cS c0)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 32.78/33.00 Found (fun (x8:((and (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))
% 32.78/33.00 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x20)) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 32.78/33.00 Found (and_rect40 (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x20))) as proof of (cNUMBER Xn)
% 32.78/33.00 Found ((and_rect4 (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x20))) as proof of (cNUMBER Xn)
% 32.78/33.00 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x20))) as proof of (cNUMBER Xn)
% 33.57/33.79 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x20)))) as proof of (cNUMBER Xn)
% 33.57/33.79 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x20)))) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 33.57/33.79 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x20)))) as proof of (((and ((and (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)))
% 33.57/33.79 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 33.57/33.79 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 33.57/33.79 Found (x3 x20) as proof of (cNUMBER Xn)
% 33.57/33.79 Found (x3 x20) as proof of (cNUMBER Xn)
% 33.57/33.79 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 33.57/33.79 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 33.57/33.79 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 33.57/33.79 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 33.57/33.79 Found (x3 x20) as proof of (cNUMBER Xn)
% 33.57/33.79 Found (x3 x20) as proof of (cNUMBER Xn)
% 33.57/33.79 Found (x3 x20) as proof of (cNUMBER Xn)
% 33.57/33.79 Found x50:=(x5 x40):(cNUMBER Xn00)
% 33.57/33.79 Instantiate: Xn00:=Xn:fofType
% 33.57/33.79 Found (x5 x40) as proof of (cNUMBER Xn)
% 33.57/33.79 Found (x5 x40) as proof of (cNUMBER Xn)
% 33.57/33.79 Found x30:=(x3 x20):(cNUMBER Xn0)
% 33.57/33.79 Instantiate: Xn0:=Xn:fofType
% 33.57/33.79 Found (x3 x20) as proof of (cNUMBER Xn)
% 33.57/33.79 Found (x3 x20) as proof of (cNUMBER Xn)
% 33.57/33.79 Found x80:((or (cEVEN Xn0)) (cODD Xn0))
% 33.57/33.79 Found x80 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 33.57/33.79 Found (x9 x80) as proof of (cNUMBER Xn)
% 33.57/33.79 Found (x9 x80) as proof of (cNUMBER Xn)
% 33.57/33.79 Found (fun (x9:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x9 x80)) as proof of (cNUMBER Xn)
% 33.57/33.79 Found (fun (x9:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x9 x80)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 33.57/33.79 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 33.57/33.79 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 33.57/33.79 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 33.57/33.79 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 33.57/33.79 Found (fun (x7:((and (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)))
% 33.57/33.79 Found (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0))))
% 33.57/33.79 Found (and_rect40 (fun (x7:((and (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))
% 33.57/33.79 Found ((and_rect4 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (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))
% 33.57/33.79 Found (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (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))
% 33.57/33.79 Found (fun (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (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))
% 33.57/33.79 Found (fun (x5:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (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)))
% 33.57/33.79 Found (fun (x5:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of (((and ((and (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))))
% 33.57/33.79 Found (and_rect30 (fun (x5:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (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))
% 34.25/34.44 Found ((and_rect3 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x5:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (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))
% 34.25/34.44 Found (((fun (P:Type) (x5:(((and ((and (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 (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x5) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x5:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (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))
% 34.25/34.44 Found (((fun (P:Type) (x5:(((and ((and (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 (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x5) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x5:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (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))
% 34.25/34.44 Found x50:(cNUMBER Xn0)
% 34.25/34.44 Instantiate: Xn0:=Xn:fofType
% 34.25/34.44 Found x50 as proof of (cNUMBER Xn)
% 34.25/34.44 Found x30:(cNUMBER Xn0)
% 34.25/34.44 Instantiate: Xn0:=Xn:fofType
% 34.25/34.44 Found (fun (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30) as proof of (cNUMBER Xn)
% 34.25/34.44 Found (fun (x5:(cODD Xn0)) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 34.25/34.44 Found (fun (x5:(cODD Xn0)) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30) as proof of ((cODD Xn0)->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn)))
% 34.25/34.47 Found x30:(cNUMBER Xn0)
% 34.25/34.47 Instantiate: Xn0:=Xn:fofType
% 34.25/34.47 Found (fun (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30) as proof of (cNUMBER Xn)
% 34.25/34.47 Found (fun (x5:(cEVEN Xn0)) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 34.25/34.47 Found (fun (x5:(cEVEN Xn0)) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30) as proof of ((cEVEN Xn0)->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn)))
% 34.25/34.47 Found ((or_ind00 (fun (x5:(cEVEN Xn0)) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30)) (fun (x5:(cODD Xn0)) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 34.25/34.47 Found (((or_ind0 ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))) (fun (x5:(cEVEN Xn0)) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30)) (fun (x5:(cODD Xn0)) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 34.25/34.47 Found ((((fun (P:Prop) (x5:((cEVEN Xn0)->P)) (x6:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x5) x6) x20)) ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))) (fun (x5:(cEVEN Xn0)) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30)) (fun (x5:(cODD Xn0)) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 34.50/34.68 Found ((((fun (P:Prop) (x5:((cEVEN Xn0)->P)) (x6:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x5) x6) (x2 x30))) ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))) (fun (x5:(cEVEN Xn0)) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30)) (fun (x5:(cODD Xn0)) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 34.50/34.68 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))))=> ((((fun (P:Prop) (x5:((cEVEN Xn0)->P)) (x6:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x5) x6) (x2 x30))) ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))) (fun (x5:(cEVEN Xn0)) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30)) (fun (x5:(cODD Xn0)) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30))) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 34.50/34.68 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))))=> ((((fun (P:Prop) (x5:((cEVEN Xn0)->P)) (x6:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x5) x6) (x2 x30))) ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))) (fun (x5:(cEVEN Xn0)) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30)) (fun (x5:(cODD Xn0)) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30))) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn)))
% 34.50/34.68 Found x30:(cNUMBER Xn0)
% 34.50/34.68 Instantiate: Xn0:=Xn:fofType
% 34.50/34.68 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x30) as proof of (cNUMBER Xn)
% 35.51/35.69 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x30) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 35.51/35.69 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x30) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 35.51/35.69 Found x30:=(x3 x20):(cNUMBER Xn0)
% 35.51/35.69 Found (x3 x20) as proof of (cNUMBER Xn0)
% 35.51/35.69 Found (x3 x20) as proof of (cNUMBER Xn0)
% 35.51/35.69 Found x30:=(x3 x21):(cNUMBER Xn0)
% 35.51/35.69 Instantiate: Xn0:=Xn:fofType
% 35.51/35.69 Found (x3 x21) as proof of (cNUMBER Xn)
% 35.51/35.69 Found (x3 x21) as proof of (cNUMBER Xn)
% 35.51/35.69 Found x30:=(x3 x20):(cNUMBER Xn0)
% 35.51/35.69 Found (x3 x20) as proof of (cNUMBER Xn)
% 35.51/35.69 Found (x3 x20) as proof of (cNUMBER Xn)
% 35.51/35.69 Found (x3 x20) as proof of (cNUMBER Xn)
% 35.51/35.69 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 35.51/35.69 Instantiate: Xn00:=Xn:fofType
% 35.51/35.69 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 35.51/35.69 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 35.51/35.69 Instantiate: Xn0:=Xn:fofType
% 35.51/35.69 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 35.51/35.69 Found x50:=(x5 x40):(cNUMBER Xn0)
% 35.51/35.69 Instantiate: Xn0:=Xn:fofType
% 35.51/35.69 Found (x5 x40) as proof of (cNUMBER Xn)
% 35.51/35.69 Found (fun (x9:(cODD (cS c0)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 35.51/35.69 Found (fun (x8:((and (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))
% 35.51/35.69 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x40)) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 35.51/35.69 Found (and_rect40 (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x40))) as proof of (cNUMBER Xn)
% 35.51/35.69 Found ((and_rect4 (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x40))) as proof of (cNUMBER Xn)
% 35.51/35.69 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x40))) as proof of (cNUMBER Xn)
% 35.51/35.69 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x40))) as proof of (cNUMBER Xn)
% 35.51/35.69 Found x60:((or (cEVEN Xn0)) (cODD Xn0))
% 35.51/35.69 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 35.51/35.69 Found (x7 x60) as proof of (cNUMBER Xn)
% 35.51/35.69 Found (x7 x60) as proof of (cNUMBER Xn)
% 35.51/35.69 Found (fun (x9:(cODD (cS c0)))=> (x7 x60)) as proof of (cNUMBER Xn)
% 35.51/35.69 Found (fun (x9:(cODD (cS c0)))=> (x7 x60)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 35.51/35.69 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 35.51/35.69 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 35.51/35.69 Found (x3 x20) as proof of (cNUMBER Xn)
% 35.51/35.69 Found (x3 x20) as proof of (cNUMBER Xn)
% 35.51/35.69 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 35.51/35.69 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 35.68/35.89 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn)))
% 35.68/35.89 Found x30:=(x3 x20):(cNUMBER Xn0)
% 35.68/35.89 Instantiate: Xn0:=Xn:fofType
% 35.68/35.89 Found (x3 x20) as proof of (cNUMBER Xn)
% 35.68/35.89 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 35.68/35.89 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 35.68/35.89 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 35.68/35.89 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 35.68/35.89 Found (x3 x20) as proof of (cNUMBER Xn)
% 35.68/35.89 Found (x3 x20) as proof of (cNUMBER Xn)
% 35.68/35.89 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 35.68/35.89 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 35.68/35.89 Found x50:=(x5 x40):(cNUMBER Xn00)
% 35.68/35.89 Instantiate: Xn00:=Xn:fofType
% 35.68/35.89 Found (x5 x40) as proof of (cNUMBER Xn)
% 35.68/35.89 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 35.68/35.89 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 35.68/35.89 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 35.68/35.89 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 35.68/35.89 Found (x3 x20) as proof of (cNUMBER Xn)
% 35.68/35.89 Found (x3 x20) as proof of (cNUMBER Xn)
% 35.68/35.89 Found (x3 x20) as proof of (cNUMBER Xn)
% 35.68/35.89 Found x30:(cNUMBER Xn0)
% 35.68/35.89 Instantiate: Xn0:=Xn:fofType
% 35.68/35.89 Found (fun (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30) as proof of (cNUMBER Xn)
% 35.68/35.89 Found (fun (x5:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 35.68/35.89 Found (fun (x4:(cEVEN Xn0)) (x5:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn)))
% 35.68/35.93 Found (fun (x4:(cEVEN Xn0)) (x5:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30) as proof of ((cEVEN Xn0)->(((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))))
% 35.68/35.93 Found x30:(cNUMBER Xn0)
% 35.68/35.93 Instantiate: Xn0:=Xn:fofType
% 35.68/35.93 Found (fun (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30) as proof of (cNUMBER Xn)
% 35.68/35.93 Found (fun (x5:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 35.68/35.93 Found (fun (x4:(cODD Xn0)) (x5:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn)))
% 35.68/35.93 Found (fun (x4:(cODD Xn0)) (x5:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30) as proof of ((cODD Xn0)->(((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))))
% 35.68/35.93 Found ((or_ind00 (fun (x4:(cEVEN Xn0)) (x5:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30)) (fun (x4:(cODD Xn0)) (x5:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30)) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn)))
% 35.68/35.93 Found (((or_ind0 (((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn)))) (fun (x4:(cEVEN Xn0)) (x5:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30)) (fun (x4:(cODD Xn0)) (x5:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30)) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn)))
% 35.68/35.93 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 (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn)))) (fun (x4:(cEVEN Xn0)) (x5:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30)) (fun (x4:(cODD Xn0)) (x5:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30)) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn)))
% 35.76/35.94 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 (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn)))) (fun (x4:(cEVEN Xn0)) (x5:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30)) (fun (x4:(cODD Xn0)) (x5:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30)) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn)))
% 35.76/35.94 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 (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn)))) (fun (x4:(cEVEN Xn0)) (x5:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30)) (fun (x4:(cODD Xn0)) (x5:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30)) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn)))
% 36.10/36.33 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 36.10/36.33 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 36.10/36.33 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 36.10/36.33 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 36.10/36.33 Found (fun (x8:((and (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)))
% 36.10/36.33 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0))))
% 36.10/36.33 Found (and_rect40 (fun (x8:((and (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))
% 36.10/36.33 Found ((and_rect4 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (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))
% 36.10/36.33 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (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 (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))
% 36.10/36.33 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (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 (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))
% 36.10/36.33 Found (x3 (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (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 (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of (cNUMBER Xn0)
% 36.10/36.33 Found (x3 (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (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 (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of (cNUMBER Xn0)
% 36.10/36.33 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 36.10/36.33 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 36.10/36.33 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 36.10/36.33 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 36.10/36.33 Found (fun (x7:((and (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)))
% 36.10/36.33 Found (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0))))
% 36.72/36.94 Found (and_rect40 (fun (x7:((and (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))
% 36.72/36.94 Found ((and_rect4 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (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))
% 36.72/36.94 Found (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (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 (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))
% 36.72/36.94 Found (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (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 (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))
% 36.72/36.94 Found (x5 (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (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 (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of (cNUMBER Xn0)
% 36.72/36.94 Found (x5 (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (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 (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of (cNUMBER Xn0)
% 36.72/36.94 Found x50:(cNUMBER Xn0)
% 36.72/36.94 Instantiate: Xn0:=Xn:fofType
% 36.72/36.94 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x50) as proof of (cNUMBER Xn)
% 36.72/36.94 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x50) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 36.72/36.94 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 36.72/36.94 Instantiate: Xn00:=Xn:fofType
% 36.72/36.94 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 36.72/36.94 Found x50:=(x5 x40):(cNUMBER Xn0)
% 36.72/36.94 Instantiate: Xn0:=Xn:fofType
% 36.72/36.94 Found (x5 x40) as proof of (cNUMBER Xn)
% 36.72/36.94 Found (fun (x9:(cODD (cS c0)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 36.72/36.94 Found (fun (x8:((and (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))
% 36.72/36.94 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x40)) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 36.72/36.94 Found (and_rect40 (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x40))) as proof of (cNUMBER Xn)
% 36.72/36.94 Found ((and_rect4 (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x40))) as proof of (cNUMBER Xn)
% 36.72/36.94 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x40))) as proof of (cNUMBER Xn)
% 37.65/37.92 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x40)))) as proof of (cNUMBER Xn)
% 37.65/37.92 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x40)))) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 37.65/37.92 Found x9:(cODD (cS c0))
% 37.65/37.92 Instantiate: Xn0:=(cS c0):fofType
% 37.65/37.92 Found x9 as proof of (cODD Xn0)
% 37.65/37.92 Found (or_intror00 x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 37.65/37.92 Found ((or_intror0 (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 37.65/37.92 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 37.65/37.92 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 37.65/37.92 Found x30:=(x3 x20):(cNUMBER Xn0)
% 37.65/37.92 Instantiate: Xn0:=Xn:fofType
% 37.65/37.92 Found (x3 x20) as proof of (cNUMBER Xn)
% 37.65/37.92 Found (x3 x20) as proof of (cNUMBER Xn)
% 37.65/37.92 Found x60:((or (cEVEN Xn0)) (cODD Xn0))
% 37.65/37.92 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 37.65/37.92 Found (x7 x60) as proof of (cNUMBER Xn)
% 37.65/37.92 Found (x7 x60) as proof of (cNUMBER Xn)
% 37.65/37.92 Found (fun (x9:(cODD (cS c0)))=> (x7 x60)) as proof of (cNUMBER Xn)
% 37.65/37.92 Found (fun (x8:((and (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))
% 37.65/37.92 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x7 x60)) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 37.65/37.92 Found x50:=(x5 x40):(cNUMBER Xn0)
% 37.65/37.92 Instantiate: Xn0:=Xn:fofType
% 37.65/37.92 Found (x5 x40) as proof of (cNUMBER Xn)
% 37.65/37.92 Found (fun (x9:(cODD (cS c0)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 37.65/37.92 Found (fun (x8:((and (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))
% 37.65/37.92 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x40)) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 37.65/37.92 Found (and_rect40 (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x40))) as proof of (cNUMBER Xn)
% 37.65/37.92 Found ((and_rect4 (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x40))) as proof of (cNUMBER Xn)
% 37.65/37.92 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x40))) as proof of (cNUMBER Xn)
% 37.65/37.92 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x40)))) as proof of (cNUMBER Xn)
% 38.19/38.44 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x40)))) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 38.19/38.44 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x40)))) as proof of (((and ((and (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)))
% 38.19/38.44 Found x30:=(x3 x20):(cNUMBER Xn0)
% 38.19/38.44 Instantiate: Xn0:=Xn:fofType
% 38.19/38.44 Found (x3 x20) as proof of (cNUMBER Xn)
% 38.19/38.44 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 38.19/38.44 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))
% 38.19/38.44 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)))
% 38.19/38.44 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 38.19/38.44 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 38.19/38.44 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 38.19/38.44 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 38.19/38.44 Found (fun (x8:((and (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)))
% 38.19/38.44 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0))))
% 38.19/38.44 Found (and_rect40 (fun (x8:((and (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))
% 38.19/38.44 Found ((and_rect4 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (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))
% 38.19/38.44 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (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))
% 38.19/38.44 Found (fun (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (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))
% 38.19/38.44 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (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)))
% 38.19/38.44 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of (((and ((and (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))))
% 38.19/38.44 Found (and_rect30 (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (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))
% 38.19/38.44 Found ((and_rect3 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (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))
% 38.19/38.44 Found (((fun (P:Type) (x6:(((and ((and (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 (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) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (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))
% 39.37/39.57 Found (((fun (P:Type) (x6:(((and ((and (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 (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) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (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))
% 39.37/39.57 Found x30:=(x3 x20):(cNUMBER Xn0)
% 39.37/39.57 Found (x3 x20) as proof of (cNUMBER Xn)
% 39.37/39.57 Found (x3 x20) as proof of (cNUMBER Xn)
% 39.37/39.57 Found (x3 x20) as proof of (cNUMBER Xn)
% 39.37/39.57 Found x50:=(x5 x40):(cNUMBER Xn00)
% 39.37/39.57 Found (x5 x40) as proof of (cNUMBER Xn)
% 39.37/39.57 Found (x5 x40) as proof of (cNUMBER Xn)
% 39.37/39.57 Found (x5 x40) as proof of (cNUMBER Xn)
% 39.37/39.57 Found x70:(cNUMBER Xn0)
% 39.37/39.57 Instantiate: Xn0:=Xn:fofType
% 39.37/39.57 Found x70 as proof of (cNUMBER Xn)
% 39.37/39.57 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 39.37/39.57 Instantiate: Xn00:=Xn:fofType
% 39.37/39.57 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x40) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 39.37/39.57 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)))
% 39.37/39.57 Found x50:(cNUMBER Xn0)
% 39.37/39.57 Instantiate: Xn0:=Xn:fofType
% 39.37/39.57 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x50) as proof of (cNUMBER Xn)
% 39.37/39.57 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x50) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 39.37/39.57 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x50) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 39.37/39.57 Found x70:=(x7 x60):(cNUMBER Xn0)
% 39.37/39.57 Instantiate: Xn0:=Xn:fofType
% 39.37/39.57 Found (x7 x60) as proof of (cNUMBER Xn)
% 39.37/39.57 Found (fun (x9:(cODD (cS c0)))=> (x7 x60)) as proof of (cNUMBER Xn)
% 39.37/39.57 Found (fun (x8:((and (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))
% 39.37/39.57 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x7 x60)) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 39.37/39.57 Found (and_rect40 (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x7 x60))) as proof of (cNUMBER Xn)
% 39.37/39.57 Found ((and_rect4 (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x7 x60))) as proof of (cNUMBER Xn)
% 39.37/39.57 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x4)) (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x7 x60))) as proof of (cNUMBER Xn)
% 39.37/39.57 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x4)) (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x7 x60))) as proof of (cNUMBER Xn)
% 40.72/40.92 Found x30:=(x3 x20):(cNUMBER Xn0)
% 40.72/40.92 Instantiate: Xn0:=Xn:fofType
% 40.72/40.92 Found (x3 x20) as proof of (cNUMBER Xn)
% 40.72/40.92 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 40.72/40.92 Found (fun (x12:(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))
% 40.72/40.92 Found x30:(cNUMBER Xn0)
% 40.72/40.92 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30) as proof of (cNUMBER Xn0)
% 40.72/40.92 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn0))
% 40.72/40.92 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 40.72/40.92 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x20) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 40.72/40.92 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x20) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 40.72/40.92 Found x30:=(x3 x20):(cNUMBER Xn0)
% 40.72/40.92 Found (x3 x20) as proof of (cNUMBER Xn)
% 40.72/40.92 Found (x3 x20) as proof of (cNUMBER Xn)
% 40.72/40.92 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 40.72/40.92 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 40.72/40.92 Found x50:=(x5 x40):(cNUMBER Xn0)
% 40.72/40.92 Found (x5 x40) as proof of (cNUMBER Xn)
% 40.72/40.92 Found (x5 x40) as proof of (cNUMBER Xn)
% 40.72/40.92 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 40.72/40.92 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x5 x40)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 40.72/40.92 Found x50:=(x5 x40):(cNUMBER Xn00)
% 40.72/40.92 Found (x5 x40) as proof of (cNUMBER Xn)
% 40.72/40.92 Found (x5 x40) as proof of (cNUMBER Xn)
% 40.72/40.92 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 40.72/40.92 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 40.72/40.92 Found x30:=(x3 x20):(cNUMBER Xn0)
% 40.72/40.92 Instantiate: Xn0:=Xn:fofType
% 40.72/40.92 Found (x3 x20) as proof of (cNUMBER Xn)
% 40.72/40.92 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 40.72/40.92 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 40.72/40.92 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn)))
% 40.72/40.92 Found (and_rect20 (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 40.72/40.92 Found ((and_rect2 (cNUMBER Xn)) (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 40.72/40.92 Found (((fun (P:Type) (x4:(((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->P)))=> (((((and_rect ((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))) P) x4) x0)) (cNUMBER Xn)) (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 40.72/40.93 Found (((fun (P:Type) (x4:(((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->P)))=> (((((and_rect ((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))) P) x4) x0)) (cNUMBER Xn)) (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 41.59/41.85 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 41.59/41.85 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 41.59/41.85 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 41.59/41.85 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 41.59/41.85 Found (fun (x8:((and (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)))
% 41.59/41.85 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0))))
% 41.59/41.85 Found (and_rect40 (fun (x8:((and (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))
% 41.59/41.85 Found ((and_rect4 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (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))
% 41.59/41.85 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (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 (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))
% 41.59/41.85 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (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 (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))
% 41.59/41.85 Found (x5 (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (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 (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of (cNUMBER Xn0)
% 41.59/41.85 Found (x5 (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (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 (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of (cNUMBER Xn0)
% 41.59/41.85 Found x70:(cNUMBER Xn0)
% 41.59/41.85 Instantiate: Xn0:=Xn:fofType
% 41.59/41.85 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x70) as proof of (cNUMBER Xn)
% 41.59/41.85 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x70) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 41.59/41.85 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 41.59/41.85 Instantiate: Xn0:=Xn:fofType
% 41.59/41.85 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 42.78/43.03 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 42.78/43.03 Found x40:=(x4 x50):((or (cEVEN Xn00)) (cODD Xn00))
% 42.78/43.03 Instantiate: Xn00:=Xn:fofType
% 42.78/43.03 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 42.78/43.03 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 42.78/43.03 Found x70:=(x7 x60):(cNUMBER Xn0)
% 42.78/43.03 Instantiate: Xn0:=Xn:fofType
% 42.78/43.03 Found (x7 x60) as proof of (cNUMBER Xn)
% 42.78/43.03 Found (fun (x9:(cODD (cS c0)))=> (x7 x60)) as proof of (cNUMBER Xn)
% 42.78/43.03 Found (fun (x8:((and (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))
% 42.78/43.03 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x7 x60)) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 42.78/43.03 Found (and_rect40 (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x7 x60))) as proof of (cNUMBER Xn)
% 42.78/43.03 Found ((and_rect4 (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x7 x60))) as proof of (cNUMBER Xn)
% 42.78/43.03 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x4)) (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x7 x60))) as proof of (cNUMBER Xn)
% 42.78/43.03 Found (fun (x7:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x4)) (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x7 x60)))) as proof of (cNUMBER Xn)
% 42.78/43.03 Found (fun (x7:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x4)) (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x7 x60)))) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 42.78/43.03 Found x9:(cODD (cS c0))
% 42.78/43.03 Instantiate: Xn0:=(cS c0):fofType
% 42.78/43.03 Found x9 as proof of (cODD Xn0)
% 42.78/43.03 Found (or_intror00 x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 42.78/43.03 Found ((or_intror0 (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 42.78/43.03 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 42.78/43.03 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 42.78/43.03 Found x120:(cNUMBER Xn0)
% 42.78/43.03 Instantiate: Xn0:=Xn:fofType
% 42.78/43.03 Found x120 as proof of (cNUMBER Xn)
% 42.78/43.03 Found x50:=(x5 x40):(cNUMBER Xn0)
% 42.78/43.03 Instantiate: Xn0:=Xn:fofType
% 42.78/43.03 Found (x5 x40) as proof of (cNUMBER Xn)
% 42.78/43.03 Found (x5 x40) as proof of (cNUMBER Xn)
% 42.78/43.03 Found x30:=(x3 x20):(cNUMBER Xn0)
% 42.78/43.03 Instantiate: Xn0:=Xn:fofType
% 42.78/43.03 Found (x3 x20) as proof of (cNUMBER Xn)
% 42.78/43.03 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 42.78/43.03 Found (fun (x11:(cEVEN c0)) (x12:(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))
% 42.78/43.03 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 42.78/43.03 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 42.78/43.03 Instantiate: Xn00:=Xn:fofType
% 42.78/43.03 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 42.78/43.03 Found (x3 x40) as proof of (cNUMBER Xn)
% 43.38/43.62 Found (x3 x40) as proof of (cNUMBER Xn)
% 43.38/43.62 Found (x3 x40) as proof of (cNUMBER Xn)
% 43.38/43.62 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 43.38/43.62 Found x40 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 43.38/43.62 Found (x5 x40) as proof of (cNUMBER Xn)
% 43.38/43.62 Found (x5 x40) as proof of (cNUMBER Xn)
% 43.38/43.62 Found (x5 x40) as proof of (cNUMBER Xn)
% 43.38/43.62 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 43.38/43.62 Instantiate: Xn0:=Xn:fofType
% 43.38/43.62 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 43.38/43.62 Found (x5 x20) as proof of (cNUMBER Xn)
% 43.38/43.62 Found (x5 x20) as proof of (cNUMBER Xn)
% 43.38/43.62 Found (x5 x20) as proof of (cNUMBER Xn)
% 43.38/43.62 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 43.38/43.62 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 43.38/43.62 Found (x3 x20) as proof of (cNUMBER Xn)
% 43.38/43.62 Found (x3 x20) as proof of (cNUMBER Xn)
% 43.38/43.62 Found (x3 x20) as proof of (cNUMBER Xn)
% 43.38/43.62 Found x30:(cNUMBER Xn0)
% 43.38/43.62 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30) as proof of (cNUMBER Xn0)
% 43.38/43.62 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn0))
% 43.38/43.62 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn0)))
% 43.38/43.62 Found x30:=(x3 x20):(cNUMBER Xn0)
% 43.38/43.62 Found (x3 x20) as proof of (cNUMBER Xn0)
% 43.38/43.62 Found (x3 x20) as proof of (cNUMBER Xn0)
% 43.38/43.62 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 43.38/43.62 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 43.38/43.62 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 43.38/43.62 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 43.38/43.62 Found (fun (x8:((and (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)))
% 43.38/43.62 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0))))
% 43.38/43.62 Found (and_rect40 (fun (x8:((and (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))
% 43.38/43.62 Found ((and_rect4 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (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))
% 43.38/43.62 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (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))
% 43.38/43.62 Found (fun (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (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))
% 43.38/43.62 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (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)))
% 43.38/43.62 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of (((and ((and (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))))
% 43.38/43.62 Found (and_rect30 (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (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))
% 43.38/43.62 Found ((and_rect3 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (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))
% 43.38/43.62 Found (((fun (P:Type) (x6:(((and ((and (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 (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) x2)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (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))
% 43.87/44.09 Found (((fun (P:Type) (x6:(((and ((and (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 (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) x2)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (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))
% 43.87/44.09 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 43.87/44.09 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x20) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 43.87/44.09 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x20) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 43.87/44.09 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x20) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->((or (cEVEN Xn0)) (cODD Xn0))))
% 43.87/44.09 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 43.87/44.09 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 43.87/44.09 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 43.87/44.09 Found x31:(cNUMBER Xn0)
% 43.87/44.09 Instantiate: Xn0:=Xn:fofType
% 43.87/44.09 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x31) as proof of (cNUMBER Xn)
% 43.87/44.09 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x31) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 44.15/44.37 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x31) as proof of (((and ((and (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)))
% 44.15/44.37 Found x30:=(x3 x20):(cNUMBER Xn0)
% 44.15/44.37 Found (x3 x20) as proof of (cNUMBER Xn)
% 44.15/44.37 Found (x3 x20) as proof of (cNUMBER Xn)
% 44.15/44.37 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 44.15/44.37 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))
% 44.15/44.37 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)))
% 44.15/44.37 Found x30:=(x3 x20):(cNUMBER Xn0)
% 44.15/44.37 Instantiate: Xn0:=Xn:fofType
% 44.15/44.37 Found (x3 x20) as proof of (cNUMBER Xn)
% 44.15/44.37 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 44.15/44.37 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 44.15/44.37 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn)))
% 44.15/44.37 Found (and_rect20 (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 44.15/44.37 Found ((and_rect2 (cNUMBER Xn)) (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 44.15/44.37 Found (((fun (P:Type) (x4:(((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->P)))=> (((((and_rect ((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))) P) x4) x0)) (cNUMBER Xn)) (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 45.25/45.44 Found (((fun (P:Type) (x4:(((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->P)))=> (((((and_rect ((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))) P) x4) x0)) (cNUMBER Xn)) (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 45.25/45.44 Found x90:(cNUMBER Xn0)
% 45.25/45.44 Instantiate: Xn0:=Xn:fofType
% 45.25/45.44 Found x90 as proof of (cNUMBER Xn)
% 45.25/45.44 Found x40:=(x4 x50):((or (cEVEN Xn00)) (cODD Xn00))
% 45.25/45.44 Instantiate: Xn00:=Xn:fofType
% 45.25/45.44 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 45.25/45.44 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 45.25/45.44 Found x70:(cNUMBER Xn0)
% 45.25/45.44 Instantiate: Xn0:=Xn:fofType
% 45.25/45.44 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x70) as proof of (cNUMBER Xn)
% 45.25/45.44 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x70) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 45.25/45.44 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x70) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 45.25/45.44 Found x30:=(x3 x20):(cNUMBER Xn0)
% 45.25/45.44 Found (x3 x20) as proof of (cNUMBER Xn)
% 45.25/45.44 Found (x3 x20) as proof of (cNUMBER Xn)
% 45.25/45.44 Found (x3 x20) as proof of (cNUMBER Xn)
% 45.25/45.44 Found x50:=(x5 x40):(cNUMBER Xn0)
% 45.25/45.44 Instantiate: Xn0:=Xn:fofType
% 45.25/45.44 Found (x5 x40) as proof of (cNUMBER Xn)
% 45.25/45.44 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 45.25/45.44 Found (fun (x12:(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))
% 45.25/45.44 Found x31:(cNUMBER Xn0)
% 45.25/45.44 Instantiate: Xn0:=Xn:fofType
% 45.25/45.44 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x31) as proof of (cNUMBER Xn)
% 45.25/45.44 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x31) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 46.18/46.43 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 46.18/46.43 Instantiate: Xn0:=Xn:fofType
% 46.18/46.43 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 46.18/46.43 Found (x5 x20) as proof of (cNUMBER Xn)
% 46.18/46.43 Found (x5 x20) as proof of (cNUMBER Xn)
% 46.18/46.43 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x20)) as proof of (cNUMBER Xn)
% 46.18/46.43 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x20)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 46.18/46.43 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 46.18/46.43 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 46.18/46.43 Found (x3 x20) as proof of (cNUMBER Xn)
% 46.18/46.43 Found (x3 x20) as proof of (cNUMBER Xn)
% 46.18/46.43 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 46.18/46.43 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 46.18/46.43 Found x7:(cODD (cS c0))
% 46.18/46.43 Instantiate: Xn0:=(cS c0):fofType
% 46.18/46.43 Found x7 as proof of (cODD Xn0)
% 46.18/46.43 Found (or_intror00 x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 46.18/46.43 Found ((or_intror0 (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 46.18/46.43 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 46.18/46.43 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 46.18/46.43 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 46.18/46.43 Instantiate: Xn00:=Xn:fofType
% 46.18/46.43 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 46.18/46.43 Found (x3 x40) as proof of (cNUMBER Xn)
% 46.18/46.43 Found (x3 x40) as proof of (cNUMBER Xn)
% 46.18/46.43 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x40)) as proof of (cNUMBER Xn)
% 46.18/46.43 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x40)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 46.18/46.43 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 46.18/46.43 Found x40 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 46.18/46.43 Found (x5 x40) as proof of (cNUMBER Xn)
% 46.18/46.43 Found (x5 x40) as proof of (cNUMBER Xn)
% 46.18/46.43 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 46.18/46.43 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 46.18/46.43 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 46.18/46.43 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 46.18/46.43 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 46.18/46.43 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 46.18/46.43 Found (fun (x8:((and (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)))
% 46.18/46.43 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0))))
% 46.18/46.43 Found (and_rect40 (fun (x8:((and (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))
% 46.18/46.43 Found ((and_rect4 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (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))
% 46.18/46.43 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (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))
% 46.18/46.43 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (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))
% 47.64/47.83 Found (x7 (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of (cNUMBER Xn0)
% 47.64/47.83 Found (x7 (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of (cNUMBER Xn0)
% 47.64/47.83 Found x90:(cNUMBER Xn0)
% 47.64/47.83 Instantiate: Xn0:=Xn:fofType
% 47.64/47.83 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x90) as proof of (cNUMBER Xn)
% 47.64/47.83 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x90) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 47.64/47.83 Found x30:=(x3 x20):(cNUMBER Xn0)
% 47.64/47.83 Found (x3 x20) as proof of (cNUMBER Xn0)
% 47.64/47.83 Found (x3 x20) as proof of (cNUMBER Xn0)
% 47.64/47.83 Found x30:=(x3 x21):(cNUMBER Xn0)
% 47.64/47.83 Instantiate: Xn0:=Xn:fofType
% 47.64/47.83 Found (x3 x21) as proof of (cNUMBER Xn)
% 47.64/47.83 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21)) as proof of (cNUMBER Xn)
% 47.64/47.83 Found (fun (x7:(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))
% 47.64/47.83 Found x30:=(x3 x21):(cNUMBER Xn0)
% 47.64/47.83 Instantiate: Xn0:=Xn:fofType
% 47.64/47.83 Found (x3 x21) as proof of (cNUMBER Xn)
% 47.64/47.83 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21)) as proof of (cNUMBER Xn)
% 47.64/47.83 Found (fun (x6:((and ((and (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 x21)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 47.64/47.83 Found (fun (x6:((and ((and (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 x21)) as proof of (((and ((and (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)))
% 47.64/47.83 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 47.64/47.83 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 47.64/47.83 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 47.64/47.83 Found x9:(cODD (cS c0))
% 47.64/47.83 Instantiate: Xn0:=(cS c0):fofType
% 47.64/47.83 Found x9 as proof of (cODD Xn0)
% 47.64/47.83 Found (or_intror00 x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 47.64/47.83 Found ((or_intror0 (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 47.64/47.83 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 47.64/47.83 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 47.64/47.83 Found x30:=(x3 x20):(cNUMBER Xn0)
% 47.64/47.83 Found (x3 x20) as proof of (cNUMBER Xn)
% 47.64/47.83 Found (x3 x20) as proof of (cNUMBER Xn)
% 47.64/47.83 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 47.64/47.83 Found (fun (x12:(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))
% 47.64/47.83 Found x70:=(x7 x60):(cNUMBER Xn0)
% 47.64/47.83 Instantiate: Xn0:=Xn:fofType
% 48.25/48.50 Found (x7 x60) as proof of (cNUMBER Xn)
% 48.25/48.50 Found (x7 x60) as proof of (cNUMBER Xn)
% 48.25/48.50 Found x50:=(x5 x40):(cNUMBER Xn0)
% 48.25/48.50 Instantiate: Xn0:=Xn:fofType
% 48.25/48.50 Found (x5 x40) as proof of (cNUMBER Xn)
% 48.25/48.50 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 48.25/48.50 Found (fun (x11:(cEVEN c0)) (x12:(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))
% 48.25/48.50 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 48.25/48.50 Found x40:=(x4 x50):((or (cEVEN Xn00)) (cODD Xn00))
% 48.25/48.50 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 48.25/48.50 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 48.25/48.50 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 48.25/48.50 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 48.25/48.50 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 48.25/48.50 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 48.25/48.50 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 48.25/48.50 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 48.25/48.50 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 48.25/48.50 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 48.25/48.50 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 48.25/48.50 Found (fun (x7:((and (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)))
% 48.25/48.50 Found (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0))))
% 48.25/48.50 Found (and_rect40 (fun (x7:((and (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))
% 48.25/48.50 Found ((and_rect4 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (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))
% 48.25/48.50 Found (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (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))
% 48.25/48.50 Found (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (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))
% 48.25/48.50 Found (x3 (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of (cNUMBER Xn0)
% 48.25/48.50 Found (fun (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x3 (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))))) as proof of (cNUMBER Xn0)
% 48.33/48.51 Found (fun (x5:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x3 (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (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))
% 48.33/48.51 Found (fun (x5:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x3 (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))))) as proof of (((and ((and (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)))
% 48.33/48.51 Found (and_rect30 (fun (x5:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x3 (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))))) as proof of (cNUMBER Xn0)
% 48.33/48.51 Found ((and_rect3 (cNUMBER Xn0)) (fun (x5:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x3 (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))))) as proof of (cNUMBER Xn0)
% 48.33/48.51 Found (((fun (P:Type) (x5:(((and ((and (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 (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x5) x4)) (cNUMBER Xn0)) (fun (x5:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x3 (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))))) as proof of (cNUMBER Xn0)
% 48.33/48.52 Found (((fun (P:Type) (x5:(((and ((and (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 (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x5) x4)) (cNUMBER Xn0)) (fun (x5:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x3 (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))))) as proof of (cNUMBER Xn0)
% 48.33/48.52 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 48.33/48.52 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 48.33/48.52 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 48.33/48.52 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 48.33/48.52 Found (fun (x7:((and (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)))
% 48.33/48.52 Found (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0))))
% 48.33/48.52 Found (and_rect40 (fun (x7:((and (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))
% 48.33/48.52 Found ((and_rect4 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (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))
% 48.33/48.52 Found (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (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))
% 48.33/48.52 Found (fun (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (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))
% 48.33/48.52 Found (fun (x5:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (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)))
% 48.33/48.52 Found (fun (x5:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of (((and ((and (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))))
% 48.33/48.52 Found (and_rect30 (fun (x5:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (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))
% 48.33/48.52 Found ((and_rect3 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x5:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (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))
% 48.33/48.52 Found (((fun (P:Type) (x5:(((and ((and (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 (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x5) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x5:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (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))
% 48.33/48.52 Found (((fun (P:Type) (x5:(((and ((and (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 (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x5) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x5:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (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))
% 48.50/48.71 Found (x3 (((fun (P:Type) (x5:(((and ((and (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 (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x5) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x5:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))))) as proof of (cNUMBER Xn0)
% 48.50/48.71 Found (x3 (((fun (P:Type) (x5:(((and ((and (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 (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x5) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x5:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))))) as proof of (cNUMBER Xn0)
% 48.50/48.71 Found x31:(cNUMBER Xn0)
% 48.50/48.71 Instantiate: Xn0:=Xn:fofType
% 48.50/48.71 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x31) as proof of (cNUMBER Xn)
% 48.50/48.71 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x31) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 48.50/48.71 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 48.50/48.71 Instantiate: Xn0:=Xn:fofType
% 48.50/48.71 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 48.50/48.71 Found (x5 x20) as proof of (cNUMBER Xn)
% 48.50/48.71 Found (x5 x20) as proof of (cNUMBER Xn)
% 48.50/48.71 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x20)) as proof of (cNUMBER Xn)
% 48.50/48.71 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))
% 48.50/48.71 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)))
% 48.50/48.71 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 48.50/48.71 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 48.50/48.71 Found (x3 x20) as proof of (cNUMBER Xn)
% 48.50/48.71 Found (x3 x20) as proof of (cNUMBER Xn)
% 48.50/48.71 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 48.50/48.71 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))
% 50.27/50.47 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)))
% 50.27/50.47 Found x50:=(x5 x40):(cNUMBER Xn0)
% 50.27/50.47 Found (x5 x40) as proof of (cNUMBER Xn0)
% 50.27/50.47 Found (x5 x40) as proof of (cNUMBER Xn0)
% 50.27/50.47 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 50.27/50.47 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 50.27/50.47 Found (x5 x40) as proof of (cNUMBER Xn)
% 50.27/50.47 Found (x5 x40) as proof of (cNUMBER Xn)
% 50.27/50.47 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 50.27/50.47 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x5 x40)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 50.27/50.47 Found x40:=(x4 x50):((or (cEVEN Xn0)) (cODD Xn0))
% 50.27/50.47 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 50.27/50.47 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 50.27/50.47 Found x51:(cNUMBER Xn0)
% 50.27/50.47 Instantiate: Xn0:=Xn:fofType
% 50.27/50.47 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x51) as proof of (cNUMBER Xn)
% 50.27/50.47 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x51) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 50.27/50.47 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x51) as proof of (((and ((and (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)))
% 50.27/50.47 Found x90:(cNUMBER Xn0)
% 50.27/50.47 Instantiate: Xn0:=Xn:fofType
% 50.27/50.47 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x90) as proof of (cNUMBER Xn)
% 50.27/50.47 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x90) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 50.27/50.47 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x90) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 50.27/50.47 Found x30:=(x3 x20):(cNUMBER Xn0)
% 50.27/50.47 Found (x3 x20) as proof of (cNUMBER Xn0)
% 50.27/50.47 Found (x3 x20) as proof of (cNUMBER Xn0)
% 50.27/50.47 Found x30:=(x3 x21):(cNUMBER Xn0)
% 50.27/50.47 Instantiate: Xn0:=Xn:fofType
% 50.27/50.47 Found (x3 x21) as proof of (cNUMBER Xn)
% 50.27/50.47 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21)) as proof of (cNUMBER Xn)
% 50.27/50.47 Found (fun (x7:(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))
% 50.27/50.47 Found x50:=(x5 x40):(cNUMBER Xn0)
% 50.27/50.47 Found (x5 x40) as proof of (cNUMBER Xn)
% 50.27/50.47 Found (x5 x40) as proof of (cNUMBER Xn)
% 50.27/50.47 Found (x5 x40) as proof of (cNUMBER Xn)
% 50.27/50.47 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 50.27/50.47 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 50.27/50.47 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 50.27/50.47 Found x30:=(x3 x20):(cNUMBER Xn0)
% 50.27/50.47 Found (x3 x20) as proof of (cNUMBER Xn)
% 50.27/50.47 Found (x3 x20) as proof of (cNUMBER Xn)
% 50.27/50.47 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 50.27/50.47 Found (fun (x11:(cEVEN c0)) (x12:(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))
% 50.27/50.47 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 50.27/50.47 Found x40:=(x4 x50):((or (cEVEN Xn00)) (cODD Xn00))
% 50.27/50.47 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 50.27/50.47 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 50.27/50.47 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 50.27/50.47 Found x70:=(x7 x60):(cNUMBER Xn0)
% 52.09/52.32 Instantiate: Xn0:=Xn:fofType
% 52.09/52.32 Found (x7 x60) as proof of (cNUMBER Xn)
% 52.09/52.32 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)) as proof of (cNUMBER Xn)
% 52.09/52.32 Found (fun (x12:(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))
% 52.09/52.32 Found x51:(cNUMBER Xn0)
% 52.09/52.32 Instantiate: Xn0:=Xn:fofType
% 52.09/52.32 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x51) as proof of (cNUMBER Xn)
% 52.09/52.32 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x51) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 52.09/52.32 Found x30:=(x3 x20):(cNUMBER Xn0)
% 52.09/52.32 Found (x3 x20) as proof of (cNUMBER Xn0)
% 52.09/52.32 Found (x3 x20) as proof of (cNUMBER Xn0)
% 52.09/52.32 Found x30:=(x3 x21):(cNUMBER Xn0)
% 52.09/52.32 Instantiate: Xn0:=Xn:fofType
% 52.09/52.32 Found (x3 x21) as proof of (cNUMBER Xn)
% 52.09/52.32 Found (x3 x21) as proof of (cNUMBER Xn)
% 52.09/52.32 Found x30:=(x3 x20):(cNUMBER Xn0)
% 52.09/52.32 Found (x3 x20) as proof of (cNUMBER Xn)
% 52.09/52.32 Found (x3 x20) as proof of (cNUMBER Xn)
% 52.09/52.32 Found (x3 x20) as proof of (cNUMBER Xn)
% 52.09/52.32 Found x30:=(x3 x20):(cNUMBER Xn0)
% 52.09/52.32 Found (x3 x20) as proof of (cNUMBER Xn)
% 52.09/52.32 Found (x3 x20) as proof of (cNUMBER Xn)
% 52.09/52.32 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 52.09/52.32 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))
% 52.09/52.32 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 52.09/52.32 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 52.09/52.32 Found (x3 x20) as proof of (cNUMBER Xn)
% 52.09/52.32 Found (x3 x20) as proof of (cNUMBER Xn)
% 52.09/52.32 Found (x3 x20) as proof of (cNUMBER Xn)
% 52.09/52.32 Found x120:=(x12 x110):(cNUMBER Xn0)
% 52.09/52.32 Instantiate: Xn0:=Xn:fofType
% 52.09/52.32 Found (x12 x110) as proof of (cNUMBER Xn)
% 52.09/52.32 Found (x12 x110) as proof of (cNUMBER Xn)
% 52.09/52.32 Found x9:(cODD (cS c0))
% 52.09/52.32 Instantiate: Xn0:=(cS c0):fofType
% 52.09/52.32 Found x9 as proof of (cODD Xn0)
% 52.09/52.32 Found (or_intror00 x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 52.09/52.32 Found ((or_intror0 (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 52.09/52.32 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 52.09/52.32 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 52.09/52.32 Found (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9)) as proof of (cNUMBER Xn0)
% 52.09/52.32 Found (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9)) as proof of (cNUMBER Xn0)
% 52.09/52.32 Found x50:=(x5 x40):(cNUMBER Xn0)
% 52.09/52.32 Found (x5 x40) as proof of (cNUMBER Xn0)
% 52.09/52.32 Found (x5 x40) as proof of (cNUMBER Xn0)
% 52.09/52.32 Found x50:=(x5 x41):(cNUMBER Xn0)
% 52.09/52.32 Instantiate: Xn0:=Xn:fofType
% 52.09/52.32 Found (x5 x41) as proof of (cNUMBER Xn)
% 52.09/52.32 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x41)) as proof of (cNUMBER Xn)
% 52.09/52.32 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x41)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 52.09/52.32 Found x40:=(x4 x50):((or (cEVEN Xn0)) (cODD Xn0))
% 52.09/52.32 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 52.09/52.32 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 52.09/52.32 Found x50:=(x5 x41):(cNUMBER Xn0)
% 52.09/52.32 Instantiate: Xn0:=Xn:fofType
% 52.09/52.32 Found (x5 x41) as proof of (cNUMBER Xn)
% 52.09/52.32 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x41)) as proof of (cNUMBER Xn)
% 52.09/52.32 Found (fun (x6:((and ((and (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 x41)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 52.09/52.32 Found (fun (x6:((and ((and (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 x41)) as proof of (((and ((and (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)))
% 52.09/52.32 Found x50:=(x5 x40):(cNUMBER Xn0)
% 52.09/52.32 Found (x5 x40) as proof of (cNUMBER Xn)
% 52.09/52.32 Found (x5 x40) as proof of (cNUMBER Xn)
% 53.07/53.26 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 53.07/53.26 Found (fun (x12:(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))
% 53.07/53.26 Found x90:=(x9 x80):(cNUMBER Xn0)
% 53.07/53.26 Instantiate: Xn0:=Xn:fofType
% 53.07/53.26 Found (x9 x80) as proof of (cNUMBER Xn)
% 53.07/53.26 Found (x9 x80) as proof of (cNUMBER Xn)
% 53.07/53.26 Found x30:(cNUMBER Xn0)
% 53.07/53.26 Found x30 as proof of (cNUMBER Xn0)
% 53.07/53.26 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 53.07/53.26 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 53.07/53.26 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 53.07/53.26 Found x50:(cNUMBER Xn00)
% 53.07/53.26 Found x50 as proof of (cNUMBER Xn00)
% 53.07/53.26 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 53.07/53.26 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 53.07/53.26 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 53.07/53.26 Found x70:=(x7 x60):(cNUMBER Xn0)
% 53.07/53.26 Instantiate: Xn0:=Xn:fofType
% 53.07/53.26 Found (x7 x60) as proof of (cNUMBER Xn)
% 53.07/53.26 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)) as proof of (cNUMBER Xn)
% 53.07/53.26 Found (fun (x11:(cEVEN c0)) (x12:(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))
% 53.07/53.26 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 53.07/53.26 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 53.07/53.26 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 53.07/53.26 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 53.07/53.26 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 53.07/53.26 Found (fun (x8:((and (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)))
% 53.07/53.26 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0))))
% 53.07/53.26 Found (and_rect40 (fun (x8:((and (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))
% 53.07/53.26 Found ((and_rect4 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (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))
% 53.07/53.26 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (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))
% 53.07/53.26 Found (fun (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (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))
% 53.07/53.26 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (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)))
% 53.07/53.27 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of (((and ((and (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))))
% 53.07/53.27 Found (and_rect30 (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (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))
% 53.07/53.27 Found ((and_rect3 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (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))
% 53.07/53.27 Found (((fun (P:Type) (x6:(((and ((and (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 (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) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (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))
% 53.07/53.27 Found (((fun (P:Type) (x6:(((and ((and (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 (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) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (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))
% 53.11/53.29 Found (x3 (((fun (P:Type) (x6:(((and ((and (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 (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) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))))) as proof of (cNUMBER Xn0)
% 53.11/53.29 Found (x3 (((fun (P:Type) (x6:(((and ((and (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 (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) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))))) as proof of (cNUMBER Xn0)
% 53.11/53.29 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 53.11/53.29 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 53.11/53.29 Found (x3 x20) as proof of (cNUMBER Xn)
% 53.11/53.29 Found (x3 x20) as proof of (cNUMBER Xn)
% 53.11/53.29 Found (x3 x20) as proof of (cNUMBER Xn)
% 53.11/53.29 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 53.11/53.29 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 53.11/53.29 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 53.11/53.29 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 53.11/53.29 Found (fun (x8:((and (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)))
% 53.11/53.29 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0))))
% 53.11/53.29 Found (and_rect40 (fun (x8:((and (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))
% 53.11/53.30 Found ((and_rect4 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (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))
% 53.11/53.30 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (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))
% 53.11/53.30 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (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))
% 53.11/53.30 Found (x3 (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of (cNUMBER Xn0)
% 53.11/53.30 Found (fun (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x3 (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))))) as proof of (cNUMBER Xn0)
% 53.11/53.30 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x3 (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (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))
% 53.11/53.30 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x3 (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))))) as proof of (((and ((and (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)))
% 53.11/53.30 Found (and_rect30 (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x3 (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))))) as proof of (cNUMBER Xn0)
% 53.18/53.40 Found ((and_rect3 (cNUMBER Xn0)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x3 (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))))) as proof of (cNUMBER Xn0)
% 53.18/53.40 Found (((fun (P:Type) (x6:(((and ((and (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 (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) x4)) (cNUMBER Xn0)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x3 (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))))) as proof of (cNUMBER Xn0)
% 53.18/53.40 Found (((fun (P:Type) (x6:(((and ((and (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 (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) x4)) (cNUMBER Xn0)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x3 (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))))) as proof of (cNUMBER Xn0)
% 53.18/53.40 Found x30:=(x3 x20):(cNUMBER Xn0)
% 53.18/53.40 Found (x3 x20) as proof of (cNUMBER Xn0)
% 53.18/53.40 Found (x3 x20) as proof of (cNUMBER Xn0)
% 53.18/53.40 Found x30:=(x3 x21):(cNUMBER Xn0)
% 53.18/53.40 Instantiate: Xn0:=Xn:fofType
% 53.18/53.40 Found (x3 x21) as proof of (cNUMBER Xn)
% 53.18/53.40 Found (x3 x21) as proof of (cNUMBER Xn)
% 53.18/53.40 Found x30:=(x3 x20):(cNUMBER Xn0)
% 53.18/53.40 Found (x3 x20) as proof of (cNUMBER Xn)
% 53.18/53.40 Found (x3 x20) as proof of (cNUMBER Xn)
% 53.18/53.40 Found (x3 x20) as proof of (cNUMBER Xn)
% 53.18/53.40 Found x51:(cNUMBER Xn0)
% 53.18/53.40 Instantiate: Xn0:=Xn:fofType
% 53.18/53.40 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x51) as proof of (cNUMBER Xn)
% 53.18/53.40 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x51) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 53.18/53.40 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 53.18/53.40 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 53.18/53.40 Found (x3 x20) as proof of (cNUMBER Xn)
% 53.18/53.40 Found (x3 x20) as proof of (cNUMBER Xn)
% 53.18/53.40 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 54.34/54.54 Found (fun (x12:(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))
% 54.34/54.54 Found x30:=(x3 x20):(cNUMBER Xn0)
% 54.34/54.54 Found (x3 x20) as proof of (cNUMBER Xn)
% 54.34/54.54 Found (x3 x20) as proof of (cNUMBER Xn)
% 54.34/54.54 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 54.34/54.54 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))
% 54.34/54.54 Found x30:=(x3 x20):(cNUMBER Xn0)
% 54.34/54.54 Found (x3 x20) as proof of (cNUMBER Xn)
% 54.34/54.54 Found (x3 x20) as proof of (cNUMBER Xn)
% 54.34/54.54 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 54.34/54.54 Found (fun (x6:((and ((and (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))
% 54.34/54.54 Found (fun (x6:((and ((and (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 (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)))
% 54.34/54.54 Found x120:=(x12 x110):(cNUMBER Xn0)
% 54.34/54.54 Instantiate: Xn0:=Xn:fofType
% 54.34/54.54 Found (x12 x110) as proof of (cNUMBER Xn)
% 54.34/54.54 Found (fun (x12:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x12 x110)) as proof of (cNUMBER Xn)
% 54.34/54.54 Found (fun (x12:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x12 x110)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 54.34/54.54 Found x70:=(x7 x60):(cNUMBER Xn0)
% 54.34/54.54 Found (x7 x60) as proof of (cNUMBER Xn0)
% 54.34/54.54 Found (x7 x60) as proof of (cNUMBER Xn0)
% 54.34/54.54 Found x70:=(x7 x61):(cNUMBER Xn0)
% 54.34/54.54 Instantiate: Xn0:=Xn:fofType
% 54.34/54.54 Found (x7 x61) as proof of (cNUMBER Xn)
% 54.34/54.54 Found (x7 x61) as proof of (cNUMBER Xn)
% 54.34/54.54 Found x70:=(x7 x61):(cNUMBER Xn0)
% 54.34/54.54 Found (x7 x61) as proof of (cNUMBER Xn)
% 54.34/54.54 Found (x7 x61) as proof of (cNUMBER Xn)
% 54.34/54.54 Found (x7 x61) as proof of (cNUMBER Xn)
% 54.34/54.54 Found x8:(cODD (cS c0))
% 54.34/54.54 Instantiate: Xn0:=(cS c0):fofType
% 54.34/54.54 Found (fun (x8:(cODD (cS c0)))=> x8) as proof of (cODD Xn0)
% 54.34/54.54 Found (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> x8) as proof of ((cODD (cS c0))->(cODD Xn0))
% 54.34/54.54 Found (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> x8) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->(cODD Xn0)))
% 54.34/54.54 Found (and_rect40 (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> x8)) as proof of (cODD Xn0)
% 54.34/54.54 Found ((and_rect4 (cODD Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> x8)) as proof of (cODD Xn0)
% 54.34/54.54 Found (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x7) x6)) (cODD Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> x8)) as proof of (cODD Xn0)
% 54.34/54.54 Found (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x7) x6)) (cODD Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> x8)) as proof of (cODD Xn0)
% 54.34/54.54 Found (or_intror00 (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x7) x6)) (cODD Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> x8))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 54.59/54.77 Found ((or_intror0 (cODD Xn0)) (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x6)) (cODD Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> x8))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 54.59/54.77 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x6)) (cODD Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> x8))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 54.59/54.77 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x6)) (cODD Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> x8))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 54.59/54.77 Found x50:=(x5 x40):(cNUMBER Xn0)
% 54.59/54.77 Found (x5 x40) as proof of (cNUMBER Xn0)
% 54.59/54.77 Found (x5 x40) as proof of (cNUMBER Xn0)
% 54.59/54.77 Found x50:=(x5 x41):(cNUMBER Xn0)
% 54.59/54.77 Instantiate: Xn0:=Xn:fofType
% 54.59/54.77 Found (x5 x41) as proof of (cNUMBER Xn)
% 54.59/54.77 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x41)) as proof of (cNUMBER Xn)
% 54.59/54.77 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x41)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 54.59/54.77 Found or_introl00:=(or_introl0 (cEVEN Xn0)):((cODD (cS c0))->((or (cODD (cS c0))) (cEVEN Xn0)))
% 54.59/54.77 Found (or_introl0 (cEVEN Xn0)) as proof of ((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0)))
% 54.59/54.77 Found ((or_introl (cODD (cS c0))) (cEVEN Xn0)) as proof of ((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0)))
% 54.59/54.77 Found ((or_introl (cODD (cS c0))) (cEVEN Xn0)) as proof of ((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0)))
% 54.59/54.77 Found (fun (x7:((and (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)))
% 54.59/54.77 Found (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0))))
% 54.59/54.77 Found (and_rect40 (fun (x7:((and (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))
% 54.59/54.77 Found ((and_rect4 ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x7:((and (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))
% 54.59/54.77 Found (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x7) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x7:((and (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))
% 54.59/54.77 Found (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x7) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x7:((and (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))
% 55.36/55.55 Found (or_comm_i00 (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x7) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x7:((and (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))
% 55.36/55.55 Found ((or_comm_i0 (cEVEN Xn0)) (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x7:((and (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))
% 55.36/55.55 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x7:((and (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))
% 55.36/55.55 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x7:((and (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))
% 55.36/55.55 Found x70:=(x7 x60):(cNUMBER Xn0)
% 55.36/55.55 Found (x7 x60) as proof of (cNUMBER Xn)
% 55.36/55.55 Found (x7 x60) as proof of (cNUMBER Xn)
% 55.36/55.55 Found (x7 x60) as proof of (cNUMBER Xn)
% 55.36/55.55 Found x30:=(x3 x20):(cNUMBER Xn0)
% 55.36/55.55 Instantiate: Xn0:=Xn:fofType
% 55.36/55.55 Found (x3 x20) as proof of (cNUMBER Xn)
% 55.36/55.55 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 55.36/55.55 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))
% 55.36/55.55 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)))
% 55.36/55.55 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)
% 55.36/55.55 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)
% 55.36/55.55 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)
% 55.36/55.55 Found x50:(cNUMBER Xn00)
% 56.18/56.41 Found x50 as proof of (cNUMBER Xn00)
% 56.18/56.41 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 56.18/56.41 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 56.18/56.41 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 56.18/56.41 Found x40:=(x4 x50):((or (cEVEN Xn0)) (cODD Xn0))
% 56.18/56.41 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 56.18/56.41 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 56.18/56.41 Found x50:=(x5 x40):(cNUMBER Xn0)
% 56.18/56.41 Found (x5 x40) as proof of (cNUMBER Xn)
% 56.18/56.41 Found (x5 x40) as proof of (cNUMBER Xn)
% 56.18/56.41 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 56.18/56.41 Found (fun (x11:(cEVEN c0)) (x12:(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))
% 56.18/56.41 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 56.18/56.41 Found x90:=(x9 x80):(cNUMBER Xn0)
% 56.18/56.41 Instantiate: Xn0:=Xn:fofType
% 56.18/56.41 Found (x9 x80) as proof of (cNUMBER Xn)
% 56.18/56.41 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x9 x80)) as proof of (cNUMBER Xn)
% 56.18/56.41 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x9 x80)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 56.18/56.41 Found x50:=(x5 x40):(cNUMBER Xn0)
% 56.18/56.41 Found (x5 x40) as proof of (cNUMBER Xn0)
% 56.18/56.41 Found (x5 x40) as proof of (cNUMBER Xn0)
% 56.18/56.41 Found x50:=(x5 x41):(cNUMBER Xn0)
% 56.18/56.41 Instantiate: Xn0:=Xn:fofType
% 56.18/56.41 Found (x5 x41) as proof of (cNUMBER Xn)
% 56.18/56.41 Found (x5 x41) as proof of (cNUMBER Xn)
% 56.18/56.41 Found x50:=(x5 x40):(cNUMBER Xn0)
% 56.18/56.41 Found (x5 x40) as proof of (cNUMBER Xn)
% 56.18/56.41 Found (x5 x40) as proof of (cNUMBER Xn)
% 56.18/56.41 Found (x5 x40) as proof of (cNUMBER Xn)
% 56.18/56.41 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 56.18/56.41 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 56.18/56.41 Found (x3 x20) as proof of (cNUMBER Xn)
% 56.18/56.41 Found (x3 x20) as proof of (cNUMBER Xn)
% 56.18/56.41 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 56.18/56.41 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))
% 56.18/56.41 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 56.18/56.41 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 56.18/56.41 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 56.18/56.41 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 56.18/56.41 Found (fun (x8:((and (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)))
% 56.18/56.41 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0))))
% 56.18/56.41 Found (and_rect40 (fun (x8:((and (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))
% 56.18/56.41 Found ((and_rect4 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (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))
% 56.18/56.41 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (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))
% 56.18/56.41 Found (fun (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (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))
% 56.18/56.41 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (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)))
% 56.18/56.41 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of (((and ((and (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))))
% 56.18/56.41 Found (and_rect30 (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (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))
% 56.18/56.41 Found ((and_rect3 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (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))
% 56.18/56.41 Found (((fun (P:Type) (x6:(((and ((and (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 (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (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))
% 56.18/56.42 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (((fun (P:Type) (x6:(((and ((and (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 (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (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))
% 56.18/56.42 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (((fun (P:Type) (x6:(((and ((and (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 (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))))) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 56.18/56.42 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (((fun (P:Type) (x6:(((and ((and (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 (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))))) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->((or (cEVEN Xn0)) (cODD Xn0))))
% 56.18/56.42 Found (and_rect20 (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (((fun (P:Type) (x6:(((and ((and (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 (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (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))
% 56.18/56.42 Found ((and_rect2 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (((fun (P:Type) (x6:(((and ((and (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 (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (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))
% 56.18/56.43 Found (((fun (P:Type) (x4:(((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->P)))=> (((((and_rect ((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))) P) x4) x0)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (((fun (P:Type) (x6:(((and ((and (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 (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (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))
% 56.18/56.43 Found (((fun (P:Type) (x4:(((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->P)))=> (((((and_rect ((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))) P) x4) x0)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (((fun (P:Type) (x6:(((and ((and (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 (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (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))
% 57.11/57.34 Found x50:=(x5 x40):(cNUMBER Xn0)
% 57.11/57.34 Found (x5 x40) as proof of (cNUMBER Xn)
% 57.11/57.34 Found (x5 x40) as proof of (cNUMBER Xn)
% 57.11/57.34 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 57.11/57.34 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))
% 57.11/57.34 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 57.11/57.34 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 57.11/57.34 Found (x5 x40) as proof of (cNUMBER Xn)
% 57.11/57.34 Found (x5 x40) as proof of (cNUMBER Xn)
% 57.11/57.34 Found (x5 x40) as proof of (cNUMBER Xn)
% 57.11/57.34 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 57.11/57.34 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 57.11/57.34 Found (x3 x20) as proof of (cNUMBER Xn)
% 57.11/57.34 Found (x3 x20) as proof of (cNUMBER Xn)
% 57.11/57.34 Found (x3 x20) as proof of (cNUMBER Xn)
% 57.11/57.34 Found x30:=(x3 x20):(cNUMBER Xn0)
% 57.11/57.34 Found (x3 x20) as proof of (cNUMBER Xn0)
% 57.11/57.34 Found (x3 x20) as proof of (cNUMBER Xn0)
% 57.11/57.34 Found x30:=(x3 x21):(cNUMBER Xn0)
% 57.11/57.34 Instantiate: Xn0:=Xn:fofType
% 57.11/57.34 Found (x3 x21) as proof of (cNUMBER Xn)
% 57.11/57.34 Found (x3 x21) as proof of (cNUMBER Xn)
% 57.11/57.34 Found x30:=(x3 x20):(cNUMBER Xn0)
% 57.11/57.34 Found (x3 x20) as proof of (cNUMBER Xn)
% 57.11/57.34 Found (x3 x20) as proof of (cNUMBER Xn)
% 57.11/57.34 Found (x3 x20) as proof of (cNUMBER Xn)
% 57.11/57.34 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 57.11/57.34 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 57.11/57.34 Found (x3 x20) as proof of (cNUMBER Xn)
% 57.11/57.34 Found (x3 x20) as proof of (cNUMBER Xn)
% 57.11/57.34 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 57.11/57.34 Found (fun (x11:(cEVEN c0)) (x12:(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))
% 57.11/57.34 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 57.11/57.34 Found x9:(cODD (cS c0))
% 57.11/57.34 Instantiate: Xn0:=(cS c0):fofType
% 57.11/57.34 Found x9 as proof of (cODD Xn0)
% 57.11/57.34 Found (or_intror00 x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 57.11/57.34 Found ((or_intror0 (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 57.11/57.34 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 57.11/57.34 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 57.11/57.34 Found (x5 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9)) as proof of (cNUMBER Xn0)
% 57.11/57.34 Found (x5 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9)) as proof of (cNUMBER Xn0)
% 57.11/57.34 Found x70:=(x7 x60):(cNUMBER Xn0)
% 57.11/57.34 Found (x7 x60) as proof of (cNUMBER Xn0)
% 57.11/57.34 Found (x7 x60) as proof of (cNUMBER Xn0)
% 57.11/57.34 Found x70:=(x7 x61):(cNUMBER Xn0)
% 57.11/57.34 Instantiate: Xn0:=Xn:fofType
% 57.11/57.34 Found (x7 x61) as proof of (cNUMBER Xn)
% 57.11/57.34 Found (x7 x61) as proof of (cNUMBER Xn)
% 57.11/57.34 Found x70:=(x7 x61):(cNUMBER Xn0)
% 57.11/57.34 Found (x7 x61) as proof of (cNUMBER Xn)
% 57.11/57.34 Found (x7 x61) as proof of (cNUMBER Xn)
% 57.11/57.34 Found (x7 x61) as proof of (cNUMBER Xn)
% 57.11/57.34 Found x30:=(x3 x20):(cNUMBER Xn0)
% 57.11/57.34 Instantiate: Xn0:=Xn:fofType
% 57.11/57.34 Found (x3 x20) as proof of (cNUMBER Xn)
% 57.11/57.34 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 57.11/57.34 Found (fun (x11:(cEVEN c0)) (x12:(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))
% 57.11/57.34 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 58.59/58.79 Found (and_rect50 (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 58.59/58.79 Found ((and_rect5 (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 58.59/58.79 Found (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 58.59/58.79 Found (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 58.59/58.79 Found x61:((or (cEVEN Xn0)) (cODD Xn0))
% 58.59/58.79 Found x61 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 58.59/58.79 Found (x7 x61) as proof of (cNUMBER Xn)
% 58.59/58.79 Found (x7 x61) as proof of (cNUMBER Xn)
% 58.59/58.79 Found (x7 x61) as proof of (cNUMBER Xn)
% 58.59/58.79 Found x9:(cODD (cS c0))
% 58.59/58.79 Instantiate: Xn0:=(cS c0):fofType
% 58.59/58.79 Found x9 as proof of (cODD Xn0)
% 58.59/58.79 Found (or_intror00 x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 58.59/58.79 Found ((or_intror0 (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 58.59/58.79 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 58.59/58.79 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 58.59/58.79 Found x70:(cNUMBER Xn00)
% 58.59/58.79 Instantiate: Xn00:=Xn:fofType
% 58.59/58.79 Found x70 as proof of (cNUMBER Xn)
% 58.59/58.79 Found x50:(cNUMBER Xn0)
% 58.59/58.79 Instantiate: Xn0:=Xn:fofType
% 58.59/58.79 Found x50 as proof of (cNUMBER Xn)
% 58.59/58.79 Found x70:=(x7 x60):(cNUMBER Xn0)
% 58.59/58.79 Found (x7 x60) as proof of (cNUMBER Xn)
% 58.59/58.79 Found (x7 x60) as proof of (cNUMBER Xn)
% 58.59/58.79 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)) as proof of (cNUMBER Xn)
% 58.59/58.79 Found (fun (x12:(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))
% 58.59/58.79 Found x30:=(x3 x20):(cNUMBER Xn0)
% 58.59/58.79 Instantiate: Xn0:=Xn:fofType
% 58.59/58.79 Found (x3 x20) as proof of (cNUMBER Xn)
% 58.59/58.79 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 58.59/58.79 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))
% 58.59/58.79 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)))
% 58.59/58.79 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)
% 58.59/58.79 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)
% 58.59/58.79 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)
% 58.59/58.79 Found x30:=(x3 x21):(cNUMBER Xn0)
% 58.59/58.79 Found (x3 x21) as proof of (cNUMBER Xn0)
% 58.59/58.79 Found (x3 x21) as proof of (cNUMBER Xn0)
% 58.59/58.79 Found x30:=(x3 x22):(cNUMBER Xn0)
% 58.59/58.79 Instantiate: Xn0:=Xn:fofType
% 58.59/58.79 Found (x3 x22) as proof of (cNUMBER Xn)
% 58.59/58.79 Found (x3 x22) as proof of (cNUMBER Xn)
% 59.27/59.48 Found x30:=(x3 x22):(cNUMBER Xn0)
% 59.27/59.48 Found (x3 x22) as proof of (cNUMBER Xn)
% 59.27/59.48 Found (x3 x22) as proof of (cNUMBER Xn)
% 59.27/59.48 Found (x3 x22) as proof of (cNUMBER Xn)
% 59.27/59.48 Found or_comm_i100:=(or_comm_i10 x20):((or (cODD Xn0)) (cEVEN Xn0))
% 59.27/59.48 Found (or_comm_i10 x20) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 59.27/59.48 Found ((or_comm_i1 (cODD Xn0)) x20) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 59.27/59.48 Found (((or_comm_i (cEVEN Xn0)) (cODD Xn0)) x20) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 59.27/59.48 Found (((or_comm_i (cEVEN Xn0)) (cODD Xn0)) x20) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 59.27/59.48 Found x90:=(x9 x80):(cNUMBER Xn0)
% 59.27/59.48 Instantiate: Xn0:=Xn:fofType
% 59.27/59.48 Found (x9 x80) as proof of (cNUMBER Xn)
% 59.27/59.48 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x9 x80)) as proof of (cNUMBER Xn)
% 59.27/59.48 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x9 x80)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 59.27/59.48 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x9 x80)) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 59.27/59.48 Found x120:=(x12 x110):(cNUMBER Xn0)
% 59.27/59.48 Found (x12 x110) as proof of (cNUMBER Xn)
% 59.27/59.48 Found (x12 x110) as proof of (cNUMBER Xn)
% 59.27/59.48 Found (x12 x110) as proof of (cNUMBER Xn)
% 59.27/59.48 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 59.27/59.48 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 59.27/59.48 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 59.27/59.48 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 59.27/59.48 Found (fun (x8:((and (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)))
% 59.27/59.48 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0))))
% 59.27/59.48 Found (and_rect40 (fun (x8:((and (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))
% 59.27/59.48 Found ((and_rect4 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (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))
% 59.27/59.48 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (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))
% 59.27/59.48 Found (fun (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (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))
% 59.27/59.48 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (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)))
% 59.31/59.49 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of (((and ((and (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))))
% 59.31/59.49 Found (and_rect30 (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (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))
% 59.31/59.49 Found ((and_rect3 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (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))
% 59.31/59.49 Found (((fun (P:Type) (x6:(((and ((and (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 (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) x2)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (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))
% 59.31/59.49 Found (((fun (P:Type) (x6:(((and ((and (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 (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) x2)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (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))
% 59.31/59.50 Found (x5 (((fun (P:Type) (x6:(((and ((and (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 (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) x2)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))))) as proof of (cNUMBER Xn0)
% 59.31/59.50 Found (x5 (((fun (P:Type) (x6:(((and ((and (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 (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) x2)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))))) as proof of (cNUMBER Xn0)
% 59.31/59.50 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 59.31/59.50 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 59.31/59.50 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 59.31/59.50 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 59.31/59.50 Found (fun (x8:((and (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)))
% 59.31/59.50 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0))))
% 59.31/59.50 Found (and_rect40 (fun (x8:((and (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))
% 59.31/59.50 Found ((and_rect4 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (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))
% 59.31/59.50 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (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))
% 59.31/59.50 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (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))
% 59.31/59.50 Found (x5 (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of (cNUMBER Xn0)
% 59.31/59.50 Found (fun (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x5 (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))))) as proof of (cNUMBER Xn0)
% 59.31/59.50 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x5 (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (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))
% 59.31/59.50 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x5 (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))))) as proof of (((and ((and (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)))
% 59.31/59.50 Found (and_rect30 (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x5 (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))))) as proof of (cNUMBER Xn0)
% 59.31/59.50 Found ((and_rect3 (cNUMBER Xn0)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x5 (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))))) as proof of (cNUMBER Xn0)
% 59.38/59.62 Found (((fun (P:Type) (x6:(((and ((and (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 (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) x2)) (cNUMBER Xn0)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x5 (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))))) as proof of (cNUMBER Xn0)
% 59.38/59.62 Found (((fun (P:Type) (x6:(((and ((and (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 (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) x2)) (cNUMBER Xn0)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x5 (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))))) as proof of (cNUMBER Xn0)
% 59.38/59.62 Found x50:=(x5 x40):(cNUMBER Xn0)
% 59.38/59.62 Found (x5 x40) as proof of (cNUMBER Xn0)
% 59.38/59.62 Found (x5 x40) as proof of (cNUMBER Xn0)
% 59.38/59.62 Found x50:=(x5 x41):(cNUMBER Xn0)
% 59.38/59.62 Instantiate: Xn0:=Xn:fofType
% 59.38/59.62 Found (x5 x41) as proof of (cNUMBER Xn)
% 59.38/59.62 Found (x5 x41) as proof of (cNUMBER Xn)
% 59.38/59.62 Found x50:=(x5 x40):(cNUMBER Xn0)
% 59.38/59.62 Found (x5 x40) as proof of (cNUMBER Xn)
% 59.38/59.62 Found (x5 x40) as proof of (cNUMBER Xn)
% 59.38/59.62 Found (x5 x40) as proof of (cNUMBER Xn)
% 59.38/59.62 Found x22:((or (cEVEN Xn0)) (cODD Xn0))
% 59.38/59.62 Found x22 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 59.38/59.62 Found (x3 x22) as proof of (cNUMBER Xn)
% 59.38/59.62 Found (x3 x22) as proof of (cNUMBER Xn)
% 59.38/59.62 Found (x3 x22) as proof of (cNUMBER Xn)
% 59.38/59.62 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 59.38/59.62 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 59.38/59.62 Found (x5 x40) as proof of (cNUMBER Xn)
% 59.38/59.62 Found (x5 x40) as proof of (cNUMBER Xn)
% 59.38/59.62 Found (x5 x40) as proof of (cNUMBER Xn)
% 59.38/59.62 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 59.38/59.62 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 59.38/59.62 Found (x5 x40) as proof of (cNUMBER Xn)
% 59.38/59.62 Found (x5 x40) as proof of (cNUMBER Xn)
% 59.38/59.62 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 59.38/59.62 Found (fun (x12:(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))
% 59.38/59.62 Found x50:=(x5 x40):(cNUMBER Xn0)
% 59.38/59.62 Found (x5 x40) as proof of (cNUMBER Xn)
% 60.56/60.82 Found (x5 x40) as proof of (cNUMBER Xn)
% 60.56/60.82 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 60.56/60.82 Found (fun (x6:((and ((and (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))
% 60.56/60.82 Found (fun (x6:((and ((and (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 (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)))
% 60.56/60.82 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 60.56/60.82 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 60.56/60.82 Found (x3 x20) as proof of (cNUMBER Xn)
% 60.56/60.82 Found (x3 x20) as proof of (cNUMBER Xn)
% 60.56/60.82 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 60.56/60.82 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))
% 60.56/60.82 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 60.56/60.82 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 60.56/60.82 Found (x3 x20) as proof of (cNUMBER Xn)
% 60.56/60.82 Found (x3 x20) as proof of (cNUMBER Xn)
% 60.56/60.82 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 60.56/60.82 Found (fun (x6:((and ((and (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))
% 60.56/60.82 Found (fun (x6:((and ((and (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 (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)))
% 60.56/60.82 Found x50:=(x5 x40):(cNUMBER Xn0)
% 60.56/60.82 Found (x5 x40) as proof of (cNUMBER Xn)
% 60.56/60.82 Found (x5 x40) as proof of (cNUMBER Xn)
% 60.56/60.82 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 60.56/60.82 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))
% 60.56/60.82 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 60.56/60.82 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 60.56/60.82 Found (x3 x20) as proof of (cNUMBER Xn)
% 60.56/60.82 Found (x3 x20) as proof of (cNUMBER Xn)
% 60.56/60.82 Found (x3 x20) as proof of (cNUMBER Xn)
% 60.56/60.82 Found x70:(cNUMBER Xn00)
% 60.56/60.82 Instantiate: Xn00:=Xn:fofType
% 60.56/60.82 Found x70 as proof of (cNUMBER Xn)
% 60.56/60.82 Found x30:(cNUMBER Xn0)
% 60.56/60.82 Instantiate: Xn0:=Xn:fofType
% 60.56/60.82 Found x30 as proof of (cNUMBER Xn)
% 60.56/60.82 Found x61:((or (cEVEN Xn0)) (cODD Xn0))
% 60.56/60.82 Found x61 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 60.56/60.82 Found (x7 x61) as proof of (cNUMBER Xn)
% 60.56/60.82 Found (x7 x61) as proof of (cNUMBER Xn)
% 60.56/60.82 Found (x7 x61) as proof of (cNUMBER Xn)
% 60.56/60.82 Found x30:=(x3 x20):(cNUMBER Xn0)
% 60.56/60.82 Instantiate: Xn0:=Xn:fofType
% 60.56/60.82 Found (x3 x20) as proof of (cNUMBER Xn)
% 60.56/60.82 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 60.56/60.82 Found (fun (x11:(cEVEN c0)) (x12:(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))
% 60.56/60.82 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 60.56/60.82 Found (and_rect50 (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 60.56/60.82 Found ((and_rect5 (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 60.81/61.03 Found (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 60.81/61.03 Found (fun (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)))) as proof of (cNUMBER Xn)
% 60.81/61.03 Found (fun (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)))) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 60.81/61.03 Found x70:=(x7 x61):(cNUMBER Xn0)
% 60.81/61.03 Instantiate: Xn0:=Xn:fofType
% 60.81/61.03 Found (x7 x61) as proof of (cNUMBER Xn)
% 60.81/61.03 Found (fun (x7:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x7 x61)) as proof of (cNUMBER Xn)
% 60.81/61.03 Found (fun (x7:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x7 x61)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 60.81/61.03 Found x8:(cODD (cS c0))
% 60.81/61.03 Instantiate: Xn0:=(cS c0):fofType
% 60.81/61.03 Found (fun (x8:(cODD (cS c0)))=> x8) as proof of (cODD Xn0)
% 60.81/61.03 Found (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> x8) as proof of ((cODD (cS c0))->(cODD Xn0))
% 60.81/61.03 Found (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> x8) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->(cODD Xn0)))
% 60.81/61.03 Found (and_rect40 (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> x8)) as proof of (cODD Xn0)
% 60.81/61.03 Found ((and_rect4 (cODD Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> x8)) as proof of (cODD Xn0)
% 60.81/61.03 Found (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x7) x6)) (cODD Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> x8)) as proof of (cODD Xn0)
% 60.81/61.03 Found (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x7) x6)) (cODD Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> x8)) as proof of (cODD Xn0)
% 60.81/61.03 Found (or_intror00 (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x7) x6)) (cODD Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> x8))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 60.81/61.03 Found ((or_intror0 (cODD Xn0)) (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x6)) (cODD Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> x8))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 61.03/61.25 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x6)) (cODD Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> x8))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 61.03/61.25 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x6)) (cODD Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> x8))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 61.03/61.25 Found x50:(cNUMBER Xn0)
% 61.03/61.25 Instantiate: Xn0:=Xn:fofType
% 61.03/61.25 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x50) as proof of (cNUMBER Xn)
% 61.03/61.25 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x50) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 61.03/61.25 Found or_introl00:=(or_introl0 (cEVEN Xn0)):((cODD (cS c0))->((or (cODD (cS c0))) (cEVEN Xn0)))
% 61.03/61.25 Found (or_introl0 (cEVEN Xn0)) as proof of ((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0)))
% 61.03/61.25 Found ((or_introl (cODD (cS c0))) (cEVEN Xn0)) as proof of ((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0)))
% 61.03/61.25 Found ((or_introl (cODD (cS c0))) (cEVEN Xn0)) as proof of ((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0)))
% 61.03/61.25 Found (fun (x7:((and (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)))
% 61.03/61.25 Found (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0))))
% 61.03/61.25 Found (and_rect40 (fun (x7:((and (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))
% 61.03/61.25 Found ((and_rect4 ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x7:((and (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))
% 61.03/61.25 Found (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x7) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x7:((and (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))
% 61.03/61.25 Found (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x7) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x7:((and (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))
% 61.03/61.25 Found (or_comm_i00 (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x7) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x7:((and (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))
% 61.03/61.25 Found ((or_comm_i0 (cEVEN Xn0)) (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x7:((and (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))
% 61.12/61.30 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x7:((and (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))
% 61.12/61.30 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x7:((and (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))
% 61.12/61.30 Found x7:(cODD (cS c0))
% 61.12/61.30 Instantiate: Xn0:=(cS c0):fofType
% 61.12/61.30 Found x7 as proof of (cODD Xn0)
% 61.12/61.30 Found (or_intror00 x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 61.12/61.30 Found ((or_intror0 (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 61.12/61.30 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 61.12/61.30 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 61.12/61.30 Found (x9 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7)) as proof of (cNUMBER Xn0)
% 61.12/61.30 Found (x9 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7)) as proof of (cNUMBER Xn0)
% 61.12/61.30 Found x70:=(x7 (cS c0)):((cODD (cS c0))->(cODD (cS (cS (cS c0)))))
% 61.12/61.30 Found (x7 (cS c0)) as proof of ((cODD (cS c0))->(cODD Xn0))
% 61.12/61.30 Found (x7 (cS c0)) as proof of ((cODD (cS c0))->(cODD Xn0))
% 61.12/61.30 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x7 (cS c0))) as proof of ((cODD (cS c0))->(cODD Xn0))
% 61.12/61.30 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x7 (cS c0))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->(cODD Xn0)))
% 61.12/61.30 Found (and_rect40 (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x7 (cS c0)))) as proof of (cODD Xn0)
% 61.12/61.30 Found ((and_rect4 (cODD Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x7 (cS c0)))) as proof of (cODD Xn0)
% 61.12/61.30 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cODD Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x7 (cS c0)))) as proof of (cODD Xn0)
% 61.12/61.30 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cODD Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x7 (cS c0)))) as proof of (cODD Xn0)
% 61.12/61.30 Found (or_intror00 (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cODD Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x7 (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 61.15/61.37 Found ((or_intror0 (cODD Xn0)) (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) (cODD Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x7 (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 61.15/61.37 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) (cODD Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x7 (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 61.15/61.37 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) (cODD Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x7 (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 61.15/61.37 Found x90:=(x9 x80):(cNUMBER Xn0)
% 61.15/61.37 Found (x9 x80) as proof of (cNUMBER Xn)
% 61.15/61.37 Found (x9 x80) as proof of (cNUMBER Xn)
% 61.15/61.37 Found (x9 x80) as proof of (cNUMBER Xn)
% 61.15/61.37 Found or_introl00:=(or_introl0 (cEVEN Xn0)):((cODD (cS c0))->((or (cODD (cS c0))) (cEVEN Xn0)))
% 61.15/61.37 Found (or_introl0 (cEVEN Xn0)) as proof of ((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0)))
% 61.15/61.37 Found ((or_introl (cODD (cS c0))) (cEVEN Xn0)) as proof of ((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0)))
% 61.15/61.37 Found ((or_introl (cODD (cS c0))) (cEVEN Xn0)) as proof of ((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0)))
% 61.15/61.37 Found (fun (x8:((and (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)))
% 61.15/61.37 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0))))
% 61.15/61.37 Found (and_rect40 (fun (x8:((and (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))
% 61.15/61.37 Found ((and_rect4 ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x8:((and (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))
% 61.15/61.37 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x8:((and (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))
% 61.15/61.37 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x8:((and (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))
% 61.15/61.37 Found (or_comm_i00 (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x8:((and (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))
% 61.45/61.72 Found ((or_comm_i0 (cEVEN Xn0)) (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x8:((and (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))
% 61.45/61.72 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x8:((and (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))
% 61.45/61.72 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x8:((and (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))
% 61.45/61.72 Found x30:=(x3 x20):(cNUMBER Xn0)
% 61.45/61.72 Instantiate: Xn0:=Xn:fofType
% 61.45/61.72 Found (x3 x20) as proof of (cNUMBER Xn)
% 61.45/61.72 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 61.45/61.72 Found (fun (x11:(cEVEN c0)) (x12:(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))
% 61.45/61.72 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 61.45/61.72 Found (and_rect50 (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 61.45/61.72 Found ((and_rect5 (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 61.45/61.72 Found (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 61.45/61.72 Found (fun (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)))) as proof of (cNUMBER Xn)
% 61.45/61.72 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)))) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 61.45/61.72 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)))) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 61.93/62.11 Found x30:=(x3 x21):(cNUMBER Xn0)
% 61.93/62.11 Found (x3 x21) as proof of (cNUMBER Xn0)
% 61.93/62.11 Found (x3 x21) as proof of (cNUMBER Xn0)
% 61.93/62.11 Found x30:=(x3 x22):(cNUMBER Xn0)
% 61.93/62.11 Instantiate: Xn0:=Xn:fofType
% 61.93/62.11 Found (x3 x22) as proof of (cNUMBER Xn)
% 61.93/62.11 Found (x3 x22) as proof of (cNUMBER Xn)
% 61.93/62.11 Found x30:=(x3 x22):(cNUMBER Xn0)
% 61.93/62.11 Found (x3 x22) as proof of (cNUMBER Xn)
% 61.93/62.11 Found (x3 x22) as proof of (cNUMBER Xn)
% 61.93/62.11 Found (x3 x22) as proof of (cNUMBER Xn)
% 61.93/62.11 Found x70:=(x7 x60):(cNUMBER Xn0)
% 61.93/62.11 Found (x7 x60) as proof of (cNUMBER Xn)
% 61.93/62.11 Found (x7 x60) as proof of (cNUMBER Xn)
% 61.93/62.11 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)) as proof of (cNUMBER Xn)
% 61.93/62.11 Found (fun (x11:(cEVEN c0)) (x12:(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))
% 61.93/62.11 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 61.93/62.11 Found x30:(cNUMBER Xn0)
% 61.93/62.11 Instantiate: Xn0:=Xn:fofType
% 61.93/62.11 Found (fun (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of (cNUMBER Xn)
% 61.93/62.11 Found (fun (x7:(cEVEN Xn0)) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 61.93/62.11 Found (fun (x7:(cEVEN Xn0)) (x8:(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)))
% 61.93/62.11 Found x30:(cNUMBER Xn0)
% 61.93/62.11 Instantiate: Xn0:=Xn:fofType
% 61.93/62.11 Found (fun (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of (cNUMBER Xn)
% 61.93/62.11 Found (fun (x7:(cODD Xn0)) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 61.93/62.11 Found (fun (x7:(cODD Xn0)) (x8:(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)))
% 61.93/62.11 Found ((or_ind00 (fun (x7:(cEVEN Xn0)) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30)) (fun (x7:(cODD Xn0)) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 61.93/62.11 Found (((or_ind0 ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))) (fun (x7:(cEVEN Xn0)) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30)) (fun (x7:(cODD Xn0)) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 61.93/62.11 Found ((((fun (P:Prop) (x7:((cEVEN Xn0)->P)) (x8:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x7) x8) x20)) ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->(cNUMBER Xn))) (fun (x7:(cEVEN Xn0)) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x30)) (fun (x7:(cODD Xn0)) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x30)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 61.93/62.11 Found ((((fun (P:Prop) (x7:((cEVEN Xn0)->P)) (x8:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x7) x8) (x2 x30))) ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->(cNUMBER Xn))) (fun (x7:(cEVEN Xn0)) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x30)) (fun (x7:(cODD Xn0)) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x30)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 62.97/63.22 Found ((((fun (P:Prop) (x7:((cEVEN Xn0)->P)) (x8:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x7) x8) (x2 x30))) ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->(cNUMBER Xn))) (fun (x7:(cEVEN Xn0)) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x30)) (fun (x7:(cODD Xn0)) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x30)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 62.97/63.22 Found x30:(cNUMBER Xn0)
% 62.97/63.22 Instantiate: Xn0:=Xn:fofType
% 62.97/63.22 Found x30 as proof of (cNUMBER Xn)
% 62.97/63.22 Found x50:(cNUMBER Xn00)
% 62.97/63.22 Instantiate: Xn00:=Xn:fofType
% 62.97/63.22 Found x50 as proof of (cNUMBER Xn)
% 62.97/63.22 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 62.97/63.22 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 62.97/63.22 Found (x5 x40) as proof of (cNUMBER Xn)
% 62.97/63.22 Found (x5 x40) as proof of (cNUMBER Xn)
% 62.97/63.22 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 62.97/63.22 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))
% 62.97/63.22 Found x120:=(x12 x110):(cNUMBER Xn0)
% 62.97/63.22 Found (x12 x110) as proof of (cNUMBER Xn)
% 62.97/63.22 Found (x12 x110) as proof of (cNUMBER Xn)
% 62.97/63.22 Found (fun (x12:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x12 x110)) as proof of (cNUMBER Xn)
% 62.97/63.22 Found (fun (x12:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x12 x110)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 62.97/63.22 Found x60:((or (cEVEN Xn0)) (cODD Xn0))
% 62.97/63.22 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 62.97/63.22 Found (x7 x60) as proof of (cNUMBER Xn)
% 62.97/63.22 Found (x7 x60) as proof of (cNUMBER Xn)
% 62.97/63.22 Found (x7 x60) as proof of (cNUMBER Xn)
% 62.97/63.22 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 62.97/63.22 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 62.97/63.22 Found (x5 x40) as proof of (cNUMBER Xn)
% 62.97/63.22 Found (x5 x40) as proof of (cNUMBER Xn)
% 62.97/63.22 Found (x5 x40) as proof of (cNUMBER Xn)
% 62.97/63.22 Found x22:((or (cEVEN Xn0)) (cODD Xn0))
% 62.97/63.22 Found x22 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 62.97/63.22 Found (x3 x22) as proof of (cNUMBER Xn)
% 62.97/63.22 Found (x3 x22) as proof of (cNUMBER Xn)
% 62.97/63.22 Found (x3 x22) as proof of (cNUMBER Xn)
% 62.97/63.22 Found x50:=(x5 x40):(cNUMBER Xn0)
% 62.97/63.22 Found (x5 x40) as proof of (cNUMBER Xn0)
% 62.97/63.22 Found (x5 x40) as proof of (cNUMBER Xn0)
% 62.97/63.22 Found x50:=(x5 x41):(cNUMBER Xn0)
% 62.97/63.22 Instantiate: Xn0:=Xn:fofType
% 62.97/63.22 Found (x5 x41) as proof of (cNUMBER Xn)
% 62.97/63.22 Found (x5 x41) as proof of (cNUMBER Xn)
% 62.97/63.22 Found x50:=(x5 x40):(cNUMBER Xn0)
% 62.97/63.22 Found (x5 x40) as proof of (cNUMBER Xn)
% 62.97/63.22 Found (x5 x40) as proof of (cNUMBER Xn)
% 62.97/63.22 Found (x5 x40) as proof of (cNUMBER Xn)
% 62.97/63.22 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 62.97/63.22 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 62.97/63.22 Found (x5 x40) as proof of (cNUMBER Xn)
% 62.97/63.22 Found (x5 x40) as proof of (cNUMBER Xn)
% 62.97/63.22 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 62.97/63.22 Found (fun (x11:(cEVEN c0)) (x12:(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))
% 62.97/63.22 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 62.97/63.22 Found x9:(cODD (cS c0))
% 62.97/63.22 Instantiate: Xn0:=(cS c0):fofType
% 62.97/63.22 Found x9 as proof of (cODD Xn0)
% 62.97/63.22 Found (or_intror00 x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 62.97/63.22 Found ((or_intror0 (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 62.97/63.22 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 62.97/63.22 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 62.97/63.22 Found x11:(cEVEN c0)
% 62.97/63.22 Instantiate: Xn0:=c0:fofType
% 62.97/63.22 Found x11 as proof of (cEVEN Xn0)
% 62.97/63.22 Found (or_introl00 x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 62.97/63.22 Found ((or_introl0 (cODD Xn0)) x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 62.97/63.22 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 62.97/63.22 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 65.32/65.57 Found x30:(cNUMBER Xn0)
% 65.32/65.57 Instantiate: Xn0:=Xn:fofType
% 65.32/65.57 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30) as proof of (cNUMBER Xn)
% 65.32/65.57 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 65.32/65.57 Found x9:(cODD (cS c0))
% 65.32/65.57 Instantiate: Xn0:=(cS c0):fofType
% 65.32/65.57 Found x9 as proof of (cODD Xn0)
% 65.32/65.57 Found (or_intror00 x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 65.32/65.57 Found ((or_intror0 (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 65.32/65.57 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 65.32/65.57 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 65.32/65.57 Found (x7 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9)) as proof of (cNUMBER Xn0)
% 65.32/65.57 Found (x7 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9)) as proof of (cNUMBER Xn0)
% 65.32/65.57 Found x50:=(x5 x40):(cNUMBER Xn0)
% 65.32/65.57 Instantiate: Xn0:=Xn:fofType
% 65.32/65.57 Found (x5 x40) as proof of (cNUMBER Xn)
% 65.32/65.57 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 65.32/65.57 Found (fun (x11:(cEVEN c0)) (x12:(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))
% 65.32/65.57 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 65.32/65.57 Found (and_rect50 (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 65.32/65.57 Found ((and_rect5 (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 65.32/65.57 Found (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 65.32/65.57 Found (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 65.32/65.57 Found x9:(cODD (cS c0))
% 65.32/65.57 Instantiate: Xn0:=(cS c0):fofType
% 65.32/65.57 Found x9 as proof of (cODD Xn0)
% 65.32/65.57 Found (or_intror00 x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 65.32/65.57 Found ((or_intror0 (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 65.32/65.57 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 65.32/65.57 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 65.32/65.57 Found x50:(cNUMBER Xn0)
% 65.32/65.57 Instantiate: Xn0:=Xn:fofType
% 65.32/65.57 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x50) as proof of (cNUMBER Xn)
% 65.32/65.57 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))
% 65.32/65.57 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)))
% 65.32/65.57 Found x90:=(x9 x80):(cNUMBER Xn0)
% 65.32/65.57 Found (x9 x80) as proof of (cNUMBER Xn)
% 65.32/65.57 Found (x9 x80) as proof of (cNUMBER Xn)
% 65.32/65.57 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x9 x80)) as proof of (cNUMBER Xn)
% 65.32/65.57 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x9 x80)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 65.32/65.57 Found x30:(cNUMBER Xn0)
% 65.32/65.57 Instantiate: Xn0:=Xn:fofType
% 65.32/65.57 Found (fun (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30) as proof of (cNUMBER Xn)
% 65.55/65.76 Found (fun (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 65.55/65.76 Found x50:(cNUMBER Xn00)
% 65.55/65.76 Instantiate: Xn00:=Xn:fofType
% 65.55/65.76 Found (fun (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x50) as proof of (cNUMBER Xn)
% 65.55/65.76 Found (fun (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x50) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 65.55/65.76 Found x30:(cNUMBER Xn0)
% 65.55/65.76 Instantiate: Xn0:=Xn:fofType
% 65.55/65.76 Found (fun (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of (cNUMBER Xn)
% 65.55/65.76 Found (fun (x7:(cEVEN Xn0)) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 65.55/65.76 Found (fun (x7:(cEVEN Xn0)) (x8:(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)))
% 65.55/65.76 Found x30:(cNUMBER Xn0)
% 65.55/65.76 Instantiate: Xn0:=Xn:fofType
% 65.55/65.76 Found (fun (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of (cNUMBER Xn)
% 65.55/65.76 Found (fun (x7:(cODD Xn0)) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 65.55/65.76 Found (fun (x7:(cODD Xn0)) (x8:(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)))
% 65.55/65.76 Found ((or_ind00 (fun (x7:(cEVEN Xn0)) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30)) (fun (x7:(cODD Xn0)) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 65.55/65.76 Found (((or_ind0 ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))) (fun (x7:(cEVEN Xn0)) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30)) (fun (x7:(cODD Xn0)) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 65.55/65.76 Found ((((fun (P:Prop) (x7:((cEVEN Xn0)->P)) (x8:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x7) x8) x20)) ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->(cNUMBER Xn))) (fun (x7:(cEVEN Xn0)) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x30)) (fun (x7:(cODD Xn0)) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x30)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 65.55/65.76 Found ((((fun (P:Prop) (x7:((cEVEN Xn0)->P)) (x8:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x7) x8) (x2 x30))) ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->(cNUMBER Xn))) (fun (x7:(cEVEN Xn0)) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x30)) (fun (x7:(cODD Xn0)) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x30)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 65.99/66.21 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))))=> ((((fun (P:Prop) (x7:((cEVEN Xn0)->P)) (x8:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x7) x8) (x2 x30))) ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->(cNUMBER Xn))) (fun (x7:(cEVEN Xn0)) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x30)) (fun (x7:(cODD Xn0)) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x30))) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 65.99/66.21 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))))=> ((((fun (P:Prop) (x7:((cEVEN Xn0)->P)) (x8:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x7) x8) (x2 x30))) ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->(cNUMBER Xn))) (fun (x7:(cEVEN Xn0)) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x30)) (fun (x7:(cODD Xn0)) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x30))) as proof of (((and ((and (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)))
% 65.99/66.21 Found x30:=(x3 x21):(cNUMBER Xn0)
% 65.99/66.21 Instantiate: Xn0:=Xn:fofType
% 65.99/66.21 Found (x3 x21) as proof of (cNUMBER Xn)
% 65.99/66.21 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21)) as proof of (cNUMBER Xn)
% 65.99/66.21 Found (fun (x6:((and ((and (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 x21)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 65.99/66.21 Found (fun (x6:((and ((and (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 x21)) as proof of (((and ((and (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)))
% 65.99/66.21 Found (and_rect30 (fun (x6:((and ((and (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 x21))) as proof of (cNUMBER Xn)
% 65.99/66.21 Found ((and_rect3 (cNUMBER Xn)) (fun (x6:((and ((and (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 x21))) as proof of (cNUMBER Xn)
% 65.99/66.21 Found (((fun (P:Type) (x6:(((and ((and (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 (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) x4)) (cNUMBER Xn)) (fun (x6:((and ((and (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 x21))) as proof of (cNUMBER Xn)
% 65.99/66.21 Found (((fun (P:Type) (x6:(((and ((and (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 (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) x4)) (cNUMBER Xn)) (fun (x6:((and ((and (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 x21))) as proof of (cNUMBER Xn)
% 65.99/66.21 Found x60:((or (cEVEN Xn0)) (cODD Xn0))
% 65.99/66.21 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 65.99/66.21 Found (x7 x60) as proof of (cNUMBER Xn)
% 67.26/67.47 Found (x7 x60) as proof of (cNUMBER Xn)
% 67.26/67.47 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)) as proof of (cNUMBER Xn)
% 67.26/67.47 Found (fun (x12:(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))
% 67.26/67.47 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 67.26/67.47 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 67.26/67.47 Found (x5 x40) as proof of (cNUMBER Xn)
% 67.26/67.47 Found (x5 x40) as proof of (cNUMBER Xn)
% 67.26/67.47 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 67.26/67.47 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))
% 67.26/67.47 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 67.26/67.47 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 67.26/67.47 Found (x5 x40) as proof of (cNUMBER Xn)
% 67.26/67.47 Found (x5 x40) as proof of (cNUMBER Xn)
% 67.26/67.47 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 67.26/67.47 Found (fun (x6:((and ((and (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))
% 67.26/67.47 Found (fun (x6:((and ((and (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 (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)))
% 67.26/67.47 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 67.26/67.47 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 67.26/67.47 Found (x5 x40) as proof of (cNUMBER Xn)
% 67.26/67.47 Found (x5 x40) as proof of (cNUMBER Xn)
% 67.26/67.47 Found (x5 x40) as proof of (cNUMBER Xn)
% 67.26/67.47 Found x30:(cNUMBER Xn0)
% 67.26/67.47 Instantiate: Xn0:=Xn:fofType
% 67.26/67.47 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30) as proof of (cNUMBER Xn)
% 67.26/67.47 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))
% 67.26/67.47 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)))
% 67.26/67.47 Found x110:((or (cEVEN Xn0)) (cODD Xn0))
% 67.26/67.47 Found x110 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 67.26/67.47 Found (x12 x110) as proof of (cNUMBER Xn)
% 67.26/67.47 Found (x12 x110) as proof of (cNUMBER Xn)
% 67.26/67.47 Found (x12 x110) as proof of (cNUMBER Xn)
% 67.26/67.47 Found x50:=(x5 x40):(cNUMBER Xn0)
% 67.26/67.47 Instantiate: Xn0:=Xn:fofType
% 67.26/67.47 Found (x5 x40) as proof of (cNUMBER Xn)
% 67.26/67.47 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 67.26/67.47 Found (fun (x11:(cEVEN c0)) (x12:(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))
% 67.26/67.47 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 67.26/67.47 Found (and_rect50 (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 67.26/67.47 Found ((and_rect5 (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 67.26/67.47 Found (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 67.26/67.47 Found (fun (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)))) as proof of (cNUMBER Xn)
% 67.56/67.75 Found (fun (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)))) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 67.56/67.75 Found x30:=(x3 x21):(cNUMBER Xn0)
% 67.56/67.75 Instantiate: Xn0:=Xn:fofType
% 67.56/67.75 Found (x3 x21) as proof of (cNUMBER Xn)
% 67.56/67.75 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21)) as proof of (cNUMBER Xn)
% 67.56/67.75 Found (fun (x6:((and ((and (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 x21)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 67.56/67.76 Found (fun (x6:((and ((and (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 x21)) as proof of (((and ((and (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)))
% 67.56/67.76 Found (and_rect30 (fun (x6:((and ((and (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 x21))) as proof of (cNUMBER Xn)
% 67.56/67.76 Found ((and_rect3 (cNUMBER Xn)) (fun (x6:((and ((and (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 x21))) as proof of (cNUMBER Xn)
% 67.56/67.76 Found (((fun (P:Type) (x6:(((and ((and (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 (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) x4)) (cNUMBER Xn)) (fun (x6:((and ((and (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 x21))) as proof of (cNUMBER Xn)
% 67.56/67.76 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (((fun (P:Type) (x6:(((and ((and (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 (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) x4)) (cNUMBER Xn)) (fun (x6:((and ((and (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 x21)))) as proof of (cNUMBER Xn)
% 67.56/67.76 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (((fun (P:Type) (x6:(((and ((and (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 (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) x4)) (cNUMBER Xn)) (fun (x6:((and ((and (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 x21)))) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 68.21/68.41 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (((fun (P:Type) (x6:(((and ((and (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 (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) x4)) (cNUMBER Xn)) (fun (x6:((and ((and (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 x21)))) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn)))
% 68.21/68.41 Found x8:(cODD (cS c0))
% 68.21/68.41 Instantiate: Xn0:=(cS c0):fofType
% 68.21/68.41 Found x8 as proof of (cODD Xn0)
% 68.21/68.41 Found (or_intror00 x8) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 68.21/68.41 Found ((or_intror0 (cODD Xn0)) x8) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 68.21/68.41 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x8) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 68.21/68.41 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x8) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 68.21/68.41 Found (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x8)) as proof of (cNUMBER Xn0)
% 68.21/68.41 Found (fun (x8:(cODD (cS c0)))=> (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x8))) as proof of (cNUMBER Xn0)
% 68.21/68.41 Found (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x8))) as proof of ((cODD (cS c0))->(cNUMBER Xn0))
% 68.21/68.41 Found (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x8))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->(cNUMBER Xn0)))
% 68.21/68.41 Found (and_rect40 (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x8)))) as proof of (cNUMBER Xn0)
% 68.21/68.41 Found ((and_rect4 (cNUMBER Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x8)))) as proof of (cNUMBER Xn0)
% 68.21/68.41 Found (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x7) x6)) (cNUMBER Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x8)))) as proof of (cNUMBER Xn0)
% 68.63/68.89 Found (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x7) x6)) (cNUMBER Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x8)))) as proof of (cNUMBER Xn0)
% 68.63/68.89 Found x70:=(x7 (cS c0)):((cODD (cS c0))->(cODD (cS (cS (cS c0)))))
% 68.63/68.89 Found (x7 (cS c0)) as proof of ((cODD (cS c0))->(cODD Xn0))
% 68.63/68.89 Found (x7 (cS c0)) as proof of ((cODD (cS c0))->(cODD Xn0))
% 68.63/68.89 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x7 (cS c0))) as proof of ((cODD (cS c0))->(cODD Xn0))
% 68.63/68.89 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x7 (cS c0))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->(cODD Xn0)))
% 68.63/68.89 Found (and_rect40 (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x7 (cS c0)))) as proof of (cODD Xn0)
% 68.63/68.89 Found ((and_rect4 (cODD Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x7 (cS c0)))) as proof of (cODD Xn0)
% 68.63/68.89 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cODD Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x7 (cS c0)))) as proof of (cODD Xn0)
% 68.63/68.89 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cODD Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x7 (cS c0)))) as proof of (cODD Xn0)
% 68.63/68.89 Found (or_intror00 (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cODD Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x7 (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 68.63/68.89 Found ((or_intror0 (cODD Xn0)) (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) (cODD Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x7 (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 68.63/68.89 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) (cODD Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x7 (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 68.63/68.89 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) (cODD Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x7 (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 68.63/68.89 Found or_introl00:=(or_introl0 (cEVEN Xn0)):((cODD (cS c0))->((or (cODD (cS c0))) (cEVEN Xn0)))
% 68.63/68.89 Found (or_introl0 (cEVEN Xn0)) as proof of ((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0)))
% 68.63/68.90 Found ((or_introl (cODD (cS c0))) (cEVEN Xn0)) as proof of ((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0)))
% 68.63/68.90 Found ((or_introl (cODD (cS c0))) (cEVEN Xn0)) as proof of ((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0)))
% 68.63/68.90 Found (fun (x8:((and (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)))
% 68.63/68.90 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0))))
% 68.63/68.90 Found (and_rect40 (fun (x8:((and (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))
% 68.63/68.90 Found ((and_rect4 ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x8:((and (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))
% 68.63/68.90 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x8:((and (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))
% 68.63/68.90 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x8:((and (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))
% 68.63/68.90 Found (or_comm_i00 (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x8:((and (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))
% 68.63/68.90 Found ((or_comm_i0 (cEVEN Xn0)) (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x8:((and (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))
% 68.63/68.90 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x8:((and (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))
% 68.63/68.90 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x8:((and (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))
% 68.79/68.98 Found x30:(cNUMBER Xn0)
% 68.79/68.98 Instantiate: Xn0:=Xn:fofType
% 68.79/68.98 Found (fun (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of (cNUMBER Xn)
% 68.79/68.98 Found (fun (x7:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 68.79/68.98 Found (fun (x6:(cEVEN Xn0)) (x7:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of (((and ((and (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)))
% 68.79/68.98 Found (fun (x6:(cEVEN Xn0)) (x7:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of ((cEVEN Xn0)->(((and ((and (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))))
% 68.79/68.98 Found x30:(cNUMBER Xn0)
% 68.79/68.98 Instantiate: Xn0:=Xn:fofType
% 68.79/68.98 Found (fun (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of (cNUMBER Xn)
% 68.79/68.98 Found (fun (x7:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 68.79/68.98 Found (fun (x6:(cODD Xn0)) (x7:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of (((and ((and (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)))
% 68.79/68.98 Found (fun (x6:(cODD Xn0)) (x7:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of ((cODD Xn0)->(((and ((and (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))))
% 68.79/68.98 Found ((or_ind00 (fun (x6:(cEVEN Xn0)) (x7:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30)) (fun (x6:(cODD Xn0)) (x7:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30)) as proof of (((and ((and (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)))
% 68.79/68.98 Found (((or_ind0 (((and ((and (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 (x6:(cEVEN Xn0)) (x7:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30)) (fun (x6:(cODD Xn0)) (x7:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30)) as proof of (((and ((and (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)))
% 68.79/68.98 Found ((((fun (P:Prop) (x6:((cEVEN Xn0)->P)) (x7:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x6) x7) x20)) (((and ((and (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 (x6:(cEVEN Xn0)) (x7:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x30)) (fun (x6:(cODD Xn0)) (x7:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x30)) as proof of (((and ((and (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)))
% 69.08/69.33 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 (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 (x6:(cEVEN Xn0)) (x7:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x30)) (fun (x6:(cODD Xn0)) (x7:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x30)) as proof of (((and ((and (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)))
% 69.08/69.33 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 (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 (x6:(cEVEN Xn0)) (x7:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x30)) (fun (x6:(cODD Xn0)) (x7:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x30)) as proof of (((and ((and (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)))
% 69.08/69.33 Found x50:=(x5 x40):(cNUMBER Xn0)
% 69.08/69.33 Instantiate: Xn0:=Xn:fofType
% 69.08/69.33 Found (x5 x40) as proof of (cNUMBER Xn)
% 69.08/69.33 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 69.08/69.33 Found (fun (x11:(cEVEN c0)) (x12:(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))
% 69.08/69.33 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 69.08/69.33 Found (and_rect50 (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 69.08/69.33 Found ((and_rect5 (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 69.08/69.33 Found (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 69.08/69.33 Found (fun (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)))) as proof of (cNUMBER Xn)
% 69.17/69.38 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)))) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 69.17/69.38 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)))) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 69.17/69.38 Found x70:=(x7 x60):(cNUMBER Xn00)
% 69.17/69.38 Instantiate: Xn00:=Xn:fofType
% 69.17/69.38 Found (x7 x60) as proof of (cNUMBER Xn)
% 69.17/69.38 Found (x7 x60) as proof of (cNUMBER Xn)
% 69.17/69.38 Found x50:(cNUMBER Xn0)
% 69.17/69.38 Instantiate: Xn0:=Xn:fofType
% 69.17/69.38 Found (fun (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of (cNUMBER Xn)
% 69.17/69.38 Found (fun (x7:(cEVEN Xn0)) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 69.17/69.38 Found (fun (x7:(cEVEN Xn0)) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of ((cEVEN Xn0)->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 69.17/69.38 Found x50:(cNUMBER Xn0)
% 69.17/69.38 Instantiate: Xn0:=Xn:fofType
% 69.17/69.38 Found (fun (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of (cNUMBER Xn)
% 69.17/69.38 Found (fun (x7:(cODD Xn0)) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 69.17/69.38 Found (fun (x7:(cODD Xn0)) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of ((cODD Xn0)->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 69.17/69.38 Found ((or_ind00 (fun (x7:(cEVEN Xn0)) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50)) (fun (x7:(cODD Xn0)) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 69.17/69.38 Found (((or_ind0 ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))) (fun (x7:(cEVEN Xn0)) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50)) (fun (x7:(cODD Xn0)) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 69.17/69.38 Found ((((fun (P:Prop) (x7:((cEVEN Xn0)->P)) (x8:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x7) x8) x40)) ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->(cNUMBER Xn))) (fun (x7:(cEVEN Xn0)) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x50)) (fun (x7:(cODD Xn0)) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x50)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 69.17/69.38 Found ((((fun (P:Prop) (x7:((cEVEN Xn0)->P)) (x8:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x7) x8) (x4 x50))) ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->(cNUMBER Xn))) (fun (x7:(cEVEN Xn0)) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x50)) (fun (x7:(cODD Xn0)) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x50)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 69.38/69.62 Found ((((fun (P:Prop) (x7:((cEVEN Xn0)->P)) (x8:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x7) x8) (x4 x50))) ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->(cNUMBER Xn))) (fun (x7:(cEVEN Xn0)) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x50)) (fun (x7:(cODD Xn0)) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x50)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 69.38/69.62 Found x50:=(x5 x40):(cNUMBER Xn0)
% 69.38/69.62 Instantiate: Xn0:=Xn:fofType
% 69.38/69.62 Found (x5 x40) as proof of (cNUMBER Xn)
% 69.38/69.62 Found (x5 x40) as proof of (cNUMBER Xn)
% 69.38/69.62 Found x90:=(x9 x80):(cNUMBER Xn0)
% 69.38/69.62 Found (x9 x80) as proof of (cNUMBER Xn)
% 69.38/69.62 Found (x9 x80) as proof of (cNUMBER Xn)
% 69.38/69.62 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x9 x80)) as proof of (cNUMBER Xn)
% 69.38/69.62 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x9 x80)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 69.38/69.62 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x9 x80)) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 69.38/69.62 Found x30:=(x3 x21):(cNUMBER Xn0)
% 69.38/69.62 Instantiate: Xn0:=Xn:fofType
% 69.38/69.62 Found (x3 x21) as proof of (cNUMBER Xn)
% 69.38/69.62 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21)) as proof of (cNUMBER Xn)
% 69.38/69.62 Found (fun (x6:((and ((and (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 x21)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 69.38/69.62 Found (fun (x6:((and ((and (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 x21)) as proof of (((and ((and (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)))
% 69.38/69.62 Found (and_rect30 (fun (x6:((and ((and (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 x21))) as proof of (cNUMBER Xn)
% 69.38/69.62 Found ((and_rect3 (cNUMBER Xn)) (fun (x6:((and ((and (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 x21))) as proof of (cNUMBER Xn)
% 69.38/69.62 Found (((fun (P:Type) (x6:(((and ((and (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 (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) x4)) (cNUMBER Xn)) (fun (x6:((and ((and (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 x21))) as proof of (cNUMBER Xn)
% 69.38/69.62 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (((fun (P:Type) (x6:(((and ((and (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 (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) x4)) (cNUMBER Xn)) (fun (x6:((and ((and (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 x21)))) as proof of (cNUMBER Xn)
% 69.38/69.62 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (((fun (P:Type) (x6:(((and ((and (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 (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) x4)) (cNUMBER Xn)) (fun (x6:((and ((and (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 x21)))) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 69.87/70.12 Found x30:=(x3 x21):(cNUMBER Xn0)
% 69.87/70.12 Instantiate: Xn0:=Xn:fofType
% 69.87/70.12 Found (x3 x21) as proof of (cNUMBER Xn)
% 69.87/70.12 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21)) as proof of (cNUMBER Xn)
% 69.87/70.12 Found (fun (x6:((and ((and (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 x21)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 69.87/70.12 Found (fun (x6:((and ((and (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 x21)) as proof of (((and ((and (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)))
% 69.87/70.12 Found (and_rect30 (fun (x6:((and ((and (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 x21))) as proof of (cNUMBER Xn)
% 69.87/70.12 Found ((and_rect3 (cNUMBER Xn)) (fun (x6:((and ((and (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 x21))) as proof of (cNUMBER Xn)
% 69.87/70.12 Found (((fun (P:Type) (x6:(((and ((and (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 (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) x4)) (cNUMBER Xn)) (fun (x6:((and ((and (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 x21))) as proof of (cNUMBER Xn)
% 69.87/70.12 Found (((fun (P:Type) (x6:(((and ((and (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 (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) x4)) (cNUMBER Xn)) (fun (x6:((and ((and (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 x21))) as proof of (cNUMBER Xn)
% 69.87/70.12 Found x50:(cNUMBER Xn00)
% 69.87/70.12 Instantiate: Xn00:=Xn:fofType
% 69.87/70.12 Found (fun (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x50) as proof of (cNUMBER Xn)
% 69.87/70.12 Found (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x50) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 70.16/70.39 Found (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x50) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn)))
% 70.16/70.39 Found x80:((or (cEVEN Xn0)) (cODD Xn0))
% 70.16/70.39 Found x80 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 70.16/70.39 Found (x9 x80) as proof of (cNUMBER Xn)
% 70.16/70.39 Found (x9 x80) as proof of (cNUMBER Xn)
% 70.16/70.39 Found (x9 x80) as proof of (cNUMBER Xn)
% 70.16/70.39 Found x30:(cNUMBER Xn0)
% 70.16/70.39 Instantiate: Xn0:=Xn:fofType
% 70.16/70.39 Found (fun (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30) as proof of (cNUMBER Xn)
% 70.16/70.39 Found (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 70.16/70.39 Found (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn)))
% 70.16/70.39 Found x11:(cEVEN c0)
% 70.16/70.39 Instantiate: Xn0:=c0:fofType
% 70.16/70.39 Found x11 as proof of (cEVEN Xn0)
% 70.16/70.39 Found (or_introl00 x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 70.16/70.39 Found ((or_introl0 (cODD Xn0)) x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 70.16/70.39 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 70.16/70.39 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 70.16/70.39 Found x9:(cODD (cS c0))
% 70.16/70.39 Instantiate: Xn0:=(cS c0):fofType
% 70.16/70.39 Found x9 as proof of (cODD Xn0)
% 70.16/70.39 Found (or_intror00 x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 70.16/70.39 Found ((or_intror0 (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 70.16/70.39 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 70.16/70.39 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 70.75/70.99 Found x60:((or (cEVEN Xn0)) (cODD Xn0))
% 70.75/70.99 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 70.75/70.99 Found (x7 x60) as proof of (cNUMBER Xn)
% 70.75/70.99 Found (x7 x60) as proof of (cNUMBER Xn)
% 70.75/70.99 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)) as proof of (cNUMBER Xn)
% 70.75/70.99 Found (fun (x11:(cEVEN c0)) (x12:(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))
% 70.75/70.99 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 70.75/70.99 Found x9:(cODD (cS c0))
% 70.75/70.99 Instantiate: Xn0:=(cS c0):fofType
% 70.75/70.99 Found x9 as proof of (cODD Xn0)
% 70.75/70.99 Found (or_intror00 x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 70.75/70.99 Found ((or_intror0 (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 70.75/70.99 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 70.75/70.99 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 70.75/70.99 Found x11:(cEVEN c0)
% 70.75/70.99 Instantiate: Xn0:=c0:fofType
% 70.75/70.99 Found x11 as proof of (cEVEN Xn0)
% 70.75/70.99 Found (or_introl00 x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 70.75/70.99 Found ((or_introl0 (cODD Xn0)) x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 70.75/70.99 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 70.75/70.99 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 70.75/70.99 Found x30:=(x3 x21):(cNUMBER Xn0)
% 70.75/70.99 Instantiate: Xn0:=Xn:fofType
% 70.75/70.99 Found (x3 x21) as proof of (cNUMBER Xn)
% 70.75/70.99 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21)) as proof of (cNUMBER Xn)
% 70.75/70.99 Found (fun (x6:((and ((and (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 x21)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 70.75/70.99 Found (fun (x6:((and ((and (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 x21)) as proof of (((and ((and (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)))
% 70.75/70.99 Found (and_rect30 (fun (x6:((and ((and (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 x21))) as proof of (cNUMBER Xn)
% 70.75/70.99 Found ((and_rect3 (cNUMBER Xn)) (fun (x6:((and ((and (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 x21))) as proof of (cNUMBER Xn)
% 70.75/70.99 Found (((fun (P:Type) (x6:(((and ((and (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 (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) x4)) (cNUMBER Xn)) (fun (x6:((and ((and (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 x21))) as proof of (cNUMBER Xn)
% 70.75/70.99 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (((fun (P:Type) (x6:(((and ((and (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 (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) x4)) (cNUMBER Xn)) (fun (x6:((and ((and (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 x21)))) as proof of (cNUMBER Xn)
% 71.85/72.10 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (((fun (P:Type) (x6:(((and ((and (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 (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) x4)) (cNUMBER Xn)) (fun (x6:((and ((and (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 x21)))) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 71.85/72.10 Found x30:=(x3 x21):(cNUMBER Xn0)
% 71.85/72.10 Instantiate: Xn0:=Xn:fofType
% 71.85/72.10 Found (x3 x21) as proof of (cNUMBER Xn)
% 71.85/72.10 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21)) as proof of (cNUMBER Xn)
% 71.85/72.10 Found (fun (x6:((and ((and (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 x21)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 71.85/72.10 Found (fun (x6:((and ((and (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 x21)) as proof of (((and ((and (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)))
% 71.85/72.10 Found (and_rect30 (fun (x6:((and ((and (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 x21))) as proof of (cNUMBER Xn)
% 71.85/72.10 Found ((and_rect3 (cNUMBER Xn)) (fun (x6:((and ((and (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 x21))) as proof of (cNUMBER Xn)
% 71.85/72.10 Found (((fun (P:Type) (x6:(((and ((and (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 (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) x4)) (cNUMBER Xn)) (fun (x6:((and ((and (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 x21))) as proof of (cNUMBER Xn)
% 71.85/72.10 Found (((fun (P:Type) (x6:(((and ((and (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 (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) x4)) (cNUMBER Xn)) (fun (x6:((and ((and (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 x21))) as proof of (cNUMBER Xn)
% 71.85/72.10 Found x70:=(x7 x60):(cNUMBER Xn0)
% 71.85/72.10 Instantiate: Xn0:=Xn:fofType
% 71.85/72.10 Found (x7 x60) as proof of (cNUMBER Xn)
% 71.85/72.10 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)) as proof of (cNUMBER Xn)
% 73.12/73.35 Found (fun (x11:(cEVEN c0)) (x12:(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))
% 73.12/73.35 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 73.12/73.35 Found (and_rect50 (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60))) as proof of (cNUMBER Xn)
% 73.12/73.35 Found ((and_rect5 (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60))) as proof of (cNUMBER Xn)
% 73.12/73.35 Found (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60))) as proof of (cNUMBER Xn)
% 73.12/73.35 Found (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60))) as proof of (cNUMBER Xn)
% 73.12/73.35 Found x110:((or (cEVEN Xn0)) (cODD Xn0))
% 73.12/73.35 Found x110 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 73.12/73.35 Found (x12 x110) as proof of (cNUMBER Xn)
% 73.12/73.35 Found (x12 x110) as proof of (cNUMBER Xn)
% 73.12/73.35 Found (fun (x12:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x12 x110)) as proof of (cNUMBER Xn)
% 73.12/73.35 Found (fun (x12:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x12 x110)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 73.12/73.35 Found x70:=(x7 x60):(cNUMBER Xn00)
% 73.12/73.35 Instantiate: Xn00:=Xn:fofType
% 73.12/73.35 Found (x7 x60) as proof of (cNUMBER Xn)
% 73.12/73.35 Found (x7 x60) as proof of (cNUMBER Xn)
% 73.12/73.35 Found x9:(cODD (cS c0))
% 73.12/73.35 Instantiate: Xn0:=(cS c0):fofType
% 73.12/73.35 Found x9 as proof of (cODD Xn0)
% 73.12/73.35 Found (or_intror00 x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 73.12/73.35 Found ((or_intror0 (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 73.12/73.35 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 73.12/73.35 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 73.12/73.35 Found x30:=(x3 x20):(cNUMBER Xn0)
% 73.12/73.35 Instantiate: Xn0:=Xn:fofType
% 73.12/73.35 Found (x3 x20) as proof of (cNUMBER Xn)
% 73.12/73.35 Found (x3 x20) as proof of (cNUMBER Xn)
% 73.12/73.35 Found x30:=(x3 x20):(cNUMBER Xn0)
% 73.12/73.35 Instantiate: Xn0:=Xn:fofType
% 73.12/73.35 Found (x3 x20) as proof of (cNUMBER Xn)
% 73.12/73.35 Found (fun (x4:(cEVEN Xn0))=> (x3 x20)) as proof of (cNUMBER Xn)
% 73.12/73.35 Found (fun (x4:(cEVEN Xn0))=> (x3 x20)) as proof of ((cEVEN Xn0)->(cNUMBER Xn))
% 73.12/73.35 Found x30:=(x3 x20):(cNUMBER Xn0)
% 73.12/73.35 Instantiate: Xn0:=Xn:fofType
% 73.12/73.35 Found (x3 x20) as proof of (cNUMBER Xn)
% 73.12/73.35 Found (fun (x4:(cODD Xn0))=> (x3 x20)) as proof of (cNUMBER Xn)
% 73.12/73.35 Found (fun (x4:(cODD Xn0))=> (x3 x20)) as proof of ((cODD Xn0)->(cNUMBER Xn))
% 73.12/73.35 Found ((or_ind00 (fun (x4:(cEVEN Xn0))=> (x3 x20))) (fun (x4:(cODD Xn0))=> (x3 x20))) as proof of (cNUMBER Xn)
% 73.12/73.35 Found (((or_ind0 (cNUMBER Xn)) (fun (x4:(cEVEN Xn0))=> (x3 x20))) (fun (x4:(cODD Xn0))=> (x3 x20))) as proof of (cNUMBER Xn)
% 73.12/73.35 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 x20))) (fun (x4:(cODD Xn0))=> (x3 x20))) as proof of (cNUMBER Xn)
% 73.12/73.35 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 x20))) (fun (x4:(cODD Xn0))=> (x3 x20))) as proof of (cNUMBER Xn)
% 73.12/73.35 Found x30:=(x3 x20):(cNUMBER Xn0)
% 73.12/73.35 Found (x3 x20) as proof of (cNUMBER Xn0)
% 73.12/73.35 Found (x3 x20) as proof of (cNUMBER Xn0)
% 73.12/73.35 Found x50:=(x5 x40):(cNUMBER Xn0)
% 73.12/73.35 Instantiate: Xn0:=Xn:fofType
% 73.12/73.35 Found (x5 x40) as proof of (cNUMBER Xn)
% 73.12/73.35 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 74.01/74.26 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 74.01/74.26 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 74.01/74.26 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 74.01/74.26 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 74.01/74.26 Found x31:(cNUMBER Xn0)
% 74.01/74.26 Instantiate: Xn0:=Xn:fofType
% 74.01/74.26 Found (fun (x9:(cODD (cS c0)))=> x31) as proof of (cNUMBER Xn)
% 74.01/74.26 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> x31) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 74.01/74.26 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> x31) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 74.01/74.26 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 74.01/74.26 Instantiate: Xn00:=Xn:fofType
% 74.01/74.26 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 74.01/74.26 Found x70:=(x7 x60):(cNUMBER Xn00)
% 74.01/74.26 Instantiate: Xn00:=Xn:fofType
% 74.01/74.26 Found (x7 x60) as proof of (cNUMBER Xn)
% 74.01/74.26 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x7 x60)) as proof of (cNUMBER Xn)
% 74.01/74.26 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x7 x60)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 74.01/74.26 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 74.01/74.26 Instantiate: Xn0:=Xn:fofType
% 74.01/74.26 Found x40 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 74.01/74.26 Found x50:=(x5 x41):(cNUMBER Xn0)
% 74.01/74.26 Instantiate: Xn0:=Xn:fofType
% 74.01/74.26 Found (x5 x41) as proof of (cNUMBER Xn)
% 74.01/74.26 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x41)) as proof of (cNUMBER Xn)
% 74.01/74.26 Found (fun (x6:((and ((and (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 x41)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 74.01/74.26 Found (fun (x6:((and ((and (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 x41)) as proof of (((and ((and (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)))
% 74.01/74.26 Found (and_rect30 (fun (x6:((and ((and (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 x41))) as proof of (cNUMBER Xn)
% 74.01/74.26 Found ((and_rect3 (cNUMBER Xn)) (fun (x6:((and ((and (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 x41))) as proof of (cNUMBER Xn)
% 74.01/74.26 Found (((fun (P:Type) (x6:(((and ((and (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 (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) x2)) (cNUMBER Xn)) (fun (x6:((and ((and (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 x41))) as proof of (cNUMBER Xn)
% 74.01/74.26 Found (((fun (P:Type) (x6:(((and ((and (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 (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) x2)) (cNUMBER Xn)) (fun (x6:((and ((and (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 x41))) as proof of (cNUMBER Xn)
% 74.01/74.26 Found x50:(cNUMBER Xn0)
% 74.01/74.26 Instantiate: Xn0:=Xn:fofType
% 74.66/74.88 Found (fun (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of (cNUMBER Xn)
% 74.66/74.88 Found (fun (x7:(cODD Xn0)) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 74.66/74.88 Found (fun (x7:(cODD Xn0)) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of ((cODD Xn0)->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 74.66/74.88 Found x50:(cNUMBER Xn0)
% 74.66/74.88 Instantiate: Xn0:=Xn:fofType
% 74.66/74.88 Found (fun (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of (cNUMBER Xn)
% 74.66/74.88 Found (fun (x7:(cEVEN Xn0)) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 74.66/74.88 Found (fun (x7:(cEVEN Xn0)) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of ((cEVEN Xn0)->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 74.66/74.88 Found ((or_ind00 (fun (x7:(cEVEN Xn0)) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50)) (fun (x7:(cODD Xn0)) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 74.66/74.88 Found (((or_ind0 ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))) (fun (x7:(cEVEN Xn0)) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50)) (fun (x7:(cODD Xn0)) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 74.66/74.88 Found ((((fun (P:Prop) (x7:((cEVEN Xn0)->P)) (x8:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x7) x8) x40)) ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->(cNUMBER Xn))) (fun (x7:(cEVEN Xn0)) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x50)) (fun (x7:(cODD Xn0)) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x50)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 74.66/74.88 Found ((((fun (P:Prop) (x7:((cEVEN Xn0)->P)) (x8:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x7) x8) (x4 x50))) ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->(cNUMBER Xn))) (fun (x7:(cEVEN Xn0)) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x50)) (fun (x7:(cODD Xn0)) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x50)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 74.66/74.88 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))))=> ((((fun (P:Prop) (x7:((cEVEN Xn0)->P)) (x8:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x7) x8) (x4 x50))) ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->(cNUMBER Xn))) (fun (x7:(cEVEN Xn0)) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x50)) (fun (x7:(cODD Xn0)) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x50))) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 74.66/74.88 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))))=> ((((fun (P:Prop) (x7:((cEVEN Xn0)->P)) (x8:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x7) x8) (x4 x50))) ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->(cNUMBER Xn))) (fun (x7:(cEVEN Xn0)) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x50)) (fun (x7:(cODD Xn0)) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x50))) as proof of (((and ((and (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)))
% 74.66/74.88 Found x70:=(x7 x61):(cNUMBER Xn0)
% 74.66/74.88 Found (x7 x61) as proof of (cNUMBER Xn)
% 74.66/74.88 Found (x7 x61) as proof of (cNUMBER Xn)
% 76.77/76.98 Found (fun (x7:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x7 x61)) as proof of (cNUMBER Xn)
% 76.77/76.98 Found (fun (x7:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x7 x61)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 76.77/76.98 Found x80:((or (cEVEN Xn0)) (cODD Xn0))
% 76.77/76.98 Found x80 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 76.77/76.98 Found (x9 x80) as proof of (cNUMBER Xn)
% 76.77/76.98 Found (x9 x80) as proof of (cNUMBER Xn)
% 76.77/76.98 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x9 x80)) as proof of (cNUMBER Xn)
% 76.77/76.98 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x9 x80)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 76.77/76.98 Found x30:=(x3 x20):(cNUMBER Xn0)
% 76.77/76.98 Instantiate: Xn0:=Xn:fofType
% 76.77/76.98 Found (x3 x20) as proof of (cNUMBER Xn)
% 76.77/76.98 Found (x3 x20) as proof of (cNUMBER Xn)
% 76.77/76.98 Found x50:=(x5 x40):(cNUMBER Xn00)
% 76.77/76.98 Instantiate: Xn00:=Xn:fofType
% 76.77/76.98 Found (x5 x40) as proof of (cNUMBER Xn)
% 76.77/76.98 Found (x5 x40) as proof of (cNUMBER Xn)
% 76.77/76.98 Found x30:=(x3 x20):(cNUMBER Xn0)
% 76.77/76.98 Instantiate: Xn0:=Xn:fofType
% 76.77/76.98 Found (x3 x20) as proof of (cNUMBER Xn)
% 76.77/76.98 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 76.77/76.98 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 76.77/76.98 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 76.77/76.98 Instantiate: Xn00:=Xn:fofType
% 76.77/76.98 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 76.77/76.98 Found x70:=(x7 x60):(cNUMBER Xn00)
% 76.77/76.98 Instantiate: Xn00:=Xn:fofType
% 76.77/76.98 Found (x7 x60) as proof of (cNUMBER Xn)
% 76.77/76.98 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x7 x60)) as proof of (cNUMBER Xn)
% 76.77/76.98 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x7 x60)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 76.77/76.98 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 76.77/76.98 Instantiate: Xn0:=Xn:fofType
% 76.77/76.98 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 76.77/76.98 Found x70:=(x7 x60):(cNUMBER Xn0)
% 76.77/76.98 Instantiate: Xn0:=Xn:fofType
% 76.77/76.98 Found (x7 x60) as proof of (cNUMBER Xn)
% 76.77/76.98 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)) as proof of (cNUMBER Xn)
% 76.77/76.98 Found (fun (x11:(cEVEN c0)) (x12:(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))
% 76.77/76.98 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 76.77/76.98 Found (and_rect50 (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60))) as proof of (cNUMBER Xn)
% 76.77/76.98 Found ((and_rect5 (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60))) as proof of (cNUMBER Xn)
% 76.77/76.98 Found (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60))) as proof of (cNUMBER Xn)
% 76.77/76.98 Found (fun (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)))) as proof of (cNUMBER Xn)
% 76.77/76.98 Found (fun (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)))) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 76.77/76.98 Found x8:(cODD (cS c0))
% 76.77/76.98 Instantiate: Xn0:=(cS c0):fofType
% 77.18/77.40 Found x8 as proof of (cODD Xn0)
% 77.18/77.40 Found (or_intror00 x8) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 77.18/77.40 Found ((or_intror0 (cODD Xn0)) x8) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 77.18/77.40 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x8) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 77.18/77.40 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x8) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 77.18/77.40 Found (x5 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x8)) as proof of (cNUMBER Xn0)
% 77.18/77.40 Found (fun (x8:(cODD (cS c0)))=> (x5 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x8))) as proof of (cNUMBER Xn0)
% 77.18/77.40 Found (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> (x5 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x8))) as proof of ((cODD (cS c0))->(cNUMBER Xn0))
% 77.18/77.40 Found (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> (x5 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x8))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->(cNUMBER Xn0)))
% 77.18/77.40 Found (and_rect40 (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> (x5 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x8)))) as proof of (cNUMBER Xn0)
% 77.18/77.40 Found ((and_rect4 (cNUMBER Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> (x5 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x8)))) as proof of (cNUMBER Xn0)
% 77.18/77.40 Found (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x7) x6)) (cNUMBER Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> (x5 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x8)))) as proof of (cNUMBER Xn0)
% 77.18/77.40 Found (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x7) x6)) (cNUMBER Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> (x5 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x8)))) as proof of (cNUMBER Xn0)
% 77.18/77.40 Found x31:(cNUMBER Xn0)
% 77.18/77.40 Instantiate: Xn0:=Xn:fofType
% 77.18/77.40 Found (fun (x9:(cODD (cS c0)))=> x31) as proof of (cNUMBER Xn)
% 77.18/77.40 Found (fun (x9:(cODD (cS c0)))=> x31) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 77.18/77.40 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 77.18/77.40 Instantiate: Xn00:=Xn:fofType
% 77.18/77.40 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 77.18/77.40 Found x9:(cODD (cS c0))
% 77.18/77.40 Instantiate: Xn0:=(cS c0):fofType
% 77.18/77.40 Found x9 as proof of (cODD Xn0)
% 77.18/77.40 Found (or_intror00 x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 77.18/77.40 Found ((or_intror0 (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 77.18/77.40 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 77.18/77.40 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 77.18/77.40 Found (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9)) as proof of (cNUMBER Xn0)
% 77.18/77.40 Found (fun (x9:(cODD (cS c0)))=> (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9))) as proof of (cNUMBER Xn0)
% 77.18/77.40 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9))) as proof of ((cODD (cS c0))->(cNUMBER Xn0))
% 77.18/77.40 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->(cNUMBER Xn0)))
% 77.18/77.40 Found (and_rect40 (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9)))) as proof of (cNUMBER Xn0)
% 77.18/77.40 Found ((and_rect4 (cNUMBER Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9)))) as proof of (cNUMBER Xn0)
% 77.26/77.46 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cNUMBER Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9)))) as proof of (cNUMBER Xn0)
% 77.26/77.46 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cNUMBER Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9)))) as proof of (cNUMBER Xn0)
% 77.26/77.46 Found x50:=(x5 (cS c0)):((cODD (cS c0))->(cODD (cS (cS (cS c0)))))
% 77.26/77.46 Found (x5 (cS c0)) as proof of ((cODD (cS c0))->(cODD Xn0))
% 77.26/77.46 Found (x5 (cS c0)) as proof of ((cODD (cS c0))->(cODD Xn0))
% 77.26/77.46 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x5 (cS c0))) as proof of ((cODD (cS c0))->(cODD Xn0))
% 77.26/77.46 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x5 (cS c0))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->(cODD Xn0)))
% 77.26/77.46 Found (and_rect40 (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x5 (cS c0)))) as proof of (cODD Xn0)
% 77.26/77.46 Found ((and_rect4 (cODD Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x5 (cS c0)))) as proof of (cODD Xn0)
% 77.26/77.46 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x4)) (cODD Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x5 (cS c0)))) as proof of (cODD Xn0)
% 77.26/77.46 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x4)) (cODD Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x5 (cS c0)))) as proof of (cODD Xn0)
% 77.26/77.46 Found (or_intror00 (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x4)) (cODD Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x5 (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 77.26/77.46 Found ((or_intror0 (cODD Xn0)) (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x4)) (cODD Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x5 (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 77.26/77.46 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x4)) (cODD Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x5 (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 77.31/77.54 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x4)) (cODD Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x5 (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 77.31/77.54 Found or_introl00:=(or_introl0 (cEVEN Xn0)):((cODD (cS c0))->((or (cODD (cS c0))) (cEVEN Xn0)))
% 77.31/77.54 Found (or_introl0 (cEVEN Xn0)) as proof of ((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0)))
% 77.31/77.54 Found ((or_introl (cODD (cS c0))) (cEVEN Xn0)) as proof of ((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0)))
% 77.31/77.54 Found ((or_introl (cODD (cS c0))) (cEVEN Xn0)) as proof of ((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0)))
% 77.31/77.54 Found (fun (x8:((and (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)))
% 77.31/77.54 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0))))
% 77.31/77.54 Found (and_rect40 (fun (x8:((and (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))
% 77.31/77.54 Found ((and_rect4 ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x8:((and (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))
% 77.31/77.54 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x4)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x8:((and (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))
% 77.31/77.54 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x4)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x8:((and (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))
% 77.31/77.54 Found (or_comm_i00 (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x4)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x8:((and (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))
% 77.31/77.54 Found ((or_comm_i0 (cEVEN Xn0)) (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x4)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x8:((and (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))
% 77.31/77.54 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x4)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x8:((and (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))
% 77.55/77.76 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x4)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x8:((and (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))
% 77.55/77.76 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 77.55/77.76 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 77.55/77.76 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 77.55/77.76 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 77.55/77.76 Found (fun (x8:((and (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)))
% 77.55/77.76 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0))))
% 77.55/77.76 Found (and_rect40 (fun (x8:((and (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))
% 77.55/77.76 Found ((and_rect4 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (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))
% 77.55/77.76 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (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))
% 77.55/77.76 Found (fun (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (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))
% 77.55/77.76 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (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)))
% 77.55/77.76 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of (((and ((and (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))))
% 77.55/77.76 Found (and_rect30 (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (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))
% 77.55/77.76 Found ((and_rect3 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (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))
% 77.55/77.76 Found (((fun (P:Type) (x6:(((and ((and (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 (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (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))
% 77.55/77.76 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (((fun (P:Type) (x6:(((and ((and (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 (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (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))
% 77.55/77.77 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (((fun (P:Type) (x6:(((and ((and (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 (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))))) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 77.55/77.77 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (((fun (P:Type) (x6:(((and ((and (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 (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))))) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->((or (cEVEN Xn0)) (cODD Xn0))))
% 77.55/77.77 Found (and_rect20 (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (((fun (P:Type) (x6:(((and ((and (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 (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (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))
% 77.55/77.77 Found ((and_rect2 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (((fun (P:Type) (x6:(((and ((and (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 (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (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))
% 77.55/77.77 Found (((fun (P:Type) (x4:(((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->P)))=> (((((and_rect ((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))) P) x4) x0)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (((fun (P:Type) (x6:(((and ((and (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 (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (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))
% 77.55/77.78 Found (((fun (P:Type) (x4:(((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->P)))=> (((((and_rect ((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))) P) x4) x0)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (((fun (P:Type) (x6:(((and ((and (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 (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (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))
% 77.55/77.78 Found (x3 (((fun (P:Type) (x4:(((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->P)))=> (((((and_rect ((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))) P) x4) x0)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (((fun (P:Type) (x6:(((and ((and (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 (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))))))) as proof of (cNUMBER Xn0)
% 77.55/77.78 Found (x3 (((fun (P:Type) (x4:(((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->P)))=> (((((and_rect ((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))) P) x4) x0)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (((fun (P:Type) (x6:(((and ((and (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 (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))))))) as proof of (cNUMBER Xn0)
% 77.55/77.78 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 77.55/77.78 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 77.55/77.78 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 77.55/77.78 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 77.55/77.79 Found (fun (x8:((and (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)))
% 77.55/77.79 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0))))
% 77.55/77.79 Found (and_rect40 (fun (x8:((and (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))
% 77.55/77.79 Found ((and_rect4 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (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))
% 77.55/77.79 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (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))
% 77.55/77.79 Found (fun (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (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))
% 77.55/77.79 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (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)))
% 77.55/77.79 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of (((and ((and (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))))
% 77.55/77.79 Found (and_rect30 (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (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))
% 77.55/77.79 Found ((and_rect3 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (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))
% 77.55/77.79 Found (((fun (P:Type) (x6:(((and ((and (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 (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (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))
% 77.55/77.79 Found (((fun (P:Type) (x6:(((and ((and (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 (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (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))
% 77.55/77.79 Found (x3 (((fun (P:Type) (x6:(((and ((and (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 (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))))) as proof of (cNUMBER Xn0)
% 77.55/77.80 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 (((fun (P:Type) (x6:(((and ((and (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 (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))))))) as proof of (cNUMBER Xn0)
% 77.55/77.80 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 (((fun (P:Type) (x6:(((and ((and (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 (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))))))) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn0))
% 77.55/77.80 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 (((fun (P:Type) (x6:(((and ((and (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 (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))))))) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn0)))
% 77.60/77.80 Found (and_rect20 (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 (((fun (P:Type) (x6:(((and ((and (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 (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))))))) as proof of (cNUMBER Xn0)
% 77.60/77.80 Found ((and_rect2 (cNUMBER Xn0)) (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 (((fun (P:Type) (x6:(((and ((and (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 (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))))))) as proof of (cNUMBER Xn0)
% 77.60/77.80 Found (((fun (P:Type) (x4:(((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->P)))=> (((((and_rect ((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))) P) x4) x0)) (cNUMBER Xn0)) (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 (((fun (P:Type) (x6:(((and ((and (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 (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))))))) as proof of (cNUMBER Xn0)
% 77.60/77.80 Found (((fun (P:Type) (x4:(((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->P)))=> (((((and_rect ((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))) P) x4) x0)) (cNUMBER Xn0)) (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 (((fun (P:Type) (x6:(((and ((and (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 (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))))))) as proof of (cNUMBER Xn0)
% 77.65/77.89 Found x50:(cNUMBER Xn0)
% 77.65/77.89 Instantiate: Xn0:=Xn:fofType
% 77.65/77.89 Found (fun (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of (cNUMBER Xn)
% 77.65/77.89 Found (fun (x7:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 77.65/77.89 Found (fun (x6:(cODD Xn0)) (x7:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of (((and ((and (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)))
% 77.65/77.89 Found (fun (x6:(cODD Xn0)) (x7:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of ((cODD Xn0)->(((and ((and (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))))
% 77.65/77.89 Found x50:(cNUMBER Xn0)
% 77.65/77.89 Instantiate: Xn0:=Xn:fofType
% 77.65/77.89 Found (fun (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of (cNUMBER Xn)
% 77.65/77.89 Found (fun (x7:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 77.65/77.89 Found (fun (x6:(cEVEN Xn0)) (x7:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of (((and ((and (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)))
% 77.65/77.89 Found (fun (x6:(cEVEN Xn0)) (x7:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of ((cEVEN Xn0)->(((and ((and (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))))
% 77.65/77.89 Found ((or_ind00 (fun (x6:(cEVEN Xn0)) (x7:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50)) (fun (x6:(cODD Xn0)) (x7:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50)) as proof of (((and ((and (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)))
% 77.65/77.89 Found (((or_ind0 (((and ((and (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 (x6:(cEVEN Xn0)) (x7:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50)) (fun (x6:(cODD Xn0)) (x7:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50)) as proof of (((and ((and (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)))
% 77.65/77.89 Found ((((fun (P:Prop) (x6:((cEVEN Xn0)->P)) (x7:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x6) x7) x40)) (((and ((and (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 (x6:(cEVEN Xn0)) (x7:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x50)) (fun (x6:(cODD Xn0)) (x7:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x50)) as proof of (((and ((and (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)))
% 78.10/78.31 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 (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 (x6:(cEVEN Xn0)) (x7:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x50)) (fun (x6:(cODD Xn0)) (x7:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x50)) as proof of (((and ((and (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)))
% 78.10/78.31 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 (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 (x6:(cEVEN Xn0)) (x7:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x50)) (fun (x6:(cODD Xn0)) (x7:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x50)) as proof of (((and ((and (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)))
% 78.10/78.31 Found x50:=(x5 x40):(cNUMBER Xn0)
% 78.10/78.31 Instantiate: Xn0:=Xn:fofType
% 78.10/78.31 Found (x5 x40) as proof of (cNUMBER Xn)
% 78.10/78.31 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 78.10/78.31 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))
% 78.10/78.31 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)))
% 78.10/78.31 Found x70:=(x7 x60):(cNUMBER Xn0)
% 78.10/78.31 Instantiate: Xn0:=Xn:fofType
% 78.10/78.31 Found (x7 x60) as proof of (cNUMBER Xn)
% 78.10/78.31 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)) as proof of (cNUMBER Xn)
% 78.10/78.31 Found (fun (x11:(cEVEN c0)) (x12:(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))
% 78.10/78.31 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 78.10/78.31 Found (and_rect50 (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60))) as proof of (cNUMBER Xn)
% 78.88/79.09 Found ((and_rect5 (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60))) as proof of (cNUMBER Xn)
% 78.88/79.09 Found (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60))) as proof of (cNUMBER Xn)
% 78.88/79.09 Found (fun (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)))) as proof of (cNUMBER Xn)
% 78.88/79.09 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)))) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 78.88/79.09 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)))) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 78.88/79.09 Found x50:=(x5 x41):(cNUMBER Xn0)
% 78.88/79.09 Instantiate: Xn0:=Xn:fofType
% 78.88/79.09 Found (x5 x41) as proof of (cNUMBER Xn)
% 78.88/79.09 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x41)) as proof of (cNUMBER Xn)
% 78.88/79.09 Found (fun (x6:((and ((and (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 x41)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 78.88/79.09 Found (fun (x6:((and ((and (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 x41)) as proof of (((and ((and (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)))
% 78.88/79.09 Found (and_rect30 (fun (x6:((and ((and (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 x41))) as proof of (cNUMBER Xn)
% 78.88/79.09 Found ((and_rect3 (cNUMBER Xn)) (fun (x6:((and ((and (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 x41))) as proof of (cNUMBER Xn)
% 78.88/79.09 Found (((fun (P:Type) (x6:(((and ((and (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 (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) x2)) (cNUMBER Xn)) (fun (x6:((and ((and (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 x41))) as proof of (cNUMBER Xn)
% 78.88/79.09 Found (((fun (P:Type) (x6:(((and ((and (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 (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) x2)) (cNUMBER Xn)) (fun (x6:((and ((and (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 x41))) as proof of (cNUMBER Xn)
% 79.66/79.90 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 79.66/79.90 Instantiate: Xn00:=Xn:fofType
% 79.66/79.90 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 79.66/79.90 Found x50:=(x5 x40):(cNUMBER Xn00)
% 79.66/79.90 Instantiate: Xn00:=Xn:fofType
% 79.66/79.90 Found (x5 x40) as proof of (cNUMBER Xn)
% 79.66/79.90 Found (fun (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 79.66/79.90 Found (fun (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x5 x40)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 79.66/79.90 Found x30:=(x3 x20):(cNUMBER Xn0)
% 79.66/79.90 Instantiate: Xn0:=Xn:fofType
% 79.66/79.90 Found (x3 x20) as proof of (cNUMBER Xn)
% 79.66/79.90 Found (fun (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 79.66/79.90 Found (fun (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 79.66/79.90 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 79.66/79.90 Instantiate: Xn0:=Xn:fofType
% 79.66/79.90 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 79.66/79.90 Found x9:(cODD (cS c0))
% 79.66/79.90 Instantiate: Xn0:=(cS c0):fofType
% 79.66/79.90 Found x9 as proof of (cODD Xn0)
% 79.66/79.90 Found (or_intror00 x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 79.66/79.90 Found ((or_intror0 (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 79.66/79.90 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 79.66/79.90 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 79.66/79.90 Found x11:(cEVEN c0)
% 79.66/79.90 Instantiate: Xn0:=c0:fofType
% 79.66/79.90 Found x11 as proof of (cEVEN Xn0)
% 79.66/79.90 Found (or_introl00 x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 79.66/79.90 Found ((or_introl0 (cODD Xn0)) x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 79.66/79.90 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 79.66/79.90 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 79.66/79.90 Found x30:=(x3 x20):(cNUMBER Xn0)
% 79.66/79.90 Found (x3 x20) as proof of (cNUMBER Xn0)
% 79.66/79.90 Found (x3 x20) as proof of (cNUMBER Xn0)
% 79.66/79.90 Found x30:=(x3 x21):(cNUMBER Xn0)
% 79.66/79.90 Instantiate: Xn0:=Xn:fofType
% 79.66/79.90 Found (x3 x21) as proof of (cNUMBER Xn)
% 79.66/79.90 Found (fun (x9:(cODD (cS c0)))=> (x3 x21)) as proof of (cNUMBER Xn)
% 79.66/79.90 Found (fun (x9:(cODD (cS c0)))=> (x3 x21)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 79.66/79.90 Found x8:(cODD (cS c0))
% 79.66/79.90 Instantiate: Xn0:=(cS c0):fofType
% 79.66/79.90 Found (fun (x8:(cODD (cS c0)))=> x8) as proof of (cODD Xn0)
% 79.66/79.90 Found (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> x8) as proof of ((cODD (cS c0))->(cODD Xn0))
% 79.66/79.90 Found (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> x8) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->(cODD Xn0)))
% 79.66/79.90 Found (and_rect40 (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> x8)) as proof of (cODD Xn0)
% 79.66/79.90 Found ((and_rect4 (cODD Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> x8)) as proof of (cODD Xn0)
% 79.66/79.90 Found (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) (cODD Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> x8)) as proof of (cODD Xn0)
% 79.66/79.90 Found (fun (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) (cODD Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> x8))) as proof of (cODD Xn0)
% 79.66/79.90 Found (fun (x5:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) (cODD Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> x8))) as proof of ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->(cODD Xn0))
% 79.66/79.90 Found (fun (x5:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) (cODD Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> x8))) as proof of (((and ((and (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)))
% 79.66/79.90 Found (and_rect30 (fun (x5:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) (cODD Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> x8)))) as proof of (cODD Xn0)
% 79.66/79.90 Found ((and_rect3 (cODD Xn0)) (fun (x5:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) (cODD Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> x8)))) as proof of (cODD Xn0)
% 79.66/79.90 Found (((fun (P:Type) (x5:(((and ((and (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 (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x5) x4)) (cODD Xn0)) (fun (x5:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) (cODD Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> x8)))) as proof of (cODD Xn0)
% 79.66/79.91 Found (((fun (P:Type) (x5:(((and ((and (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 (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x5) x4)) (cODD Xn0)) (fun (x5:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) (cODD Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> x8)))) as proof of (cODD Xn0)
% 79.66/79.91 Found (or_intror00 (((fun (P:Type) (x5:(((and ((and (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 (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x5) x4)) (cODD Xn0)) (fun (x5:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) (cODD Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> x8))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 79.66/79.91 Found ((or_intror0 (cODD Xn0)) (((fun (P:Type) (x5:(((and ((and (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 (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x5) x4)) (cODD Xn0)) (fun (x5:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) (cODD Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> x8))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 79.66/79.91 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) (((fun (P:Type) (x5:(((and ((and (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 (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x5) x4)) (cODD Xn0)) (fun (x5:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) (cODD Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> x8))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 80.15/80.35 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) (((fun (P:Type) (x5:(((and ((and (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 (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x5) x4)) (cODD Xn0)) (fun (x5:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) (cODD Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> x8))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 80.15/80.35 Found x80:((or (cEVEN Xn0)) (cODD Xn0))
% 80.15/80.35 Found x80 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 80.15/80.35 Found (x9 x80) as proof of (cNUMBER Xn)
% 80.15/80.35 Found (x9 x80) as proof of (cNUMBER Xn)
% 80.15/80.35 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x9 x80)) as proof of (cNUMBER Xn)
% 80.15/80.35 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x9 x80)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 80.15/80.35 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x9 x80)) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 80.15/80.35 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 80.15/80.35 Instantiate: Xn00:=Xn:fofType
% 80.15/80.35 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 80.15/80.35 Found x50:=(x5 x40):(cNUMBER Xn0)
% 80.15/80.35 Found (x5 x40) as proof of (cNUMBER Xn)
% 80.15/80.35 Found (x5 x40) as proof of (cNUMBER Xn)
% 80.15/80.35 Found (x5 x40) as proof of (cNUMBER Xn)
% 80.15/80.35 Found x70:=(x7 x60):(cNUMBER Xn00)
% 80.15/80.35 Found (x7 x60) as proof of (cNUMBER Xn)
% 80.15/80.35 Found (x7 x60) as proof of (cNUMBER Xn)
% 80.15/80.35 Found (x7 x60) as proof of (cNUMBER Xn)
% 80.15/80.35 Found x11:(cEVEN c0)
% 80.15/80.35 Instantiate: Xn0:=c0:fofType
% 80.15/80.35 Found x11 as proof of (cEVEN Xn0)
% 80.15/80.35 Found (or_introl00 x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 80.15/80.35 Found ((or_introl0 (cODD Xn0)) x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 80.15/80.35 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 80.15/80.35 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 80.15/80.35 Found x9:(cODD (cS c0))
% 80.15/80.35 Instantiate: Xn0:=(cS c0):fofType
% 80.15/80.35 Found x9 as proof of (cODD Xn0)
% 80.15/80.35 Found (or_intror00 x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 80.15/80.35 Found ((or_intror0 (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 80.15/80.35 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 80.15/80.35 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 80.15/80.35 Found x9:(cODD (cS c0))
% 80.15/80.35 Instantiate: Xn0:=(cS c0):fofType
% 80.15/80.35 Found x9 as proof of (cODD Xn0)
% 80.26/80.49 Found (or_intror00 x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 80.26/80.49 Found ((or_intror0 (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 80.26/80.49 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 80.26/80.49 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 80.26/80.49 Found (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9)) as proof of (cNUMBER Xn0)
% 80.26/80.49 Found (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9)) as proof of (cNUMBER Xn0)
% 80.26/80.49 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 80.26/80.49 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 80.26/80.49 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 80.26/80.49 Found or_introl00:=(or_introl0 (cEVEN Xn0)):((cODD (cS c0))->((or (cODD (cS c0))) (cEVEN Xn0)))
% 80.26/80.49 Found (or_introl0 (cEVEN Xn0)) as proof of ((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0)))
% 80.26/80.49 Found ((or_introl (cODD (cS c0))) (cEVEN Xn0)) as proof of ((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0)))
% 80.26/80.49 Found ((or_introl (cODD (cS c0))) (cEVEN Xn0)) as proof of ((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0)))
% 80.26/80.49 Found (fun (x7:((and (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)))
% 80.26/80.49 Found (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0))))
% 80.26/80.49 Found (and_rect40 (fun (x7:((and (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))
% 80.26/80.49 Found ((and_rect4 ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x7:((and (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))
% 80.26/80.49 Found (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x7:((and (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))
% 80.26/80.49 Found (fun (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x7:((and (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))
% 80.26/80.49 Found (fun (x5:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x7:((and (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)))
% 80.26/80.49 Found (fun (x5:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0))))) as proof of (((and ((and (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))))
% 80.26/80.50 Found (and_rect30 (fun (x5:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x7:((and (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))
% 80.26/80.50 Found ((and_rect3 ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x5:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x7:((and (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))
% 80.26/80.50 Found (((fun (P:Type) (x5:(((and ((and (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 (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x5) x4)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x5:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x7:((and (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))
% 80.26/80.50 Found (((fun (P:Type) (x5:(((and ((and (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 (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x5) x4)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x5:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x7:((and (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))
% 80.26/80.50 Found (or_comm_i00 (((fun (P:Type) (x5:(((and ((and (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 (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x5) x4)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x5:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x7:((and (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))
% 80.26/80.50 Found ((or_comm_i0 (cEVEN Xn0)) (((fun (P:Type) (x5:(((and ((and (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 (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x5) x4)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x5:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x7:((and (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))
% 80.26/80.50 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((fun (P:Type) (x5:(((and ((and (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 (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x5) x4)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x5:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x7:((and (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))
% 80.26/80.50 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((fun (P:Type) (x5:(((and ((and (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 (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x5) x4)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x5:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x7:((and (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))
% 81.82/82.01 Found x90:=(x9 x80):(cNUMBER Xn0)
% 81.82/82.01 Instantiate: Xn0:=Xn:fofType
% 81.82/82.01 Found (x9 x80) as proof of (cNUMBER Xn)
% 81.82/82.01 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x9 x80)) as proof of (cNUMBER Xn)
% 81.82/82.01 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x9 x80)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 81.82/82.01 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x9 x80)) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 81.82/82.01 Found (and_rect50 (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x9 x80))) as proof of (cNUMBER Xn)
% 81.82/82.01 Found ((and_rect5 (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x9 x80))) as proof of (cNUMBER Xn)
% 81.82/82.01 Found (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x6)) (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x9 x80))) as proof of (cNUMBER Xn)
% 81.82/82.01 Found (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x6)) (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x9 x80))) as proof of (cNUMBER Xn)
% 81.82/82.01 Found x30:=(x3 x20):(cNUMBER Xn0)
% 81.82/82.01 Instantiate: Xn0:=Xn:fofType
% 81.82/82.01 Found (x3 x20) as proof of (cNUMBER Xn)
% 81.82/82.01 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 81.82/82.01 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))
% 81.82/82.01 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)))
% 81.82/82.01 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 81.82/82.01 Instantiate: Xn00:=Xn:fofType
% 81.82/82.01 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x60) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 81.82/82.01 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)))
% 81.82/82.01 Found x7:(cODD (cS c0))
% 81.82/82.01 Instantiate: Xn0:=(cS c0):fofType
% 81.82/82.01 Found x7 as proof of (cODD Xn0)
% 81.82/82.01 Found (or_intror00 x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 81.82/82.01 Found ((or_intror0 (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 81.82/82.01 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 81.82/82.01 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 81.82/82.01 Found x30:=(x3 x21):(cNUMBER Xn0)
% 81.82/82.01 Instantiate: Xn0:=Xn:fofType
% 81.82/82.01 Found (x3 x21) as proof of (cNUMBER Xn)
% 81.82/82.01 Found (fun (x9:(cODD (cS c0)))=> (x3 x21)) as proof of (cNUMBER Xn)
% 81.82/82.01 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x21)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 81.82/82.01 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x21)) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 81.82/82.01 Found x50:=(x5 x40):(cNUMBER Xn0)
% 81.82/82.01 Found (x5 x40) as proof of (cNUMBER Xn0)
% 81.82/82.01 Found (x5 x40) as proof of (cNUMBER Xn0)
% 81.82/82.01 Found x31:(cNUMBER Xn0)
% 81.82/82.01 Instantiate: Xn0:=Xn:fofType
% 81.82/82.01 Found (fun (x9:(cODD (cS c0)))=> x31) as proof of (cNUMBER Xn)
% 81.98/82.19 Found (fun (x9:(cODD (cS c0)))=> x31) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 81.98/82.19 Found x30:=(x3 x20):(cNUMBER Xn0)
% 81.98/82.19 Instantiate: Xn0:=Xn:fofType
% 81.98/82.19 Found (x3 x20) as proof of (cNUMBER Xn)
% 81.98/82.19 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 81.98/82.19 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 81.98/82.19 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn)))
% 81.98/82.19 Found (and_rect20 (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 81.98/82.19 Found ((and_rect2 (cNUMBER Xn)) (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 81.98/82.19 Found (((fun (P:Type) (x4:(((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->P)))=> (((((and_rect ((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))) P) x4) x0)) (cNUMBER Xn)) (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 83.53/83.75 Found (fun (x3:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (((fun (P:Type) (x4:(((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->P)))=> (((((and_rect ((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))) P) x4) x0)) (cNUMBER Xn)) (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)))) as proof of (cNUMBER Xn)
% 83.53/83.75 Found (fun (x3:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (((fun (P:Type) (x4:(((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->P)))=> (((((and_rect ((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))) P) x4) x0)) (cNUMBER Xn)) (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)))) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 83.53/83.75 Found x40:=(x4 x50):((or (cEVEN Xn0)) (cODD Xn0))
% 83.53/83.75 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 83.53/83.75 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 83.53/83.75 Found x51:(cNUMBER Xn0)
% 83.53/83.75 Instantiate: Xn0:=Xn:fofType
% 83.53/83.75 Found (fun (x9:(cODD (cS c0)))=> x51) as proof of (cNUMBER Xn)
% 83.53/83.75 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> x51) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 83.53/83.75 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> x51) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 83.53/83.75 Found x30:=(x3 x20):(cNUMBER Xn0)
% 83.53/83.75 Found (x3 x20) as proof of (cNUMBER Xn)
% 83.53/83.75 Found (x3 x20) as proof of (cNUMBER Xn)
% 83.53/83.75 Found (x3 x20) as proof of (cNUMBER Xn)
% 83.53/83.75 Found x70:=(x7 x60):(cNUMBER Xn00)
% 83.53/83.75 Found (x7 x60) as proof of (cNUMBER Xn)
% 83.53/83.75 Found (x7 x60) as proof of (cNUMBER Xn)
% 83.53/83.75 Found (x7 x60) as proof of (cNUMBER Xn)
% 83.53/83.75 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 83.53/83.75 Instantiate: Xn00:=Xn:fofType
% 83.53/83.75 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 83.53/83.75 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 83.53/83.75 Instantiate: Xn0:=Xn:fofType
% 83.53/83.75 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 83.53/83.75 Found x9:(cODD (cS c0))
% 83.53/83.75 Instantiate: Xn0:=(cS c0):fofType
% 83.53/83.75 Found x9 as proof of (cODD Xn0)
% 83.53/83.75 Found (or_introl00 x9) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 83.91/84.15 Found ((or_introl0 (cEVEN Xn0)) x9) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 83.91/84.15 Found (((or_introl (cODD Xn0)) (cEVEN Xn0)) x9) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 83.91/84.15 Found (((or_introl (cODD Xn0)) (cEVEN Xn0)) x9) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 83.91/84.15 Found (or_comm_i00 (((or_introl (cODD Xn0)) (cEVEN Xn0)) x9)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 83.91/84.15 Found ((or_comm_i0 (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x9)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 83.91/84.15 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x9)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 83.91/84.15 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x9)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 83.91/84.15 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 83.91/84.15 Instantiate: Xn00:=Xn:fofType
% 83.91/84.15 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x60) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 83.91/84.15 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)))
% 83.91/84.15 Found x50:=(x5 x40):(cNUMBER Xn0)
% 83.91/84.15 Found (x5 x40) as proof of (cNUMBER Xn)
% 83.91/84.15 Found (x5 x40) as proof of (cNUMBER Xn)
% 83.91/84.15 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 83.91/84.15 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 83.91/84.15 Found x50:=(x5 x40):(cNUMBER Xn00)
% 83.91/84.15 Instantiate: Xn00:=Xn:fofType
% 83.91/84.15 Found (x5 x40) as proof of (cNUMBER Xn)
% 83.91/84.15 Found (fun (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 83.91/84.15 Found (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x5 x40)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 83.91/84.15 Found (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x5 x40)) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn)))
% 83.91/84.15 Found x30:=(x3 x20):(cNUMBER Xn0)
% 83.91/84.15 Instantiate: Xn0:=Xn:fofType
% 83.91/84.15 Found (x3 x20) as proof of (cNUMBER Xn)
% 83.91/84.15 Found (fun (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 83.91/84.15 Found (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 84.98/85.23 Found (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn)))
% 84.98/85.23 Found x70:=(x7 x60):(cNUMBER Xn00)
% 84.98/85.23 Found (x7 x60) as proof of (cNUMBER Xn)
% 84.98/85.23 Found (x7 x60) as proof of (cNUMBER Xn)
% 84.98/85.23 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x7 x60)) as proof of (cNUMBER Xn)
% 84.98/85.23 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x7 x60)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 84.98/85.23 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 84.98/85.23 Instantiate: Xn00:=Xn:fofType
% 84.98/85.23 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 84.98/85.23 Found x30:=(x3 x20):(cNUMBER Xn0)
% 84.98/85.23 Found (x3 x20) as proof of (cNUMBER Xn0)
% 84.98/85.23 Found (x3 x20) as proof of (cNUMBER Xn0)
% 84.98/85.23 Found x30:=(x3 x21):(cNUMBER Xn0)
% 84.98/85.23 Instantiate: Xn0:=Xn:fofType
% 84.98/85.23 Found (x3 x21) as proof of (cNUMBER Xn)
% 84.98/85.23 Found (fun (x9:(cODD (cS c0)))=> (x3 x21)) as proof of (cNUMBER Xn)
% 84.98/85.23 Found (fun (x9:(cODD (cS c0)))=> (x3 x21)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 84.98/85.23 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 84.98/85.23 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 84.98/85.23 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 84.98/85.23 Found x90:=(x9 x80):(cNUMBER Xn0)
% 84.98/85.23 Instantiate: Xn0:=Xn:fofType
% 84.98/85.23 Found (x9 x80) as proof of (cNUMBER Xn)
% 84.98/85.23 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x9 x80)) as proof of (cNUMBER Xn)
% 84.98/85.23 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x9 x80)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 84.98/85.23 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x9 x80)) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 84.98/85.23 Found (and_rect50 (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x9 x80))) as proof of (cNUMBER Xn)
% 84.98/85.23 Found ((and_rect5 (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x9 x80))) as proof of (cNUMBER Xn)
% 84.98/85.23 Found (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x6)) (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x9 x80))) as proof of (cNUMBER Xn)
% 84.98/85.23 Found (fun (x9:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x6)) (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x9 x80)))) as proof of (cNUMBER Xn)
% 84.98/85.23 Found (fun (x9:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x6)) (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x9 x80)))) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 87.15/87.37 Found x50:=(x5 x40):(cNUMBER Xn00)
% 87.15/87.37 Found (x5 x40) as proof of (cNUMBER Xn)
% 87.15/87.37 Found (x5 x40) as proof of (cNUMBER Xn)
% 87.15/87.37 Found (x5 x40) as proof of (cNUMBER Xn)
% 87.15/87.37 Found x30:=(x3 x20):(cNUMBER Xn0)
% 87.15/87.37 Found (x3 x20) as proof of (cNUMBER Xn)
% 87.15/87.37 Found (x3 x20) as proof of (cNUMBER Xn)
% 87.15/87.37 Found (x3 x20) as proof of (cNUMBER Xn)
% 87.15/87.37 Found x51:(cNUMBER Xn0)
% 87.15/87.37 Instantiate: Xn0:=Xn:fofType
% 87.15/87.37 Found (fun (x9:(cODD (cS c0)))=> x51) as proof of (cNUMBER Xn)
% 87.15/87.37 Found (fun (x9:(cODD (cS c0)))=> x51) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 87.15/87.37 Found x9:(cODD (cS c0))
% 87.15/87.37 Instantiate: Xn0:=(cS c0):fofType
% 87.15/87.37 Found x9 as proof of (cODD Xn0)
% 87.15/87.37 Found (or_intror00 x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 87.15/87.37 Found ((or_intror0 (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 87.15/87.37 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 87.15/87.37 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 87.15/87.37 Found (x5 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9)) as proof of (cNUMBER Xn0)
% 87.15/87.37 Found (fun (x9:(cODD (cS c0)))=> (x5 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9))) as proof of (cNUMBER Xn0)
% 87.15/87.37 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> (x5 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9))) as proof of ((cODD (cS c0))->(cNUMBER Xn0))
% 87.15/87.37 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> (x5 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->(cNUMBER Xn0)))
% 87.15/87.37 Found (and_rect40 (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> (x5 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9)))) as proof of (cNUMBER Xn0)
% 87.15/87.37 Found ((and_rect4 (cNUMBER Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> (x5 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9)))) as proof of (cNUMBER Xn0)
% 87.15/87.37 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cNUMBER Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> (x5 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9)))) as proof of (cNUMBER Xn0)
% 87.15/87.37 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cNUMBER Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> (x5 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9)))) as proof of (cNUMBER Xn0)
% 87.15/87.37 Found x30:=(x3 x20):(cNUMBER Xn0)
% 87.15/87.37 Found (x3 x20) as proof of (cNUMBER Xn)
% 87.15/87.37 Found (x3 x20) as proof of (cNUMBER Xn)
% 87.15/87.37 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 87.15/87.37 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 87.15/87.37 Found x70:=(x7 x60):(cNUMBER Xn00)
% 87.15/87.37 Found (x7 x60) as proof of (cNUMBER Xn)
% 87.15/87.37 Found (x7 x60) as proof of (cNUMBER Xn)
% 87.15/87.37 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x7 x60)) as proof of (cNUMBER Xn)
% 87.15/87.37 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x7 x60)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 87.15/87.37 Found x30:=(x3 x20):(cNUMBER Xn0)
% 87.15/87.37 Found (x3 x20) as proof of (cNUMBER Xn0)
% 87.15/87.37 Found (x3 x20) as proof of (cNUMBER Xn0)
% 87.15/87.37 Found x30:=(x3 x21):(cNUMBER Xn0)
% 87.15/87.37 Instantiate: Xn0:=Xn:fofType
% 87.15/87.37 Found (x3 x21) as proof of (cNUMBER Xn)
% 88.62/88.83 Found (x3 x21) as proof of (cNUMBER Xn)
% 88.62/88.83 Found x30:=(x3 x20):(cNUMBER Xn0)
% 88.62/88.83 Found (x3 x20) as proof of (cNUMBER Xn)
% 88.62/88.83 Found (x3 x20) as proof of (cNUMBER Xn)
% 88.62/88.83 Found (x3 x20) as proof of (cNUMBER Xn)
% 88.62/88.83 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 88.62/88.83 Instantiate: Xn00:=Xn:fofType
% 88.62/88.83 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 88.62/88.83 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 88.62/88.83 Instantiate: Xn00:=Xn:fofType
% 88.62/88.83 Found (fun (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x40) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 88.62/88.83 Found (fun (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x40) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 88.62/88.83 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 88.62/88.83 Instantiate: Xn0:=Xn:fofType
% 88.62/88.83 Found (fun (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x20) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 88.62/88.83 Found (fun (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x20) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->((or (cEVEN Xn00)) (cODD Xn00)))
% 88.62/88.83 Found x40:=(x4 x50):((or (cEVEN Xn0)) (cODD Xn0))
% 88.62/88.83 Instantiate: Xn0:=Xn:fofType
% 88.62/88.83 Found (x4 x50) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 88.62/88.83 Found (x4 x50) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 88.62/88.83 Found x60:=(x6 x70):((or (cEVEN Xn00)) (cODD Xn00))
% 88.62/88.83 Instantiate: Xn00:=Xn:fofType
% 88.62/88.83 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 88.62/88.83 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 88.62/88.83 Found x9:(cODD (cS c0))
% 88.62/88.83 Instantiate: Xn0:=(cS c0):fofType
% 88.62/88.83 Found x9 as proof of (cODD Xn0)
% 88.62/88.83 Found (or_intror00 x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 88.62/88.83 Found ((or_intror0 (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 88.62/88.83 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 88.62/88.83 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 88.62/88.83 Found x11:(cEVEN c0)
% 88.62/88.83 Instantiate: Xn0:=c0:fofType
% 88.62/88.83 Found x11 as proof of (cEVEN Xn0)
% 88.62/88.83 Found (or_introl00 x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 88.62/88.83 Found ((or_introl0 (cODD Xn0)) x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 88.62/88.83 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 88.62/88.83 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 88.62/88.83 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 88.62/88.83 Instantiate: Xn00:=Xn:fofType
% 88.62/88.83 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x60) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 88.62/88.83 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)))
% 88.62/88.83 Found x30:=(x3 x20):(cNUMBER Xn0)
% 88.62/88.83 Found (x3 x20) as proof of (cNUMBER Xn)
% 88.62/88.83 Found (x3 x20) as proof of (cNUMBER Xn)
% 88.62/88.83 Found (fun (x9:(cODD (cS c0)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 88.62/88.83 Found (fun (x9:(cODD (cS c0)))=> (x3 x20)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 88.62/88.83 Found x50:=(x5 x40):(cNUMBER Xn0)
% 88.62/88.83 Found (x5 x40) as proof of (cNUMBER Xn0)
% 88.62/88.83 Found (x5 x40) as proof of (cNUMBER Xn0)
% 88.62/88.83 Found x50:=(x5 x41):(cNUMBER Xn0)
% 88.62/88.83 Instantiate: Xn0:=Xn:fofType
% 88.62/88.83 Found (x5 x41) as proof of (cNUMBER Xn)
% 88.62/88.83 Found (fun (x9:(cODD (cS c0)))=> (x5 x41)) as proof of (cNUMBER Xn)
% 89.32/89.54 Found (fun (x9:(cODD (cS c0)))=> (x5 x41)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 89.32/89.54 Found x11:(cEVEN c0)
% 89.32/89.54 Instantiate: Xn0:=c0:fofType
% 89.32/89.54 Found x11 as proof of (cEVEN Xn0)
% 89.32/89.54 Found (or_introl00 x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 89.32/89.54 Found ((or_introl0 (cODD Xn0)) x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 89.32/89.54 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 89.32/89.54 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 89.32/89.54 Found (x3 (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11)) as proof of (cNUMBER Xn0)
% 89.32/89.54 Found (x3 (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11)) as proof of (cNUMBER Xn0)
% 89.32/89.54 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 89.32/89.54 Instantiate: Xn0:=Xn:fofType
% 89.32/89.54 Found x40 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 89.32/89.54 Found (x7 x40) as proof of (cNUMBER Xn)
% 89.32/89.54 Found (x7 x40) as proof of (cNUMBER Xn)
% 89.32/89.54 Found (x7 x40) as proof of (cNUMBER Xn)
% 89.32/89.54 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 89.32/89.54 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 89.32/89.54 Found (x5 x40) as proof of (cNUMBER Xn)
% 89.32/89.54 Found (x5 x40) as proof of (cNUMBER Xn)
% 89.32/89.54 Found (x5 x40) as proof of (cNUMBER Xn)
% 89.32/89.54 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 89.32/89.54 Instantiate: Xn00:=Xn:fofType
% 89.32/89.54 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 89.32/89.54 Found (x5 x60) as proof of (cNUMBER Xn)
% 89.32/89.54 Found (x5 x60) as proof of (cNUMBER Xn)
% 89.32/89.54 Found (x5 x60) as proof of (cNUMBER Xn)
% 89.32/89.54 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 89.32/89.54 Found x60 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 89.32/89.54 Found (x7 x60) as proof of (cNUMBER Xn)
% 89.32/89.54 Found (x7 x60) as proof of (cNUMBER Xn)
% 89.32/89.54 Found (x7 x60) as proof of (cNUMBER Xn)
% 89.32/89.54 Found x50:=(x5 x40):(cNUMBER Xn0)
% 89.32/89.54 Found (x5 x40) as proof of (cNUMBER Xn)
% 89.32/89.54 Found (x5 x40) as proof of (cNUMBER Xn)
% 89.32/89.54 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 89.32/89.54 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))
% 89.32/89.54 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)))
% 89.32/89.54 Found x61:((or (cEVEN Xn0)) (cODD Xn0))
% 89.32/89.54 Found x61 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 89.32/89.54 Found (x7 x61) as proof of (cNUMBER Xn)
% 89.32/89.54 Found (x7 x61) as proof of (cNUMBER Xn)
% 89.32/89.54 Found (fun (x7:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x7 x61)) as proof of (cNUMBER Xn)
% 89.32/89.54 Found (fun (x7:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x7 x61)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 89.32/89.54 Found x7:(cODD (cS c0))
% 89.32/89.54 Instantiate: Xn0:=(cS c0):fofType
% 89.32/89.54 Found x7 as proof of (cODD Xn0)
% 89.32/89.54 Found (or_intror00 x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 89.32/89.54 Found ((or_intror0 (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 89.32/89.54 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 89.32/89.54 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 89.32/89.54 Found x11:(cEVEN c0)
% 89.32/89.54 Instantiate: Xn0:=c0:fofType
% 89.32/89.54 Found x11 as proof of (cEVEN Xn0)
% 89.32/89.54 Found (or_introl00 x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 89.32/89.54 Found ((or_introl0 (cODD Xn0)) x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 89.32/89.54 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 89.32/89.54 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 89.32/89.54 Found x9:(cODD (cS c0))
% 89.32/89.54 Instantiate: Xn0:=(cS c0):fofType
% 89.32/89.54 Found x9 as proof of (cODD Xn0)
% 89.32/89.54 Found (or_intror00 x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 89.32/89.54 Found ((or_intror0 (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 89.32/89.54 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 89.32/89.54 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 89.32/89.54 Found (x5 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9)) as proof of (cNUMBER Xn0)
% 89.32/89.54 Found (x5 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9)) as proof of (cNUMBER Xn0)
% 89.32/89.54 Found x40:=(x4 x50):((or (cEVEN Xn0)) (cODD Xn0))
% 89.36/89.58 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 89.36/89.58 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 89.36/89.58 Found x9:(cODD (cS c0))
% 89.36/89.58 Instantiate: Xn0:=(cS c0):fofType
% 89.36/89.58 Found (fun (x9:(cODD (cS c0)))=> x9) as proof of (cODD Xn0)
% 89.36/89.58 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> x9) as proof of ((cODD (cS c0))->(cODD Xn0))
% 89.36/89.58 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> x9) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->(cODD Xn0)))
% 89.36/89.58 Found (and_rect40 (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> x9)) as proof of (cODD Xn0)
% 89.36/89.58 Found ((and_rect4 (cODD Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> x9)) as proof of (cODD Xn0)
% 89.36/89.58 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) (cODD Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> x9)) as proof of (cODD Xn0)
% 89.36/89.58 Found (fun (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) (cODD Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> x9))) as proof of (cODD Xn0)
% 89.36/89.58 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) (cODD Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> x9))) as proof of ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->(cODD Xn0))
% 89.36/89.58 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) (cODD Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> x9))) as proof of (((and ((and (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)))
% 89.36/89.58 Found (and_rect30 (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) (cODD Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> x9)))) as proof of (cODD Xn0)
% 89.36/89.58 Found ((and_rect3 (cODD Xn0)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) (cODD Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> x9)))) as proof of (cODD Xn0)
% 89.36/89.59 Found (((fun (P:Type) (x6:(((and ((and (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 (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) x4)) (cODD Xn0)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) (cODD Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> x9)))) as proof of (cODD Xn0)
% 89.36/89.59 Found (((fun (P:Type) (x6:(((and ((and (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 (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) x4)) (cODD Xn0)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) (cODD Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> x9)))) as proof of (cODD Xn0)
% 89.36/89.59 Found (or_intror00 (((fun (P:Type) (x6:(((and ((and (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 (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) x4)) (cODD Xn0)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) (cODD Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> x9))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 89.36/89.59 Found ((or_intror0 (cODD Xn0)) (((fun (P:Type) (x6:(((and ((and (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 (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x4)) (cODD Xn0)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) (cODD Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> x9))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 90.03/90.27 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) (((fun (P:Type) (x6:(((and ((and (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 (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x4)) (cODD Xn0)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) (cODD Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> x9))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 90.03/90.27 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) (((fun (P:Type) (x6:(((and ((and (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 (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x4)) (cODD Xn0)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) (cODD Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> x9))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 90.03/90.27 Found or_introl00:=(or_introl0 (cEVEN Xn0)):((cODD (cS c0))->((or (cODD (cS c0))) (cEVEN Xn0)))
% 90.03/90.27 Found (or_introl0 (cEVEN Xn0)) as proof of ((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0)))
% 90.03/90.27 Found ((or_introl (cODD (cS c0))) (cEVEN Xn0)) as proof of ((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0)))
% 90.03/90.27 Found ((or_introl (cODD (cS c0))) (cEVEN Xn0)) as proof of ((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0)))
% 90.03/90.27 Found (fun (x8:((and (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)))
% 90.03/90.27 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0))))
% 90.03/90.27 Found (and_rect40 (fun (x8:((and (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))
% 90.03/90.27 Found ((and_rect4 ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x8:((and (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))
% 90.03/90.27 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x8:((and (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))
% 90.03/90.28 Found (fun (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x8:((and (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))
% 90.03/90.28 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x8:((and (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)))
% 90.03/90.28 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0))))) as proof of (((and ((and (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))))
% 90.03/90.28 Found (and_rect30 (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x8:((and (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))
% 90.03/90.28 Found ((and_rect3 ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x8:((and (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))
% 90.03/90.28 Found (((fun (P:Type) (x6:(((and ((and (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 (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) x4)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x8:((and (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))
% 90.06/90.28 Found (((fun (P:Type) (x6:(((and ((and (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 (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) x4)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x8:((and (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))
% 90.06/90.28 Found (or_comm_i00 (((fun (P:Type) (x6:(((and ((and (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 (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) x4)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x8:((and (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))
% 90.06/90.28 Found ((or_comm_i0 (cEVEN Xn0)) (((fun (P:Type) (x6:(((and ((and (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 (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x4)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x8:((and (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))
% 90.06/90.28 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((fun (P:Type) (x6:(((and ((and (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 (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x4)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x8:((and (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))
% 90.50/90.75 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((fun (P:Type) (x6:(((and ((and (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 (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x4)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x8:((and (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))
% 90.50/90.75 Found x30:=(x3 x21):(cNUMBER Xn0)
% 90.50/90.75 Found (x3 x21) as proof of (cNUMBER Xn0)
% 90.50/90.75 Found (x3 x21) as proof of (cNUMBER Xn0)
% 90.50/90.75 Found x30:=(x3 x20):(cNUMBER Xn0)
% 90.50/90.75 Found (x3 x20) as proof of (cNUMBER Xn)
% 90.50/90.75 Found (x3 x20) as proof of (cNUMBER Xn)
% 90.50/90.75 Found (fun (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 90.50/90.75 Found (fun (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 90.50/90.75 Found x50:=(x5 x40):(cNUMBER Xn00)
% 90.50/90.75 Found (x5 x40) as proof of (cNUMBER Xn)
% 90.50/90.75 Found (x5 x40) as proof of (cNUMBER Xn)
% 90.50/90.75 Found (fun (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 90.50/90.75 Found (fun (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x5 x40)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 90.50/90.75 Found x50:=(x5 x41):(cNUMBER Xn0)
% 90.50/90.75 Instantiate: Xn0:=Xn:fofType
% 90.50/90.75 Found (x5 x41) as proof of (cNUMBER Xn)
% 91.32/91.59 Found (fun (x9:(cODD (cS c0)))=> (x5 x41)) as proof of (cNUMBER Xn)
% 91.32/91.59 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x41)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 91.32/91.59 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x41)) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 91.32/91.59 Found x20:=(x2 x31):((or (cEVEN Xn0)) (cODD Xn0))
% 91.32/91.59 Found (x2 x31) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 91.32/91.59 Found (x2 x31) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 91.32/91.59 Found x32:(cNUMBER Xn0)
% 91.32/91.59 Instantiate: Xn0:=Xn:fofType
% 91.32/91.59 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x32) as proof of (cNUMBER Xn)
% 91.32/91.59 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x32) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 91.32/91.59 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x32) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn)))
% 91.32/91.59 Found x70:=(x7 x60):(cNUMBER Xn0)
% 91.32/91.59 Found (x7 x60) as proof of (cNUMBER Xn0)
% 91.32/91.59 Found (x7 x60) as proof of (cNUMBER Xn0)
% 91.32/91.59 Found x30:=(x3 x21):(cNUMBER Xn0)
% 91.32/91.59 Found (x3 x21) as proof of (cNUMBER Xn0)
% 91.32/91.59 Found (x3 x21) as proof of (cNUMBER Xn0)
% 91.32/91.59 Found x30:=(x3 x22):(cNUMBER Xn0)
% 91.32/91.59 Instantiate: Xn0:=Xn:fofType
% 91.32/91.59 Found (x3 x22) as proof of (cNUMBER Xn)
% 91.32/91.59 Found (x3 x22) as proof of (cNUMBER Xn)
% 91.32/91.59 Found x30:=(x3 x22):(cNUMBER Xn0)
% 91.32/91.59 Found (x3 x22) as proof of (cNUMBER Xn)
% 91.32/91.59 Found (x3 x22) as proof of (cNUMBER Xn)
% 91.32/91.59 Found (x3 x22) as proof of (cNUMBER Xn)
% 91.32/91.59 Found x60:=(x6 x70):((or (cEVEN Xn00)) (cODD Xn00))
% 91.32/91.59 Instantiate: Xn00:=Xn:fofType
% 91.32/91.59 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 91.32/91.59 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 91.32/91.59 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 91.32/91.59 Instantiate: Xn0:=Xn:fofType
% 91.32/91.59 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 91.32/91.59 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 91.32/91.59 Found x51:(cNUMBER Xn0)
% 91.32/91.59 Instantiate: Xn0:=Xn:fofType
% 91.32/91.59 Found (fun (x9:(cODD (cS c0)))=> x51) as proof of (cNUMBER Xn)
% 91.32/91.59 Found (fun (x9:(cODD (cS c0)))=> x51) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 91.32/91.59 Found x60:=(x6 x70):((or (cEVEN Xn0)) (cODD Xn0))
% 91.32/91.59 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 91.32/91.59 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 91.32/91.59 Found x71:(cNUMBER Xn0)
% 91.32/91.59 Instantiate: Xn0:=Xn:fofType
% 91.32/91.59 Found (fun (x9:(cODD (cS c0)))=> x71) as proof of (cNUMBER Xn)
% 91.32/91.59 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> x71) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 91.32/91.59 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> x71) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 92.36/92.63 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 92.36/92.63 Instantiate: Xn00:=Xn:fofType
% 92.36/92.63 Found (fun (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x40) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 92.36/92.63 Found (fun (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x40) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 92.36/92.63 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 92.36/92.63 Instantiate: Xn00:=Xn:fofType
% 92.36/92.63 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 92.36/92.63 Found (x3 x60) as proof of (cNUMBER Xn)
% 92.36/92.63 Found (x3 x60) as proof of (cNUMBER Xn)
% 92.36/92.63 Found (x3 x60) as proof of (cNUMBER Xn)
% 92.36/92.63 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 92.36/92.63 Found x60 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 92.36/92.63 Found (x7 x60) as proof of (cNUMBER Xn)
% 92.36/92.63 Found (x7 x60) as proof of (cNUMBER Xn)
% 92.36/92.63 Found (x7 x60) as proof of (cNUMBER Xn)
% 92.36/92.63 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 92.36/92.63 Instantiate: Xn0:=Xn:fofType
% 92.36/92.63 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 92.36/92.63 Found (x7 x20) as proof of (cNUMBER Xn)
% 92.36/92.63 Found (x7 x20) as proof of (cNUMBER Xn)
% 92.36/92.63 Found (x7 x20) as proof of (cNUMBER Xn)
% 92.36/92.63 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 92.36/92.63 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 92.36/92.63 Found (x3 x20) as proof of (cNUMBER Xn)
% 92.36/92.63 Found (x3 x20) as proof of (cNUMBER Xn)
% 92.36/92.63 Found (x3 x20) as proof of (cNUMBER Xn)
% 92.36/92.63 Found x30:=(x3 x20):(cNUMBER Xn0)
% 92.36/92.63 Found (x3 x20) as proof of (cNUMBER Xn)
% 92.36/92.63 Found (x3 x20) as proof of (cNUMBER Xn)
% 92.36/92.63 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 92.36/92.63 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))
% 92.36/92.63 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)))
% 92.36/92.63 Found x30:=(x3 x20):(cNUMBER Xn0)
% 92.36/92.63 Found (x3 x20) as proof of (cNUMBER Xn0)
% 92.36/92.63 Found (x3 x20) as proof of (cNUMBER Xn0)
% 92.36/92.63 Found x30:=(x3 x21):(cNUMBER Xn0)
% 92.36/92.63 Instantiate: Xn0:=Xn:fofType
% 92.36/92.63 Found (x3 x21) as proof of (cNUMBER Xn)
% 92.36/92.63 Found (x3 x21) as proof of (cNUMBER Xn)
% 92.36/92.63 Found x30:=(x3 x20):(cNUMBER Xn0)
% 92.36/92.63 Found (x3 x20) as proof of (cNUMBER Xn)
% 92.36/92.63 Found (x3 x20) as proof of (cNUMBER Xn)
% 92.36/92.63 Found (x3 x20) as proof of (cNUMBER Xn)
% 92.36/92.63 Found x60:=(x6 x70):((or (cEVEN Xn00)) (cODD Xn00))
% 92.36/92.63 Instantiate: Xn00:=Xn:fofType
% 92.36/92.63 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 92.36/92.63 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 92.36/92.63 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 92.36/92.63 Instantiate: Xn00:=Xn:fofType
% 92.36/92.63 Found (fun (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x40) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 92.36/92.63 Found (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x40) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 92.53/92.77 Found (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x40) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->((or (cEVEN Xn0)) (cODD Xn0))))
% 92.53/92.77 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 92.53/92.77 Instantiate: Xn0:=Xn:fofType
% 92.53/92.77 Found (fun (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x20) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 92.53/92.77 Found (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x20) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->((or (cEVEN Xn00)) (cODD Xn00)))
% 92.53/92.77 Found (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x20) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->((or (cEVEN Xn00)) (cODD Xn00))))
% 92.53/92.77 Found x32:(cNUMBER Xn0)
% 92.53/92.77 Instantiate: Xn0:=Xn:fofType
% 92.53/92.77 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x32) as proof of (cNUMBER Xn)
% 92.53/92.77 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x32) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 92.53/92.77 Found x9:(cODD (cS c0))
% 92.53/92.77 Instantiate: Xn0:=(cS c0):fofType
% 92.53/92.77 Found x9 as proof of (cODD Xn0)
% 92.53/92.77 Found (or_introl00 x9) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 92.53/92.77 Found ((or_introl0 (cEVEN Xn0)) x9) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 92.53/92.77 Found (((or_introl (cODD Xn0)) (cEVEN Xn0)) x9) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 92.53/92.77 Found (((or_introl (cODD Xn0)) (cEVEN Xn0)) x9) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 92.53/92.77 Found (or_comm_i00 (((or_introl (cODD Xn0)) (cEVEN Xn0)) x9)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 93.85/94.11 Found ((or_comm_i0 (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x9)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 93.85/94.11 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x9)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 93.85/94.11 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x9)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 93.85/94.11 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 93.85/94.11 Instantiate: Xn0:=Xn:fofType
% 93.85/94.11 Found x40 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 93.85/94.11 Found (x7 x40) as proof of (cNUMBER Xn)
% 93.85/94.11 Found (x7 x40) as proof of (cNUMBER Xn)
% 93.85/94.11 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x7 x40)) as proof of (cNUMBER Xn)
% 93.85/94.11 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x7 x40)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 93.85/94.11 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 93.85/94.11 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 93.85/94.11 Found (x5 x40) as proof of (cNUMBER Xn)
% 93.85/94.11 Found (x5 x40) as proof of (cNUMBER Xn)
% 93.85/94.11 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 93.85/94.11 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 93.85/94.11 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 93.85/94.11 Instantiate: Xn00:=Xn:fofType
% 93.85/94.11 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 93.85/94.11 Found (x5 x60) as proof of (cNUMBER Xn)
% 93.85/94.11 Found (x5 x60) as proof of (cNUMBER Xn)
% 93.85/94.11 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x60)) as proof of (cNUMBER Xn)
% 93.85/94.11 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x60)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 93.85/94.11 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 93.85/94.11 Found x60 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 93.85/94.11 Found (x7 x60) as proof of (cNUMBER Xn)
% 93.85/94.11 Found (x7 x60) as proof of (cNUMBER Xn)
% 93.85/94.11 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x7 x60)) as proof of (cNUMBER Xn)
% 93.85/94.11 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x7 x60)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 93.85/94.11 Found x30:=(x3 x20):(cNUMBER Xn0)
% 93.85/94.11 Found (x3 x20) as proof of (cNUMBER Xn)
% 93.85/94.11 Found (x3 x20) as proof of (cNUMBER Xn)
% 93.85/94.11 Found (fun (x9:(cODD (cS c0)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 93.85/94.11 Found (fun (x8:((and (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))
% 93.85/94.11 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x20)) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 93.85/94.11 Found x30:=(x3 x20):(cNUMBER Xn0)
% 93.85/94.11 Found (x3 x20) as proof of (cNUMBER Xn)
% 93.85/94.11 Found (x3 x20) as proof of (cNUMBER Xn)
% 93.85/94.11 Found (fun (x9:(cODD (cS c0)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 93.85/94.11 Found (fun (x9:(cODD (cS c0)))=> (x3 x20)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 93.85/94.11 Found x50:=(x5 x40):(cNUMBER Xn0)
% 93.85/94.11 Found (x5 x40) as proof of (cNUMBER Xn0)
% 93.85/94.11 Found (x5 x40) as proof of (cNUMBER Xn0)
% 93.85/94.11 Found x50:=(x5 x41):(cNUMBER Xn0)
% 93.85/94.11 Instantiate: Xn0:=Xn:fofType
% 93.85/94.11 Found (x5 x41) as proof of (cNUMBER Xn)
% 93.85/94.11 Found (fun (x9:(cODD (cS c0)))=> (x5 x41)) as proof of (cNUMBER Xn)
% 93.85/94.11 Found (fun (x9:(cODD (cS c0)))=> (x5 x41)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 93.85/94.11 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 93.85/94.11 Instantiate: Xn0:=Xn:fofType
% 93.85/94.11 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 93.85/94.11 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 93.85/94.11 Found x40:=(x4 x50):((or (cEVEN Xn00)) (cODD Xn00))
% 93.85/94.11 Instantiate: Xn00:=Xn:fofType
% 93.85/94.11 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 93.85/94.11 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 93.85/94.11 Found or_comm_i100:=(or_comm_i10 x20):((or (cODD Xn0)) (cEVEN Xn0))
% 93.85/94.11 Found (or_comm_i10 x20) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 93.85/94.11 Found ((or_comm_i1 (cODD Xn0)) x20) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 93.85/94.11 Found (((or_comm_i (cEVEN Xn0)) (cODD Xn0)) x20) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 94.27/94.54 Found (((or_comm_i (cEVEN Xn0)) (cODD Xn0)) x20) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 94.27/94.54 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 94.27/94.54 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 94.27/94.54 Found (x3 x20) as proof of (cNUMBER Xn)
% 94.27/94.54 Found (x3 x20) as proof of (cNUMBER Xn)
% 94.27/94.54 Found (x3 x20) as proof of (cNUMBER Xn)
% 94.27/94.54 Found x9:(cEVEN c0)
% 94.27/94.54 Instantiate: Xn0:=c0:fofType
% 94.27/94.54 Found x9 as proof of (cEVEN Xn0)
% 94.27/94.54 Found (or_introl00 x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 94.27/94.54 Found ((or_introl0 (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 94.27/94.54 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 94.27/94.54 Found (fun (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_introl (cEVEN Xn0)) (cODD Xn0)) x9)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 94.27/94.54 Found (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_introl (cEVEN Xn0)) (cODD Xn0)) x9)) as proof of ((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 94.27/94.54 Found (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_introl (cEVEN Xn0)) (cODD Xn0)) x9)) as proof of ((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0))))
% 94.27/94.54 Found (and_rect50 (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_introl (cEVEN Xn0)) (cODD Xn0)) x9))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 94.27/94.54 Found ((and_rect5 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_introl (cEVEN Xn0)) (cODD Xn0)) x9))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 94.27/94.54 Found (((fun (P:Type) (x9:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x9) x8)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_introl (cEVEN Xn0)) (cODD Xn0)) x9))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 94.27/94.54 Found (((fun (P:Type) (x9:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x9) x8)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_introl (cEVEN Xn0)) (cODD Xn0)) x9))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 94.27/94.54 Found x40:=(x4 x50):((or (cEVEN Xn0)) (cODD Xn0))
% 94.27/94.54 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 94.27/94.54 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 94.27/94.54 Found x8:(cEVEN c0)
% 94.27/94.54 Instantiate: Xn0:=c0:fofType
% 94.27/94.54 Found x8 as proof of (cEVEN Xn0)
% 94.27/94.54 Found (or_introl00 x8) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 94.27/94.54 Found ((or_introl0 (cODD Xn0)) x8) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 94.27/94.54 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x8) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 94.27/94.54 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x8) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 94.27/94.54 Found x7:(cODD (cS c0))
% 94.27/94.54 Instantiate: Xn0:=(cS c0):fofType
% 94.27/94.54 Found x7 as proof of (cODD Xn0)
% 94.27/94.54 Found (or_intror00 x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 94.27/94.54 Found ((or_intror0 (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 94.27/94.54 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 94.27/94.54 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 94.27/94.54 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 94.27/94.54 Instantiate: Xn00:=Xn:fofType
% 94.27/94.54 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 94.27/94.54 Found (x3 x40) as proof of (cNUMBER Xn)
% 94.27/94.54 Found (x3 x40) as proof of (cNUMBER Xn)
% 94.27/94.54 Found (x3 x40) as proof of (cNUMBER Xn)
% 94.27/94.54 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 94.27/94.54 Found x40 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 94.27/94.54 Found (x5 x40) as proof of (cNUMBER Xn)
% 94.27/94.54 Found (x5 x40) as proof of (cNUMBER Xn)
% 94.27/94.54 Found (x5 x40) as proof of (cNUMBER Xn)
% 94.27/94.54 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 94.27/94.54 Instantiate: Xn0:=Xn:fofType
% 94.84/95.07 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 94.84/95.07 Found (x5 x20) as proof of (cNUMBER Xn)
% 94.84/95.07 Found (x5 x20) as proof of (cNUMBER Xn)
% 94.84/95.07 Found (x5 x20) as proof of (cNUMBER Xn)
% 94.84/95.07 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 94.84/95.07 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 94.84/95.07 Found (x3 x20) as proof of (cNUMBER Xn)
% 94.84/95.07 Found (x3 x20) as proof of (cNUMBER Xn)
% 94.84/95.07 Found (x3 x20) as proof of (cNUMBER Xn)
% 94.84/95.07 Found x60:=(x6 x70):((or (cEVEN Xn00)) (cODD Xn00))
% 94.84/95.07 Instantiate: Xn00:=Xn:fofType
% 94.84/95.07 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 94.84/95.07 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 94.84/95.07 Found x71:(cNUMBER Xn0)
% 94.84/95.07 Instantiate: Xn0:=Xn:fofType
% 94.84/95.07 Found (fun (x9:(cODD (cS c0)))=> x71) as proof of (cNUMBER Xn)
% 94.84/95.07 Found (fun (x9:(cODD (cS c0)))=> x71) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 94.84/95.07 Found x50:=(x5 x40):(cNUMBER Xn00)
% 94.84/95.07 Found (x5 x40) as proof of (cNUMBER Xn)
% 94.84/95.07 Found (x5 x40) as proof of (cNUMBER Xn)
% 94.84/95.07 Found (fun (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 94.84/95.07 Found (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x5 x40)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 94.84/95.07 Found (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x5 x40)) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn)))
% 94.84/95.07 Found x30:=(x3 x20):(cNUMBER Xn0)
% 94.84/95.07 Found (x3 x20) as proof of (cNUMBER Xn)
% 94.84/95.07 Found (x3 x20) as proof of (cNUMBER Xn)
% 94.84/95.07 Found (fun (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 94.84/95.07 Found (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 94.84/95.07 Found (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn)))
% 94.99/95.24 Found x30:=(x3 x21):(cNUMBER Xn0)
% 94.99/95.24 Found (x3 x21) as proof of (cNUMBER Xn0)
% 94.99/95.24 Found (x3 x21) as proof of (cNUMBER Xn0)
% 94.99/95.24 Found x30:=(x3 x22):(cNUMBER Xn0)
% 94.99/95.24 Instantiate: Xn0:=Xn:fofType
% 94.99/95.24 Found (x3 x22) as proof of (cNUMBER Xn)
% 94.99/95.24 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x22)) as proof of (cNUMBER Xn)
% 94.99/95.24 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x22)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 94.99/95.24 Found x9:(cODD (cS c0))
% 94.99/95.24 Instantiate: Xn0:=(cS c0):fofType
% 94.99/95.24 Found x9 as proof of (cODD Xn0)
% 94.99/95.24 Found (or_intror00 x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 94.99/95.24 Found ((or_intror0 (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 94.99/95.24 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 94.99/95.24 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 94.99/95.24 Found (x7 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9)) as proof of (cNUMBER Xn0)
% 94.99/95.24 Found (fun (x9:(cODD (cS c0)))=> (x7 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9))) as proof of (cNUMBER Xn0)
% 94.99/95.24 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> (x7 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9))) as proof of ((cODD (cS c0))->(cNUMBER Xn0))
% 94.99/95.24 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> (x7 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->(cNUMBER Xn0)))
% 94.99/95.24 Found (and_rect40 (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> (x7 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9)))) as proof of (cNUMBER Xn0)
% 94.99/95.24 Found ((and_rect4 (cNUMBER Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> (x7 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9)))) as proof of (cNUMBER Xn0)
% 94.99/95.24 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x4)) (cNUMBER Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> (x7 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9)))) as proof of (cNUMBER Xn0)
% 94.99/95.24 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x4)) (cNUMBER Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> (x7 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9)))) as proof of (cNUMBER Xn0)
% 94.99/95.24 Found x30:=(x3 x22):(cNUMBER Xn0)
% 94.99/95.24 Instantiate: Xn0:=Xn:fofType
% 94.99/95.24 Found (x3 x22) as proof of (cNUMBER Xn)
% 94.99/95.24 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x22)) as proof of (cNUMBER Xn)
% 95.52/95.79 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x22)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 95.52/95.79 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x22)) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn)))
% 95.52/95.79 Found x30:=(x3 x22):(cNUMBER Xn0)
% 95.52/95.79 Instantiate: Xn0:=Xn:fofType
% 95.52/95.79 Found (x3 x22) as proof of (cNUMBER Xn)
% 95.52/95.79 Found (fun (x3:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x3 x22)) as proof of (cNUMBER Xn)
% 95.52/95.79 Found (fun (x3:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x3 x22)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 95.52/95.79 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 95.52/95.79 Instantiate: Xn0:=Xn:fofType
% 95.52/95.79 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 95.52/95.79 Found (x7 x20) as proof of (cNUMBER Xn)
% 95.52/95.79 Found (x7 x20) as proof of (cNUMBER Xn)
% 95.52/95.79 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x7 x20)) as proof of (cNUMBER Xn)
% 95.52/95.79 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x7 x20)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 95.52/95.79 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 95.52/95.79 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 95.52/95.79 Found (x3 x20) as proof of (cNUMBER Xn)
% 95.52/95.79 Found (x3 x20) as proof of (cNUMBER Xn)
% 95.52/95.79 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 95.52/95.79 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 95.52/95.79 Found x20:=(x2 x31):((or (cEVEN Xn0)) (cODD Xn0))
% 95.52/95.79 Found (x2 x31) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 95.52/95.79 Found (x2 x31) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 95.52/95.79 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 95.52/95.79 Instantiate: Xn00:=Xn:fofType
% 95.52/95.79 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 95.52/95.79 Found (x3 x60) as proof of (cNUMBER Xn)
% 95.52/95.79 Found (x3 x60) as proof of (cNUMBER Xn)
% 95.52/95.79 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x60)) as proof of (cNUMBER Xn)
% 95.52/95.79 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x60)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 95.52/95.79 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 95.52/95.79 Found x60 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 95.52/95.79 Found (x7 x60) as proof of (cNUMBER Xn)
% 95.52/95.79 Found (x7 x60) as proof of (cNUMBER Xn)
% 95.52/95.79 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x7 x60)) as proof of (cNUMBER Xn)
% 95.52/95.79 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x7 x60)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 95.52/95.79 Found x50:=(x5 x40):(cNUMBER Xn0)
% 95.52/95.79 Found (x5 x40) as proof of (cNUMBER Xn0)
% 95.52/95.79 Found (x5 x40) as proof of (cNUMBER Xn0)
% 95.52/95.79 Found x50:=(x5 x41):(cNUMBER Xn0)
% 95.52/95.79 Instantiate: Xn0:=Xn:fofType
% 95.52/95.79 Found (x5 x41) as proof of (cNUMBER Xn)
% 95.52/95.79 Found (x5 x41) as proof of (cNUMBER Xn)
% 95.52/95.79 Found x50:=(x5 x41):(cNUMBER Xn0)
% 96.96/97.18 Found (x5 x41) as proof of (cNUMBER Xn)
% 96.96/97.18 Found (x5 x41) as proof of (cNUMBER Xn)
% 96.96/97.18 Found (x5 x41) as proof of (cNUMBER Xn)
% 96.96/97.18 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 96.96/97.18 Instantiate: Xn00:=Xn:fofType
% 96.96/97.18 Found (fun (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x40) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 96.96/97.18 Found (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x40) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 96.96/97.18 Found (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x40) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->((or (cEVEN Xn0)) (cODD Xn0))))
% 96.96/97.18 Found x30:=(x3 x20):(cNUMBER Xn0)
% 96.96/97.18 Found (x3 x20) as proof of (cNUMBER Xn0)
% 96.96/97.18 Found (x3 x20) as proof of (cNUMBER Xn0)
% 96.96/97.18 Found x30:=(x3 x21):(cNUMBER Xn0)
% 96.96/97.18 Instantiate: Xn0:=Xn:fofType
% 96.96/97.18 Found (x3 x21) as proof of (cNUMBER Xn)
% 96.96/97.18 Found (x3 x21) as proof of (cNUMBER Xn)
% 96.96/97.18 Found x30:=(x3 x20):(cNUMBER Xn0)
% 96.96/97.18 Found (x3 x20) as proof of (cNUMBER Xn)
% 96.96/97.18 Found (x3 x20) as proof of (cNUMBER Xn)
% 96.96/97.18 Found (x3 x20) as proof of (cNUMBER Xn)
% 96.96/97.18 Found x11:(cEVEN c0)
% 96.96/97.18 Instantiate: Xn0:=c0:fofType
% 96.96/97.18 Found x11 as proof of (cEVEN Xn0)
% 96.96/97.18 Found (or_introl00 x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 96.96/97.18 Found ((or_introl0 (cODD Xn0)) x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 96.96/97.18 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 96.96/97.18 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 96.96/97.18 Found (x3 (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11)) as proof of (cNUMBER Xn0)
% 96.96/97.18 Found (x3 (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11)) as proof of (cNUMBER Xn0)
% 96.96/97.18 Found x50:=(x5 x41):(cNUMBER Xn0)
% 96.96/97.18 Found (x5 x41) as proof of (cNUMBER Xn)
% 96.96/97.18 Found (x5 x41) as proof of (cNUMBER Xn)
% 96.96/97.18 Found (fun (x9:(cODD (cS c0)))=> (x5 x41)) as proof of (cNUMBER Xn)
% 96.96/97.18 Found (fun (x9:(cODD (cS c0)))=> (x5 x41)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 96.96/97.18 Found x7:(cODD (cS c0))
% 96.96/97.18 Instantiate: Xn0:=(cS c0):fofType
% 96.96/97.18 Found x7 as proof of (cODD Xn0)
% 96.96/97.18 Found (or_intror00 x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 96.96/97.18 Found ((or_intror0 (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 96.96/97.18 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 96.96/97.18 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 96.96/97.18 Found x11:(cEVEN c0)
% 96.96/97.18 Instantiate: Xn0:=c0:fofType
% 96.96/97.18 Found x11 as proof of (cEVEN Xn0)
% 96.96/97.18 Found (or_introl00 x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 96.96/97.18 Found ((or_introl0 (cODD Xn0)) x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 96.96/97.18 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 96.96/97.18 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 96.96/97.18 Found x9:(cODD (cS c0))
% 96.96/97.18 Instantiate: Xn0:=(cS c0):fofType
% 97.53/97.78 Found x9 as proof of (cODD Xn0)
% 97.53/97.78 Found (or_intror00 x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 97.53/97.78 Found ((or_intror0 (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 97.53/97.78 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 97.53/97.78 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 97.53/97.78 Found (x5 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9)) as proof of (cNUMBER Xn0)
% 97.53/97.78 Found (x5 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9)) as proof of (cNUMBER Xn0)
% 97.53/97.78 Found x70:=(x7 x60):(cNUMBER Xn0)
% 97.53/97.78 Found (x7 x60) as proof of (cNUMBER Xn0)
% 97.53/97.78 Found (x7 x60) as proof of (cNUMBER Xn0)
% 97.53/97.78 Found x70:=(x7 x61):(cNUMBER Xn0)
% 97.53/97.78 Instantiate: Xn0:=Xn:fofType
% 97.53/97.78 Found (x7 x61) as proof of (cNUMBER Xn)
% 97.53/97.78 Found (fun (x9:(cODD (cS c0)))=> (x7 x61)) as proof of (cNUMBER Xn)
% 97.53/97.78 Found (fun (x9:(cODD (cS c0)))=> (x7 x61)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 97.53/97.78 Found x32:(cNUMBER Xn0)
% 97.53/97.78 Instantiate: Xn0:=Xn:fofType
% 97.53/97.78 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x32) as proof of (cNUMBER Xn)
% 97.53/97.78 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x32) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 97.53/97.78 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 97.53/97.78 Instantiate: Xn0:=Xn:fofType
% 97.53/97.78 Found x40 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 97.53/97.78 Found (x7 x40) as proof of (cNUMBER Xn)
% 97.53/97.78 Found (x7 x40) as proof of (cNUMBER Xn)
% 97.53/97.78 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x7 x40)) as proof of (cNUMBER Xn)
% 97.53/97.78 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))
% 97.53/97.78 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)))
% 97.53/97.78 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 97.53/97.78 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 97.53/97.78 Found (x5 x40) as proof of (cNUMBER Xn)
% 97.53/97.78 Found (x5 x40) as proof of (cNUMBER Xn)
% 97.53/97.78 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 97.53/97.78 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))
% 97.53/97.78 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)))
% 97.53/97.78 Found x32:(cNUMBER Xn0)
% 97.53/97.78 Instantiate: Xn0:=Xn:fofType
% 97.53/97.78 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x32) as proof of (cNUMBER Xn)
% 97.53/97.78 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x32) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 97.53/97.78 Found x70:=(x7 (cS c0)):((cODD (cS c0))->(cODD (cS (cS (cS c0)))))
% 97.53/97.78 Found (x7 (cS c0)) as proof of ((cODD (cS c0))->(cODD Xn0))
% 97.53/97.78 Found (x7 (cS c0)) as proof of ((cODD (cS c0))->(cODD Xn0))
% 97.53/97.78 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x7 (cS c0))) as proof of ((cODD (cS c0))->(cODD Xn0))
% 97.53/97.78 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x7 (cS c0))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->(cODD Xn0)))
% 97.53/97.78 Found (and_rect40 (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x7 (cS c0)))) as proof of (cODD Xn0)
% 97.53/97.78 Found ((and_rect4 (cODD Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x7 (cS c0)))) as proof of (cODD Xn0)
% 97.53/97.78 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) (cODD Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x7 (cS c0)))) as proof of (cODD Xn0)
% 97.53/97.78 Found (fun (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) (cODD Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x7 (cS c0))))) as proof of (cODD Xn0)
% 97.53/97.78 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) (cODD Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x7 (cS c0))))) as proof of ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->(cODD Xn0))
% 97.53/97.78 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) (cODD Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x7 (cS c0))))) as proof of (((and ((and (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)))
% 97.53/97.78 Found (and_rect30 (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) (cODD Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x7 (cS c0)))))) as proof of (cODD Xn0)
% 97.53/97.78 Found ((and_rect3 (cODD Xn0)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) (cODD Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x7 (cS c0)))))) as proof of (cODD Xn0)
% 97.53/97.79 Found (((fun (P:Type) (x6:(((and ((and (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 (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) x2)) (cODD Xn0)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) (cODD Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x7 (cS c0)))))) as proof of (cODD Xn0)
% 97.53/97.79 Found (((fun (P:Type) (x6:(((and ((and (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 (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) x2)) (cODD Xn0)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) (cODD Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x7 (cS c0)))))) as proof of (cODD Xn0)
% 97.53/97.79 Found (or_intror00 (((fun (P:Type) (x6:(((and ((and (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 (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) x2)) (cODD Xn0)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) (cODD Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x7 (cS c0))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 97.53/97.79 Found ((or_intror0 (cODD Xn0)) (((fun (P:Type) (x6:(((and ((and (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 (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x2)) (cODD Xn0)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) (cODD Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x7 (cS c0))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 98.04/98.32 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) (((fun (P:Type) (x6:(((and ((and (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 (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x2)) (cODD Xn0)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) (cODD Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x7 (cS c0))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 98.04/98.32 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) (((fun (P:Type) (x6:(((and ((and (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 (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x2)) (cODD Xn0)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) (cODD Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x7 (cS c0))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 98.04/98.32 Found x40:=(x4 x50):((or (cEVEN Xn00)) (cODD Xn00))
% 98.04/98.32 Instantiate: Xn00:=Xn:fofType
% 98.04/98.32 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 98.04/98.32 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 98.04/98.32 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 98.04/98.32 Instantiate: Xn0:=Xn:fofType
% 98.04/98.32 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 98.04/98.32 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 98.04/98.32 Found x60:=(x6 x70):((or (cEVEN Xn0)) (cODD Xn0))
% 98.04/98.32 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 98.04/98.32 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 98.04/98.32 Found x9:(cODD (cS c0))
% 98.04/98.32 Instantiate: Xn0:=(cS c0):fofType
% 98.04/98.32 Found x9 as proof of (cODD Xn0)
% 98.04/98.32 Found (or_intror00 x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 98.04/98.32 Found ((or_intror0 (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 98.04/98.32 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 98.04/98.32 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 98.04/98.32 Found (x7 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9)) as proof of (cNUMBER Xn0)
% 98.04/98.32 Found (x7 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9)) as proof of (cNUMBER Xn0)
% 98.04/98.32 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 98.04/98.32 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 98.04/98.32 Found (x3 x20) as proof of (cNUMBER Xn)
% 98.04/98.32 Found (x3 x20) as proof of (cNUMBER Xn)
% 98.04/98.32 Found (fun (x9:(cODD (cS c0)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 98.04/98.32 Found (fun (x9:(cODD (cS c0)))=> (x3 x20)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 98.04/98.32 Found x50:=(x5 x41):(cNUMBER Xn0)
% 98.04/98.32 Found (x5 x41) as proof of (cNUMBER Xn0)
% 98.04/98.32 Found (x5 x41) as proof of (cNUMBER Xn0)
% 98.04/98.32 Found x50:=(x5 x42):(cNUMBER Xn0)
% 98.04/98.32 Instantiate: Xn0:=Xn:fofType
% 98.04/98.32 Found (x5 x42) as proof of (cNUMBER Xn)
% 98.04/98.32 Found (x5 x42) as proof of (cNUMBER Xn)
% 98.04/98.32 Found x50:=(x5 x40):(cNUMBER Xn0)
% 98.04/98.32 Found (x5 x40) as proof of (cNUMBER Xn)
% 98.04/98.32 Found (x5 x40) as proof of (cNUMBER Xn)
% 98.18/98.40 Found (x5 x40) as proof of (cNUMBER Xn)
% 98.18/98.40 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 98.18/98.40 Instantiate: Xn00:=Xn:fofType
% 98.18/98.40 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 98.18/98.40 Found (x3 x40) as proof of (cNUMBER Xn)
% 98.18/98.40 Found (x3 x40) as proof of (cNUMBER Xn)
% 98.18/98.40 Found (fun (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x40)) as proof of (cNUMBER Xn)
% 98.18/98.40 Found (fun (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x40)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 98.18/98.40 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 98.18/98.40 Found x40 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 98.18/98.40 Found (x5 x40) as proof of (cNUMBER Xn)
% 98.18/98.40 Found (x5 x40) as proof of (cNUMBER Xn)
% 98.18/98.40 Found (fun (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 98.18/98.40 Found (fun (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x5 x40)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 98.18/98.40 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 98.18/98.40 Instantiate: Xn0:=Xn:fofType
% 98.18/98.40 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 98.18/98.40 Found (x5 x20) as proof of (cNUMBER Xn)
% 98.18/98.40 Found (x5 x20) as proof of (cNUMBER Xn)
% 98.18/98.40 Found (fun (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x5 x20)) as proof of (cNUMBER Xn)
% 98.18/98.40 Found (fun (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x5 x20)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 98.18/98.40 Found x7:(cODD (cS c0))
% 98.18/98.40 Instantiate: Xn0:=(cS c0):fofType
% 98.18/98.40 Found x7 as proof of (cODD Xn0)
% 98.18/98.40 Found (or_introl00 x7) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 98.18/98.40 Found ((or_introl0 (cEVEN Xn0)) x7) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 98.18/98.40 Found (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 98.18/98.40 Found (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 98.18/98.40 Found (or_comm_i00 (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 98.18/98.40 Found ((or_comm_i0 (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 98.18/98.40 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 98.18/98.40 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 98.18/98.40 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 98.18/98.40 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 98.18/98.40 Found (x3 x20) as proof of (cNUMBER Xn)
% 98.18/98.40 Found (x3 x20) as proof of (cNUMBER Xn)
% 98.18/98.40 Found (fun (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 98.23/98.49 Found (fun (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 98.23/98.49 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 98.23/98.49 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 98.23/98.49 Found (x3 x20) as proof of (cNUMBER Xn)
% 98.23/98.49 Found (x3 x20) as proof of (cNUMBER Xn)
% 98.23/98.49 Found (x3 x20) as proof of (cNUMBER Xn)
% 98.23/98.49 Found or_introl00:=(or_introl0 (cEVEN Xn0)):((cODD (cS c0))->((or (cODD (cS c0))) (cEVEN Xn0)))
% 98.23/98.49 Found (or_introl0 (cEVEN Xn0)) as proof of ((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0)))
% 98.23/98.49 Found ((or_introl (cODD (cS c0))) (cEVEN Xn0)) as proof of ((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0)))
% 98.23/98.49 Found ((or_introl (cODD (cS c0))) (cEVEN Xn0)) as proof of ((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0)))
% 98.23/98.49 Found (fun (x8:((and (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)))
% 98.23/98.49 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0))))
% 98.23/98.49 Found (and_rect40 (fun (x8:((and (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))
% 98.23/98.49 Found ((and_rect4 ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x8:((and (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))
% 98.23/98.49 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x8:((and (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))
% 98.23/98.49 Found (fun (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x8:((and (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))
% 98.23/98.49 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x8:((and (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)))
% 98.23/98.49 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0))))) as proof of (((and ((and (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))))
% 98.23/98.50 Found (and_rect30 (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x8:((and (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))
% 98.23/98.50 Found ((and_rect3 ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x8:((and (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))
% 98.23/98.50 Found (((fun (P:Type) (x6:(((and ((and (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 (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) x2)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x8:((and (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))
% 98.23/98.50 Found (((fun (P:Type) (x6:(((and ((and (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 (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) x2)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x8:((and (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))
% 98.23/98.50 Found (or_comm_i00 (((fun (P:Type) (x6:(((and ((and (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 (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) x2)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x8:((and (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))
% 98.23/98.50 Found ((or_comm_i0 (cEVEN Xn0)) (((fun (P:Type) (x6:(((and ((and (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 (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x2)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x8:((and (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))
% 98.23/98.50 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((fun (P:Type) (x6:(((and ((and (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 (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x2)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x8:((and (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))
% 98.23/98.50 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((fun (P:Type) (x6:(((and ((and (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 (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x2)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x8:((and (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))
% 100.34/100.59 Found x60:=(x6 x70):((or (cEVEN Xn00)) (cODD Xn00))
% 100.34/100.59 Instantiate: Xn00:=Xn:fofType
% 100.34/100.59 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 100.34/100.59 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 100.34/100.59 Found x70:=(x7 x61):(cNUMBER Xn0)
% 100.34/100.59 Instantiate: Xn0:=Xn:fofType
% 100.34/100.59 Found (x7 x61) as proof of (cNUMBER Xn)
% 100.34/100.59 Found (fun (x9:(cODD (cS c0)))=> (x7 x61)) as proof of (cNUMBER Xn)
% 100.34/100.59 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x7 x61)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 100.34/100.59 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x7 x61)) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 100.34/100.59 Found x40:=(x4 x50):((or (cEVEN Xn0)) (cODD Xn0))
% 100.34/100.59 Found (x4 x50) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 100.34/100.59 Found (x4 x50) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 100.34/100.59 Found (x4 x50) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 100.34/100.59 Found x60:=(x6 x70):((or (cEVEN Xn00)) (cODD Xn00))
% 100.34/100.59 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 100.34/100.59 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 100.34/100.59 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 100.34/100.59 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 100.34/100.59 Instantiate: Xn0:=Xn00:fofType
% 100.34/100.59 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 100.34/100.59 Found x30:=(x3 x21):(cNUMBER Xn0)
% 100.34/100.59 Found (x3 x21) as proof of (cNUMBER Xn0)
% 100.34/100.59 Found (x3 x21) as proof of (cNUMBER Xn0)
% 100.34/100.59 Found x30:=(x3 x22):(cNUMBER Xn0)
% 100.34/100.59 Instantiate: Xn0:=Xn:fofType
% 100.34/100.59 Found (x3 x22) as proof of (cNUMBER Xn)
% 100.34/100.59 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x22)) as proof of (cNUMBER Xn)
% 100.34/100.59 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x22)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 100.34/100.59 Found x30:(cNUMBER Xn0)
% 100.34/100.59 Instantiate: Xn00:=Xn0:fofType
% 100.34/100.59 Found x30 as proof of (cNUMBER Xn00)
% 100.34/100.59 Found x71:(cNUMBER Xn0)
% 100.34/100.59 Instantiate: Xn0:=Xn:fofType
% 100.34/100.59 Found (fun (x9:(cODD (cS c0)))=> x71) as proof of (cNUMBER Xn)
% 100.34/100.59 Found (fun (x9:(cODD (cS c0)))=> x71) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 100.34/100.59 Found x30:(cNUMBER Xn0)
% 100.34/100.59 Instantiate: Xn00:=Xn0:fofType
% 100.34/100.59 Found x30 as proof of (cNUMBER Xn00)
% 100.34/100.59 Found x30:=(x3 x21):(cNUMBER Xn0)
% 100.34/100.59 Found (x3 x21) as proof of (cNUMBER Xn0)
% 100.34/100.59 Found (x3 x21) as proof of (cNUMBER Xn0)
% 100.34/100.59 Found x30:=(x3 x22):(cNUMBER Xn0)
% 100.34/100.59 Instantiate: Xn0:=Xn:fofType
% 100.34/100.59 Found (x3 x22) as proof of (cNUMBER Xn)
% 100.34/100.59 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x22)) as proof of (cNUMBER Xn)
% 100.34/100.59 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x22)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 100.34/100.59 Found x9:(cEVEN c0)
% 100.34/100.59 Instantiate: Xn0:=c0:fofType
% 100.34/100.59 Found (fun (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x9) as proof of (cEVEN Xn0)
% 100.39/100.64 Found (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x9) as proof of ((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->(cEVEN Xn0))
% 100.39/100.64 Found (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x9) as proof of ((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->(cEVEN Xn0)))
% 100.39/100.64 Found (and_rect50 (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x9)) as proof of (cEVEN Xn0)
% 100.39/100.64 Found ((and_rect5 (cEVEN Xn0)) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x9)) as proof of (cEVEN Xn0)
% 100.39/100.64 Found (((fun (P:Type) (x9:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x9) x8)) (cEVEN Xn0)) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x9)) as proof of (cEVEN Xn0)
% 100.39/100.64 Found (((fun (P:Type) (x9:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x9) x8)) (cEVEN Xn0)) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x9)) as proof of (cEVEN Xn0)
% 100.39/100.64 Found (or_introl00 (((fun (P:Type) (x9:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x9) x8)) (cEVEN Xn0)) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x9))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 100.39/100.64 Found ((or_introl0 (cODD Xn0)) (((fun (P:Type) (x9:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x9) x8)) (cEVEN Xn0)) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x9))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 100.39/100.64 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) (((fun (P:Type) (x9:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x9) x8)) (cEVEN Xn0)) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x9))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 100.39/100.64 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) (((fun (P:Type) (x9:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x9) x8)) (cEVEN Xn0)) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x9))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 100.39/100.64 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 100.39/100.64 Instantiate: Xn0:=Xn:fofType
% 100.39/100.64 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 100.39/100.64 Found (x7 x20) as proof of (cNUMBER Xn)
% 100.39/100.64 Found (x7 x20) as proof of (cNUMBER Xn)
% 100.39/100.64 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x7 x20)) as proof of (cNUMBER Xn)
% 100.39/100.64 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))
% 100.39/100.64 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)))
% 100.39/100.64 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 100.39/100.64 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 100.39/100.64 Found (x3 x20) as proof of (cNUMBER Xn)
% 100.39/100.64 Found (x3 x20) as proof of (cNUMBER Xn)
% 100.39/100.64 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 100.39/100.64 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))
% 101.92/102.19 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)))
% 101.92/102.19 Found x20:=(x2 x31):((or (cEVEN Xn0)) (cODD Xn0))
% 101.92/102.19 Found (x2 x31) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 101.92/102.19 Found (x2 x31) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 101.92/102.19 Found x20:=(x2 x31):((or (cEVEN Xn0)) (cODD Xn0))
% 101.92/102.19 Found (x2 x31) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 101.92/102.19 Found (x2 x31) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 101.92/102.19 Found x30:=(x3 x20):(cNUMBER Xn0)
% 101.92/102.19 Found (x3 x20) as proof of (cNUMBER Xn)
% 101.92/102.19 Found (x3 x20) as proof of (cNUMBER Xn)
% 101.92/102.19 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 101.92/102.19 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 101.92/102.19 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 101.92/102.19 Instantiate: Xn0:=Xn00:fofType
% 101.92/102.19 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 101.92/102.19 Found x50:=(x5 x40):(cNUMBER Xn0)
% 101.92/102.19 Found (x5 x40) as proof of (cNUMBER Xn0)
% 101.92/102.19 Found (x5 x40) as proof of (cNUMBER Xn0)
% 101.92/102.19 Found x50:=(x5 x41):(cNUMBER Xn0)
% 101.92/102.19 Instantiate: Xn0:=Xn:fofType
% 101.92/102.19 Found (x5 x41) as proof of (cNUMBER Xn)
% 101.92/102.19 Found (x5 x41) as proof of (cNUMBER Xn)
% 101.92/102.19 Found x50:=(x5 x41):(cNUMBER Xn0)
% 101.92/102.19 Found (x5 x41) as proof of (cNUMBER Xn)
% 101.92/102.19 Found (x5 x41) as proof of (cNUMBER Xn)
% 101.92/102.19 Found (x5 x41) as proof of (cNUMBER Xn)
% 101.92/102.19 Found x9:(cODD (cS c0))
% 101.92/102.19 Instantiate: Xn0:=(cS c0):fofType
% 101.92/102.19 Found x9 as proof of (cODD Xn0)
% 101.92/102.19 Found (or_introl00 x9) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 101.92/102.19 Found ((or_introl0 (cEVEN Xn0)) x9) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 101.92/102.19 Found (((or_introl (cODD Xn0)) (cEVEN Xn0)) x9) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 101.92/102.19 Found (((or_introl (cODD Xn0)) (cEVEN Xn0)) x9) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 101.92/102.19 Found (or_comm_i00 (((or_introl (cODD Xn0)) (cEVEN Xn0)) x9)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 101.92/102.19 Found ((or_comm_i0 (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x9)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 101.92/102.19 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x9)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 101.92/102.19 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x9)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 101.92/102.19 Found x30:=(x3 x21):(cNUMBER Xn0)
% 101.92/102.19 Found (x3 x21) as proof of (cNUMBER Xn0)
% 101.92/102.19 Found (x3 x21) as proof of (cNUMBER Xn0)
% 101.92/102.19 Found x30:=(x3 x22):(cNUMBER Xn0)
% 101.92/102.19 Instantiate: Xn0:=Xn:fofType
% 101.92/102.19 Found (x3 x22) as proof of (cNUMBER Xn)
% 101.92/102.19 Found (x3 x22) as proof of (cNUMBER Xn)
% 101.92/102.19 Found x30:=(x3 x20):(cNUMBER Xn0)
% 101.92/102.19 Found (x3 x20) as proof of (cNUMBER Xn)
% 101.92/102.19 Found (x3 x20) as proof of (cNUMBER Xn)
% 101.92/102.19 Found (x3 x20) as proof of (cNUMBER Xn)
% 101.92/102.19 Found x22:((or (cEVEN Xn0)) (cODD Xn0))
% 101.92/102.19 Found x22 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 101.92/102.19 Found (x3 x22) as proof of (cNUMBER Xn)
% 101.92/102.19 Found (x3 x22) as proof of (cNUMBER Xn)
% 101.92/102.19 Found (x3 x22) as proof of (cNUMBER Xn)
% 101.92/102.19 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 101.92/102.19 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 101.92/102.19 Found (x5 x40) as proof of (cNUMBER Xn)
% 101.92/102.19 Found (x5 x40) as proof of (cNUMBER Xn)
% 101.92/102.19 Found (x5 x40) as proof of (cNUMBER Xn)
% 101.92/102.19 Found x40:=(x4 x50):((or (cEVEN Xn00)) (cODD Xn00))
% 101.92/102.19 Instantiate: Xn00:=Xn:fofType
% 101.92/102.19 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 101.92/102.19 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 101.92/102.19 Found x90:=(x9 x80):(cNUMBER Xn0)
% 102.79/103.03 Found (x9 x80) as proof of (cNUMBER Xn0)
% 102.79/103.03 Found (x9 x80) as proof of (cNUMBER Xn0)
% 102.79/103.03 Found x90:=(x9 x81):(cNUMBER Xn0)
% 102.79/103.03 Instantiate: Xn0:=Xn:fofType
% 102.79/103.03 Found (x9 x81) as proof of (cNUMBER Xn)
% 102.79/103.03 Found (x9 x81) as proof of (cNUMBER Xn)
% 102.79/103.03 Found x90:=(x9 x80):(cNUMBER Xn0)
% 102.79/103.03 Found (x9 x80) as proof of (cNUMBER Xn)
% 102.79/103.03 Found (x9 x80) as proof of (cNUMBER Xn)
% 102.79/103.03 Found (x9 x80) as proof of (cNUMBER Xn)
% 102.79/103.03 Found x50:=(x5 x41):(cNUMBER Xn0)
% 102.79/103.03 Found (x5 x41) as proof of (cNUMBER Xn)
% 102.79/103.03 Found (x5 x41) as proof of (cNUMBER Xn)
% 102.79/103.03 Found (fun (x9:(cODD (cS c0)))=> (x5 x41)) as proof of (cNUMBER Xn)
% 102.79/103.03 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x41)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 102.79/103.03 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x41)) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 102.79/103.03 Found x40:=(x4 x50):((or (cEVEN Xn00)) (cODD Xn00))
% 102.79/103.03 Instantiate: Xn00:=Xn:fofType
% 102.79/103.03 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 102.79/103.03 Found (fun (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x4 x50)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 102.79/103.03 Found (fun (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x4 x50)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 102.79/103.03 Found x50:=(x5 x41):(cNUMBER Xn0)
% 102.79/103.03 Found (x5 x41) as proof of (cNUMBER Xn)
% 102.79/103.03 Found (x5 x41) as proof of (cNUMBER Xn)
% 102.79/103.03 Found (fun (x9:(cODD (cS c0)))=> (x5 x41)) as proof of (cNUMBER Xn)
% 102.79/103.03 Found (fun (x9:(cODD (cS c0)))=> (x5 x41)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 102.79/103.03 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 102.79/103.03 Instantiate: Xn0:=Xn:fofType
% 102.79/103.03 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 102.79/103.03 Found (fun (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x2 x30)) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 102.79/103.03 Found (fun (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x2 x30)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->((or (cEVEN Xn00)) (cODD Xn00)))
% 102.79/103.03 Found x60:=(x6 x70):((or (cEVEN Xn00)) (cODD Xn00))
% 102.79/103.03 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 102.79/103.03 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 102.79/103.03 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 102.79/103.03 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 102.79/103.03 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 102.79/103.03 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 102.79/103.03 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 102.79/103.03 Found x70:=(x7 x60):(cNUMBER Xn0)
% 102.79/103.03 Found (x7 x60) as proof of (cNUMBER Xn0)
% 102.79/103.03 Found (x7 x60) as proof of (cNUMBER Xn0)
% 102.79/103.03 Found x70:=(x7 x61):(cNUMBER Xn0)
% 102.79/103.03 Instantiate: Xn0:=Xn:fofType
% 102.79/103.03 Found (x7 x61) as proof of (cNUMBER Xn)
% 102.79/103.03 Found (fun (x9:(cODD (cS c0)))=> (x7 x61)) as proof of (cNUMBER Xn)
% 102.79/103.03 Found (fun (x9:(cODD (cS c0)))=> (x7 x61)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 102.79/103.03 Found x41:((or (cEVEN Xn0)) (cODD Xn0))
% 102.79/103.03 Found x41 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 102.79/103.03 Found (x5 x41) as proof of (cNUMBER Xn)
% 102.79/103.03 Found (x5 x41) as proof of (cNUMBER Xn)
% 102.79/103.03 Found (x5 x41) as proof of (cNUMBER Xn)
% 103.31/103.56 Found x9:(cEVEN c0)
% 103.31/103.56 Instantiate: Xn0:=c0:fofType
% 103.31/103.56 Found x9 as proof of (cEVEN Xn0)
% 103.31/103.56 Found (or_introl00 x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 103.31/103.56 Found ((or_introl0 (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 103.31/103.56 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 103.31/103.56 Found (fun (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_introl (cEVEN Xn0)) (cODD Xn0)) x9)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 103.31/103.56 Found (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_introl (cEVEN Xn0)) (cODD Xn0)) x9)) as proof of ((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 103.31/103.56 Found (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_introl (cEVEN Xn0)) (cODD Xn0)) x9)) as proof of ((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0))))
% 103.31/103.56 Found (and_rect50 (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_introl (cEVEN Xn0)) (cODD Xn0)) x9))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 103.31/103.56 Found ((and_rect5 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_introl (cEVEN Xn0)) (cODD Xn0)) x9))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 103.31/103.56 Found (((fun (P:Type) (x9:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x9) x8)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_introl (cEVEN Xn0)) (cODD Xn0)) x9))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 103.31/103.56 Found (((fun (P:Type) (x9:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x9) x8)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_introl (cEVEN Xn0)) (cODD Xn0)) x9))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 103.31/103.56 Found x50:=(x5 x41):(cNUMBER Xn0)
% 103.31/103.56 Found (x5 x41) as proof of (cNUMBER Xn0)
% 103.31/103.56 Found (x5 x41) as proof of (cNUMBER Xn0)
% 103.31/103.56 Found x50:=(x5 x42):(cNUMBER Xn0)
% 103.31/103.56 Instantiate: Xn0:=Xn:fofType
% 103.31/103.56 Found (x5 x42) as proof of (cNUMBER Xn)
% 103.31/103.56 Found (x5 x42) as proof of (cNUMBER Xn)
% 103.31/103.56 Found x50:=(x5 x40):(cNUMBER Xn0)
% 103.31/103.56 Found (x5 x40) as proof of (cNUMBER Xn)
% 103.31/103.56 Found (x5 x40) as proof of (cNUMBER Xn)
% 103.31/103.56 Found (x5 x40) as proof of (cNUMBER Xn)
% 103.31/103.56 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 103.31/103.56 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 103.31/103.56 Found (x3 x20) as proof of (cNUMBER Xn)
% 103.31/103.56 Found (x3 x20) as proof of (cNUMBER Xn)
% 103.31/103.56 Found (fun (x9:(cODD (cS c0)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 103.31/103.56 Found (fun (x9:(cODD (cS c0)))=> (x3 x20)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 103.31/103.56 Found x60:=(x6 x70):((or (cEVEN Xn0)) (cODD Xn0))
% 103.31/103.56 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 103.31/103.56 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 103.31/103.56 Found x60:=(x6 x70):((or (cEVEN Xn00)) (cODD Xn00))
% 103.31/103.56 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 103.31/103.56 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 103.31/103.56 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 103.31/103.56 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 103.31/103.56 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 103.31/103.56 Found (x3 x20) as proof of (cNUMBER Xn)
% 103.31/103.56 Found (x3 x20) as proof of (cNUMBER Xn)
% 103.31/103.56 Found (fun (x9:(cODD (cS c0)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 103.31/103.56 Found (fun (x8:((and (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))
% 103.31/103.56 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x20)) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 103.31/103.56 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 103.40/103.66 Instantiate: Xn0:=Xn:fofType
% 103.40/103.66 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 103.40/103.66 Found (x5 x20) as proof of (cNUMBER Xn)
% 103.40/103.66 Found (x5 x20) as proof of (cNUMBER Xn)
% 103.40/103.66 Found (fun (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x5 x20)) as proof of (cNUMBER Xn)
% 103.40/103.66 Found (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x5 x20)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 103.40/103.66 Found (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x5 x20)) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn)))
% 103.40/103.66 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 103.40/103.66 Instantiate: Xn00:=Xn:fofType
% 103.40/103.66 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 103.40/103.66 Found (x3 x40) as proof of (cNUMBER Xn)
% 103.40/103.66 Found (x3 x40) as proof of (cNUMBER Xn)
% 103.40/103.66 Found (fun (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x40)) as proof of (cNUMBER Xn)
% 103.40/103.66 Found (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x40)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 103.40/103.66 Found (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x40)) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn)))
% 103.40/103.66 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 103.40/103.66 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 103.40/103.66 Found (x3 x20) as proof of (cNUMBER Xn)
% 103.40/103.66 Found (x3 x20) as proof of (cNUMBER Xn)
% 103.40/103.66 Found (x3 x20) as proof of (cNUMBER Xn)
% 103.40/103.66 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 103.62/103.85 Found x40 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 103.62/103.85 Found (x5 x40) as proof of (cNUMBER Xn)
% 103.62/103.85 Found (x5 x40) as proof of (cNUMBER Xn)
% 103.62/103.85 Found (fun (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 103.62/103.85 Found (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x5 x40)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 103.62/103.85 Found (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x5 x40)) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn)))
% 103.62/103.85 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 103.62/103.85 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 103.62/103.85 Found (x3 x20) as proof of (cNUMBER Xn)
% 103.62/103.85 Found (x3 x20) as proof of (cNUMBER Xn)
% 103.62/103.85 Found (fun (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 103.62/103.85 Found (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 103.62/103.85 Found (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn)))
% 103.62/103.85 Found x11:(cEVEN c0)
% 103.62/103.85 Instantiate: Xn0:=c0:fofType
% 103.62/103.85 Found x11 as proof of (cEVEN Xn0)
% 103.62/103.85 Found (or_introl00 x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 103.62/103.85 Found ((or_introl0 (cODD Xn0)) x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 103.62/103.85 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 105.92/106.22 Found (fun (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 105.92/106.22 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11)) as proof of ((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 105.92/106.22 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11)) as proof of ((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0))))
% 105.92/106.22 Found (and_rect50 (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 105.92/106.22 Found ((and_rect5 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 105.92/106.22 Found (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 105.92/106.22 Found (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 105.92/106.22 Found x50:(cNUMBER Xn00)
% 105.92/106.22 Instantiate: Xn00:=Xn:fofType
% 105.92/106.22 Found x50 as proof of (cNUMBER Xn)
% 105.92/106.22 Found x30:(cNUMBER Xn0)
% 105.92/106.22 Instantiate: Xn0:=Xn:fofType
% 105.92/106.22 Found x30 as proof of (cNUMBER Xn)
% 105.92/106.22 Found x30:(cNUMBER Xn0)
% 105.92/106.22 Instantiate: Xn00:=Xn0:fofType
% 105.92/106.22 Found x30 as proof of (cNUMBER Xn00)
% 105.92/106.22 Found x70:=(x7 x60):(cNUMBER Xn0)
% 105.92/106.22 Found (x7 x60) as proof of (cNUMBER Xn0)
% 105.92/106.22 Found (x7 x60) as proof of (cNUMBER Xn0)
% 105.92/106.22 Found x70:=(x7 x61):(cNUMBER Xn0)
% 105.92/106.22 Instantiate: Xn0:=Xn:fofType
% 105.92/106.22 Found (x7 x61) as proof of (cNUMBER Xn)
% 105.92/106.22 Found (x7 x61) as proof of (cNUMBER Xn)
% 105.92/106.22 Found x70:=(x7 x61):(cNUMBER Xn0)
% 105.92/106.22 Found (x7 x61) as proof of (cNUMBER Xn)
% 105.92/106.22 Found (x7 x61) as proof of (cNUMBER Xn)
% 105.92/106.22 Found (x7 x61) as proof of (cNUMBER Xn)
% 105.92/106.22 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 105.92/106.22 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 105.92/106.22 Found (x3 x20) as proof of (cNUMBER Xn)
% 105.92/106.22 Found (x3 x20) as proof of (cNUMBER Xn)
% 105.92/106.22 Found (x3 x20) as proof of (cNUMBER Xn)
% 105.92/106.22 Found x40:=(x4 x50):((or (cEVEN Xn00)) (cODD Xn00))
% 105.92/106.22 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 105.92/106.22 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 105.92/106.22 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 105.92/106.22 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 105.92/106.22 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 105.92/106.22 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 105.92/106.22 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 105.92/106.22 Found x30:=(x3 x20):(cNUMBER Xn0)
% 105.92/106.22 Found (x3 x20) as proof of (cNUMBER Xn)
% 105.92/106.22 Found (x3 x20) as proof of (cNUMBER Xn)
% 105.92/106.22 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 105.92/106.22 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 106.50/106.75 Found x30:=(x3 x20):(cNUMBER Xn0)
% 106.50/106.75 Found (x3 x20) as proof of (cNUMBER Xn)
% 106.50/106.75 Found (x3 x20) as proof of (cNUMBER Xn)
% 106.50/106.75 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 106.50/106.75 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 106.50/106.75 Found x30:=(x3 x20):(cNUMBER Xn0)
% 106.50/106.75 Found (x3 x20) as proof of (cNUMBER Xn)
% 106.50/106.75 Found (x3 x20) as proof of (cNUMBER Xn)
% 106.50/106.75 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 106.50/106.75 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 106.50/106.75 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn)))
% 106.50/106.75 Found x50:=(x5 x40):(cNUMBER Xn0)
% 106.50/106.75 Found (x5 x40) as proof of (cNUMBER Xn0)
% 106.50/106.75 Found (x5 x40) as proof of (cNUMBER Xn0)
% 106.50/106.75 Found x50:=(x5 x41):(cNUMBER Xn0)
% 106.50/106.75 Instantiate: Xn0:=Xn:fofType
% 106.50/106.75 Found (x5 x41) as proof of (cNUMBER Xn)
% 106.50/106.75 Found (x5 x41) as proof of (cNUMBER Xn)
% 106.50/106.75 Found x50:=(x5 x41):(cNUMBER Xn0)
% 106.50/106.75 Found (x5 x41) as proof of (cNUMBER Xn)
% 106.50/106.75 Found (x5 x41) as proof of (cNUMBER Xn)
% 106.50/106.75 Found (x5 x41) as proof of (cNUMBER Xn)
% 106.50/106.75 Found x9:(cODD (cS c0))
% 106.50/106.75 Instantiate: Xn0:=(cS c0):fofType
% 106.50/106.75 Found x9 as proof of (cODD Xn0)
% 106.50/106.75 Found (or_intror00 x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 106.50/106.75 Found ((or_intror0 (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 106.50/106.75 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 106.50/106.75 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 106.50/106.75 Found (x5 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9)) as proof of (cNUMBER Xn0)
% 106.50/106.75 Found (x5 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9)) as proof of (cNUMBER Xn0)
% 106.50/106.75 Found x30:(cNUMBER Xn0)
% 106.50/106.75 Instantiate: Xn00:=Xn0:fofType
% 106.50/106.75 Found x30 as proof of (cNUMBER Xn00)
% 106.50/106.75 Found x50:(cNUMBER Xn00)
% 106.50/106.75 Instantiate: Xn0:=Xn00:fofType
% 106.50/106.75 Found x50 as proof of (cNUMBER Xn0)
% 106.50/106.75 Found x60:=(x6 x70):((or (cEVEN Xn00)) (cODD Xn00))
% 106.50/106.75 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 106.50/106.75 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 106.50/106.75 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 107.96/108.22 Found x40:=(x4 x50):((or (cEVEN Xn00)) (cODD Xn00))
% 107.96/108.22 Instantiate: Xn00:=Xn:fofType
% 107.96/108.22 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 107.96/108.22 Found (fun (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x4 x50)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 107.96/108.22 Found (fun (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x4 x50)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 107.96/108.22 Found x30:=(x3 x21):(cNUMBER Xn0)
% 107.96/108.22 Found (x3 x21) as proof of (cNUMBER Xn0)
% 107.96/108.22 Found (x3 x21) as proof of (cNUMBER Xn0)
% 107.96/108.22 Found x30:=(x3 x22):(cNUMBER Xn0)
% 107.96/108.22 Instantiate: Xn0:=Xn:fofType
% 107.96/108.22 Found (x3 x22) as proof of (cNUMBER Xn)
% 107.96/108.22 Found (x3 x22) as proof of (cNUMBER Xn)
% 107.96/108.22 Found x30:=(x3 x20):(cNUMBER Xn0)
% 107.96/108.22 Found (x3 x20) as proof of (cNUMBER Xn)
% 107.96/108.22 Found (x3 x20) as proof of (cNUMBER Xn)
% 107.96/108.22 Found (x3 x20) as proof of (cNUMBER Xn)
% 107.96/108.22 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 107.96/108.22 Instantiate: Xn00:=Xn0:fofType
% 107.96/108.22 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 107.96/108.22 Found x30:(cNUMBER Xn0)
% 107.96/108.22 Instantiate: Xn0:=Xn:fofType
% 107.96/108.22 Found x30 as proof of (cNUMBER Xn)
% 107.96/108.22 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 107.96/108.22 Instantiate: Xn0:=Xn00:fofType
% 107.96/108.22 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 107.96/108.22 Found x30:=(x3 x21):(cNUMBER Xn0)
% 107.96/108.22 Found (x3 x21) as proof of (cNUMBER Xn0)
% 107.96/108.22 Found (x3 x21) as proof of (cNUMBER Xn0)
% 107.96/108.22 Found x30:=(x3 x22):(cNUMBER Xn0)
% 107.96/108.22 Instantiate: Xn0:=Xn:fofType
% 107.96/108.22 Found (x3 x22) as proof of (cNUMBER Xn)
% 107.96/108.22 Found (x3 x22) as proof of (cNUMBER Xn)
% 107.96/108.22 Found x30:=(x3 x20):(cNUMBER Xn0)
% 107.96/108.22 Found (x3 x20) as proof of (cNUMBER Xn)
% 107.96/108.22 Found (x3 x20) as proof of (cNUMBER Xn)
% 107.96/108.22 Found (x3 x20) as proof of (cNUMBER Xn)
% 107.96/108.22 Found x70:=(x7 x61):(cNUMBER Xn0)
% 107.96/108.22 Found (x7 x61) as proof of (cNUMBER Xn)
% 107.96/108.22 Found (x7 x61) as proof of (cNUMBER Xn)
% 107.96/108.22 Found (fun (x9:(cODD (cS c0)))=> (x7 x61)) as proof of (cNUMBER Xn)
% 107.96/108.22 Found (fun (x9:(cODD (cS c0)))=> (x7 x61)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 107.96/108.22 Found x50:(cNUMBER Xn00)
% 107.96/108.22 Instantiate: Xn00:=Xn:fofType
% 107.96/108.22 Found x50 as proof of (cNUMBER Xn)
% 107.96/108.22 Found x9:(cODD (cS c0))
% 107.96/108.22 Instantiate: Xn0:=(cS c0):fofType
% 107.96/108.22 Found x9 as proof of (cODD Xn0)
% 107.96/108.22 Found (or_intror00 x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 107.96/108.22 Found ((or_intror0 (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 107.96/108.22 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 107.96/108.22 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 107.96/108.22 Found (x7 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9)) as proof of (cNUMBER Xn0)
% 107.96/108.22 Found (x7 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9)) as proof of (cNUMBER Xn0)
% 107.96/108.22 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 107.96/108.22 Instantiate: Xn00:=Xn0:fofType
% 107.96/108.22 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 107.96/108.22 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 107.96/108.22 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 107.96/108.22 Found (x5 x40) as proof of (cNUMBER Xn)
% 107.96/108.22 Found (x5 x40) as proof of (cNUMBER Xn)
% 107.96/108.22 Found (x5 x40) as proof of (cNUMBER Xn)
% 107.96/108.22 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 107.96/108.22 Instantiate: Xn0:=Xn00:fofType
% 107.96/108.22 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 107.96/108.22 Found x90:=(x9 x80):(cNUMBER Xn0)
% 107.96/108.22 Found (x9 x80) as proof of (cNUMBER Xn0)
% 107.96/108.22 Found (x9 x80) as proof of (cNUMBER Xn0)
% 107.96/108.22 Found x90:=(x9 x81):(cNUMBER Xn0)
% 107.96/108.22 Instantiate: Xn0:=Xn:fofType
% 107.96/108.22 Found (x9 x81) as proof of (cNUMBER Xn)
% 107.96/108.22 Found (x9 x81) as proof of (cNUMBER Xn)
% 107.96/108.22 Found x90:=(x9 x80):(cNUMBER Xn0)
% 107.96/108.22 Found (x9 x80) as proof of (cNUMBER Xn)
% 107.96/108.22 Found (x9 x80) as proof of (cNUMBER Xn)
% 107.96/108.22 Found (x9 x80) as proof of (cNUMBER Xn)
% 107.96/108.22 Found x50:=(x5 x40):(cNUMBER Xn0)
% 107.96/108.22 Instantiate: Xn0:=Xn:fofType
% 107.96/108.22 Found (x5 x40) as proof of (cNUMBER Xn)
% 107.96/108.22 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 108.08/108.34 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))
% 108.08/108.34 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)))
% 108.08/108.34 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)
% 108.08/108.34 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)
% 108.08/108.34 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)
% 108.08/108.34 Found x7:(cODD (cS c0))
% 108.08/108.34 Instantiate: Xn0:=(cS c0):fofType
% 108.08/108.34 Found x7 as proof of (cODD Xn0)
% 108.08/108.34 Found (or_intror00 x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 108.08/108.34 Found ((or_intror0 (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 108.08/108.34 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 108.08/108.34 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 108.08/108.34 Found (x9 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7)) as proof of (cNUMBER Xn0)
% 108.08/108.34 Found (x9 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7)) as proof of (cNUMBER Xn0)
% 108.08/108.34 Found x41:((or (cEVEN Xn0)) (cODD Xn0))
% 108.08/108.34 Found x41 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 108.08/108.34 Found (x5 x41) as proof of (cNUMBER Xn)
% 108.08/108.34 Found (x5 x41) as proof of (cNUMBER Xn)
% 108.08/108.34 Found (fun (x9:(cODD (cS c0)))=> (x5 x41)) as proof of (cNUMBER Xn)
% 108.08/108.34 Found (fun (x9:(cODD (cS c0)))=> (x5 x41)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 108.08/108.34 Found x40:=(x4 x50):((or (cEVEN Xn00)) (cODD Xn00))
% 108.08/108.34 Instantiate: Xn00:=Xn:fofType
% 108.08/108.34 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 108.08/108.34 Found (fun (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x4 x50)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 108.08/108.34 Found (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x4 x50)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 108.08/108.34 Found (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x4 x50)) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->((or (cEVEN Xn0)) (cODD Xn0))))
% 109.21/109.46 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 109.21/109.46 Instantiate: Xn0:=Xn:fofType
% 109.21/109.46 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 109.21/109.46 Found (fun (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x2 x30)) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 109.21/109.46 Found (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x2 x30)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->((or (cEVEN Xn00)) (cODD Xn00)))
% 109.21/109.46 Found (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x2 x30)) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->((or (cEVEN Xn00)) (cODD Xn00))))
% 109.21/109.46 Found x41:((or (cEVEN Xn0)) (cODD Xn0))
% 109.21/109.46 Found x41 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 109.21/109.46 Found (x5 x41) as proof of (cNUMBER Xn)
% 109.21/109.46 Found (x5 x41) as proof of (cNUMBER Xn)
% 109.21/109.46 Found (x5 x41) as proof of (cNUMBER Xn)
% 109.21/109.46 Found x30:=(x3 x20):(cNUMBER Xn0)
% 109.21/109.46 Instantiate: Xn0:=Xn:fofType
% 109.21/109.46 Found (x3 x20) as proof of (cNUMBER Xn)
% 109.21/109.46 Found (fun (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 109.21/109.46 Found (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 109.21/109.46 Found (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn)))
% 109.21/109.46 Found (and_rect30 (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 109.21/109.46 Found ((and_rect3 (cNUMBER Xn)) (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 109.21/109.46 Found (((fun (P:Type) (x6:(((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->P)))=> (((((and_rect ((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))) P) x6) x0)) (cNUMBER Xn)) (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 109.21/109.46 Found (((fun (P:Type) (x6:(((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->P)))=> (((((and_rect ((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))) P) x6) x0)) (cNUMBER Xn)) (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 109.21/109.46 Found x50:=(x5 x40):(cNUMBER Xn00)
% 109.21/109.46 Instantiate: Xn00:=Xn:fofType
% 109.21/109.46 Found (x5 x40) as proof of (cNUMBER Xn)
% 109.21/109.46 Found (fun (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 109.21/109.46 Found (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x5 x40)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 109.21/109.47 Found (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x5 x40)) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn)))
% 109.21/109.47 Found (and_rect30 (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 109.21/109.47 Found ((and_rect3 (cNUMBER Xn)) (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 109.21/109.47 Found (((fun (P:Type) (x6:(((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->P)))=> (((((and_rect ((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))) P) x6) x0)) (cNUMBER Xn)) (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 109.21/109.47 Found (((fun (P:Type) (x6:(((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->P)))=> (((((and_rect ((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))) P) x6) x0)) (cNUMBER Xn)) (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 110.52/110.79 Found x50:(cNUMBER Xn00)
% 110.52/110.79 Instantiate: Xn00:=Xn:fofType
% 110.52/110.79 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of (cNUMBER Xn)
% 110.52/110.79 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 110.52/110.79 Found x30:(cNUMBER Xn0)
% 110.52/110.79 Instantiate: Xn0:=Xn:fofType
% 110.52/110.79 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of (cNUMBER Xn)
% 110.52/110.79 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 110.52/110.79 Found x70:(cNUMBER Xn00)
% 110.52/110.79 Found x70 as proof of (cNUMBER Xn00)
% 110.52/110.79 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 110.52/110.79 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 110.52/110.79 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 110.52/110.79 Found x50:(cNUMBER Xn0)
% 110.52/110.79 Found x50 as proof of (cNUMBER Xn0)
% 110.52/110.79 Found (x4 x50) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 110.52/110.79 Found (x4 x50) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 110.52/110.79 Found (x4 x50) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 110.52/110.79 Found x80:((or (cEVEN Xn0)) (cODD Xn0))
% 110.52/110.79 Found x80 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 110.52/110.79 Found (x9 x80) as proof of (cNUMBER Xn)
% 110.52/110.79 Found (x9 x80) as proof of (cNUMBER Xn)
% 110.52/110.79 Found (x9 x80) as proof of (cNUMBER Xn)
% 110.52/110.79 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 110.52/110.79 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 110.52/110.79 Found (x3 x20) as proof of (cNUMBER Xn)
% 110.52/110.79 Found (x3 x20) as proof of (cNUMBER Xn)
% 110.52/110.79 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 110.52/110.79 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 110.52/110.79 Found x30:=(x3 x21):(cNUMBER Xn0)
% 110.52/110.79 Instantiate: Xn0:=Xn:fofType
% 110.52/110.79 Found (x3 x21) as proof of (cNUMBER Xn)
% 110.52/110.79 Found (fun (x9:(cODD (cS c0)))=> (x3 x21)) as proof of (cNUMBER Xn)
% 110.52/110.79 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x21)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 110.52/110.79 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x21)) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 110.52/110.79 Found (and_rect40 (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x21))) as proof of (cNUMBER Xn)
% 110.52/110.79 Found ((and_rect4 (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x21))) as proof of (cNUMBER Xn)
% 110.52/110.79 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x21))) as proof of (cNUMBER Xn)
% 110.52/110.79 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x21))) as proof of (cNUMBER Xn)
% 110.92/111.16 Found x9:(cEVEN c0)
% 110.92/111.16 Instantiate: Xn0:=c0:fofType
% 110.92/111.16 Found (fun (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x9) as proof of (cEVEN Xn0)
% 110.92/111.16 Found (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x9) as proof of ((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->(cEVEN Xn0))
% 110.92/111.16 Found (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x9) as proof of ((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->(cEVEN Xn0)))
% 110.92/111.16 Found (and_rect50 (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x9)) as proof of (cEVEN Xn0)
% 110.92/111.16 Found ((and_rect5 (cEVEN Xn0)) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x9)) as proof of (cEVEN Xn0)
% 110.92/111.16 Found (((fun (P:Type) (x9:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x9) x8)) (cEVEN Xn0)) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x9)) as proof of (cEVEN Xn0)
% 110.92/111.16 Found (((fun (P:Type) (x9:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x9) x8)) (cEVEN Xn0)) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x9)) as proof of (cEVEN Xn0)
% 110.92/111.16 Found (or_introl00 (((fun (P:Type) (x9:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x9) x8)) (cEVEN Xn0)) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x9))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 110.92/111.16 Found ((or_introl0 (cODD Xn0)) (((fun (P:Type) (x9:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x9) x8)) (cEVEN Xn0)) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x9))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 110.92/111.16 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) (((fun (P:Type) (x9:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x9) x8)) (cEVEN Xn0)) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x9))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 110.92/111.16 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) (((fun (P:Type) (x9:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x9) x8)) (cEVEN Xn0)) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x9))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 110.92/111.16 Found x30:(cNUMBER Xn0)
% 110.92/111.16 Instantiate: Xn0:=Xn:fofType
% 110.92/111.16 Found (fun (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30) as proof of (cNUMBER Xn)
% 110.92/111.16 Found (fun (x5:(cODD Xn0)) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 110.92/111.19 Found (fun (x5:(cODD Xn0)) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30) as proof of ((cODD Xn0)->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn)))
% 110.92/111.19 Found x30:(cNUMBER Xn0)
% 110.92/111.19 Instantiate: Xn0:=Xn:fofType
% 110.92/111.19 Found (fun (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30) as proof of (cNUMBER Xn)
% 110.92/111.19 Found (fun (x5:(cEVEN Xn0)) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 110.92/111.19 Found (fun (x5:(cEVEN Xn0)) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30) as proof of ((cEVEN Xn0)->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn)))
% 110.92/111.19 Found ((or_ind00 (fun (x5:(cEVEN Xn0)) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30)) (fun (x5:(cODD Xn0)) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 110.92/111.19 Found (((or_ind0 ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))) (fun (x5:(cEVEN Xn0)) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30)) (fun (x5:(cODD Xn0)) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 110.92/111.19 Found ((((fun (P:Prop) (x5:((cEVEN Xn0)->P)) (x6:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x5) x6) x20)) ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))) (fun (x5:(cEVEN Xn0)) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30)) (fun (x5:(cODD Xn0)) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 111.73/112.00 Found ((((fun (P:Prop) (x5:((cEVEN Xn0)->P)) (x6:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x5) x6) (x2 x31))) ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))) (fun (x5:(cEVEN Xn0)) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30)) (fun (x5:(cODD Xn0)) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 111.73/112.00 Found ((((fun (P:Prop) (x5:((cEVEN Xn0)->P)) (x6:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x5) x6) (x2 x31))) ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))) (fun (x5:(cEVEN Xn0)) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30)) (fun (x5:(cODD Xn0)) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 111.73/112.00 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 111.73/112.00 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 111.73/112.00 Found (x3 x20) as proof of (cNUMBER Xn)
% 111.73/112.00 Found (x3 x20) as proof of (cNUMBER Xn)
% 111.73/112.00 Found (x3 x20) as proof of (cNUMBER Xn)
% 111.73/112.00 Found x40:=(x4 x50):((or (cEVEN Xn00)) (cODD Xn00))
% 111.73/112.00 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 111.73/112.00 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 111.73/112.00 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 111.73/112.00 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 111.73/112.00 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 111.73/112.00 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 111.73/112.00 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 111.73/112.00 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 111.73/112.00 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 111.73/112.00 Found (x3 x20) as proof of (cNUMBER Xn)
% 111.73/112.00 Found (x3 x20) as proof of (cNUMBER Xn)
% 111.73/112.00 Found (x3 x20) as proof of (cNUMBER Xn)
% 111.73/112.00 Found x70:=(x7 x60):(cNUMBER Xn0)
% 111.73/112.00 Found (x7 x60) as proof of (cNUMBER Xn0)
% 111.73/112.00 Found (x7 x60) as proof of (cNUMBER Xn0)
% 111.73/112.00 Found x70:=(x7 x61):(cNUMBER Xn0)
% 111.73/112.00 Instantiate: Xn0:=Xn:fofType
% 111.73/112.00 Found (x7 x61) as proof of (cNUMBER Xn)
% 111.73/112.00 Found (x7 x61) as proof of (cNUMBER Xn)
% 111.73/112.00 Found x70:=(x7 x61):(cNUMBER Xn0)
% 111.73/112.00 Found (x7 x61) as proof of (cNUMBER Xn)
% 111.73/112.00 Found (x7 x61) as proof of (cNUMBER Xn)
% 111.73/112.00 Found (x7 x61) as proof of (cNUMBER Xn)
% 111.73/112.00 Found x30:=(x3 x20):(cNUMBER Xn0)
% 112.35/112.60 Instantiate: Xn0:=Xn:fofType
% 112.35/112.60 Found (x3 x20) as proof of (cNUMBER Xn)
% 112.35/112.60 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 112.35/112.60 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))
% 112.35/112.60 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)))
% 112.35/112.60 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)
% 112.35/112.60 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)
% 112.35/112.60 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)
% 112.35/112.60 Found x90:(cNUMBER Xn00)
% 112.35/112.60 Instantiate: Xn00:=Xn:fofType
% 112.35/112.60 Found x90 as proof of (cNUMBER Xn)
% 112.35/112.60 Found x11:(cEVEN c0)
% 112.35/112.60 Instantiate: Xn0:=c0:fofType
% 112.35/112.60 Found (fun (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11) as proof of (cEVEN Xn0)
% 112.35/112.60 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11) as proof of ((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->(cEVEN Xn0))
% 112.35/112.60 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11) as proof of ((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->(cEVEN Xn0)))
% 112.35/112.60 Found (and_rect50 (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11)) as proof of (cEVEN Xn0)
% 112.35/112.60 Found ((and_rect5 (cEVEN Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11)) as proof of (cEVEN Xn0)
% 112.35/112.60 Found (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cEVEN Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11)) as proof of (cEVEN Xn0)
% 112.35/112.60 Found (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cEVEN Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11)) as proof of (cEVEN Xn0)
% 112.35/112.60 Found (or_introl00 (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cEVEN Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 112.35/112.60 Found ((or_introl0 (cODD Xn0)) (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x11) x8)) (cEVEN Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 112.35/112.60 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x11) x8)) (cEVEN Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 113.42/113.70 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x11) x8)) (cEVEN Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 113.42/113.70 Found x30:(cNUMBER Xn0)
% 113.42/113.70 Instantiate: Xn0:=Xn:fofType
% 113.42/113.70 Found x30 as proof of (cNUMBER Xn)
% 113.42/113.70 Found x50:(cNUMBER Xn00)
% 113.42/113.70 Instantiate: Xn00:=Xn:fofType
% 113.42/113.70 Found x50 as proof of (cNUMBER Xn)
% 113.42/113.70 Found x60:=(x6 x70):((or (cEVEN Xn00)) (cODD Xn00))
% 113.42/113.70 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 113.42/113.70 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 113.42/113.70 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 113.42/113.70 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 113.42/113.70 Instantiate: Xn00:=Xn0:fofType
% 113.42/113.70 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 113.42/113.70 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 113.42/113.70 Instantiate: Xn0:=Xn00:fofType
% 113.42/113.70 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 113.42/113.70 Found x30:(cNUMBER Xn0)
% 113.42/113.70 Instantiate: Xn0:=Xn:fofType
% 113.42/113.70 Found x30 as proof of (cNUMBER Xn)
% 113.42/113.70 Found x30:=(x3 x21):(cNUMBER Xn0)
% 113.42/113.70 Found (x3 x21) as proof of (cNUMBER Xn0)
% 113.42/113.70 Found (x3 x21) as proof of (cNUMBER Xn0)
% 113.42/113.70 Found x30:=(x3 x22):(cNUMBER Xn0)
% 113.42/113.70 Instantiate: Xn0:=Xn:fofType
% 113.42/113.70 Found (x3 x22) as proof of (cNUMBER Xn)
% 113.42/113.70 Found (x3 x22) as proof of (cNUMBER Xn)
% 113.42/113.70 Found x30:=(x3 x20):(cNUMBER Xn0)
% 113.42/113.70 Found (x3 x20) as proof of (cNUMBER Xn)
% 113.42/113.70 Found (x3 x20) as proof of (cNUMBER Xn)
% 113.42/113.70 Found (x3 x20) as proof of (cNUMBER Xn)
% 113.42/113.70 Found x30:=(x3 x21):(cNUMBER Xn0)
% 113.42/113.70 Found (x3 x21) as proof of (cNUMBER Xn0)
% 113.42/113.70 Found (x3 x21) as proof of (cNUMBER Xn0)
% 113.42/113.70 Found x30:=(x3 x22):(cNUMBER Xn0)
% 113.42/113.70 Instantiate: Xn0:=Xn:fofType
% 113.42/113.70 Found (x3 x22) as proof of (cNUMBER Xn)
% 113.42/113.70 Found (x3 x22) as proof of (cNUMBER Xn)
% 113.42/113.70 Found x30:=(x3 x20):(cNUMBER Xn0)
% 113.42/113.70 Found (x3 x20) as proof of (cNUMBER Xn)
% 113.42/113.70 Found (x3 x20) as proof of (cNUMBER Xn)
% 113.42/113.70 Found (x3 x20) as proof of (cNUMBER Xn)
% 113.42/113.70 Found x70:=(x7 x61):(cNUMBER Xn0)
% 113.42/113.70 Found (x7 x61) as proof of (cNUMBER Xn)
% 113.42/113.70 Found (x7 x61) as proof of (cNUMBER Xn)
% 113.42/113.70 Found (fun (x9:(cODD (cS c0)))=> (x7 x61)) as proof of (cNUMBER Xn)
% 113.42/113.70 Found (fun (x9:(cODD (cS c0)))=> (x7 x61)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 113.42/113.70 Found x40:=(x4 x50):((or (cEVEN Xn00)) (cODD Xn00))
% 113.42/113.70 Instantiate: Xn00:=Xn:fofType
% 113.42/113.70 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 113.42/113.70 Found (fun (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x4 x50)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 113.42/113.70 Found (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x4 x50)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 113.42/113.70 Found (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x4 x50)) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->((or (cEVEN Xn0)) (cODD Xn0))))
% 114.25/114.51 Found x70:=(x7 x61):(cNUMBER Xn0)
% 114.25/114.51 Found (x7 x61) as proof of (cNUMBER Xn)
% 114.25/114.51 Found (x7 x61) as proof of (cNUMBER Xn)
% 114.25/114.51 Found (fun (x9:(cODD (cS c0)))=> (x7 x61)) as proof of (cNUMBER Xn)
% 114.25/114.51 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x7 x61)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 114.25/114.51 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x7 x61)) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 114.25/114.51 Found x30:=(x3 x21):(cNUMBER Xn0)
% 114.25/114.51 Found (x3 x21) as proof of (cNUMBER Xn0)
% 114.25/114.51 Found (x3 x21) as proof of (cNUMBER Xn0)
% 114.25/114.51 Found x30:=(x3 x22):(cNUMBER Xn0)
% 114.25/114.51 Instantiate: Xn0:=Xn:fofType
% 114.25/114.51 Found (x3 x22) as proof of (cNUMBER Xn)
% 114.25/114.51 Found (x3 x22) as proof of (cNUMBER Xn)
% 114.25/114.51 Found x30:=(x3 x20):(cNUMBER Xn0)
% 114.25/114.51 Found (x3 x20) as proof of (cNUMBER Xn)
% 114.25/114.51 Found (x3 x20) as proof of (cNUMBER Xn)
% 114.25/114.51 Found (x3 x20) as proof of (cNUMBER Xn)
% 114.25/114.51 Found x30:(cNUMBER Xn0)
% 114.25/114.51 Found x30 as proof of (cNUMBER Xn0)
% 114.25/114.51 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 114.25/114.51 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 114.25/114.51 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 114.25/114.51 Found x70:(cNUMBER Xn00)
% 114.25/114.51 Found x70 as proof of (cNUMBER Xn00)
% 114.25/114.51 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 114.25/114.51 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 114.25/114.51 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 114.25/114.51 Found x50:=(x5 x40):(cNUMBER Xn0)
% 114.25/114.51 Instantiate: Xn0:=Xn:fofType
% 114.25/114.51 Found (x5 x40) as proof of (cNUMBER Xn)
% 114.25/114.51 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 114.25/114.51 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))
% 114.25/114.51 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)))
% 114.25/114.51 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)
% 114.25/114.51 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)
% 114.25/114.51 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)
% 114.25/114.51 Found x90:=(x9 x81):(cNUMBER Xn0)
% 114.25/114.51 Instantiate: Xn0:=Xn:fofType
% 114.25/114.51 Found (x9 x81) as proof of (cNUMBER Xn)
% 114.25/114.51 Found (fun (x9:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x9 x81)) as proof of (cNUMBER Xn)
% 114.25/114.51 Found (fun (x9:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x9 x81)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 114.25/114.51 Found x30:=(x3 x21):(cNUMBER Xn0)
% 114.25/114.51 Instantiate: Xn0:=Xn:fofType
% 114.25/114.51 Found (x3 x21) as proof of (cNUMBER Xn)
% 114.25/114.51 Found (fun (x9:(cODD (cS c0)))=> (x3 x21)) as proof of (cNUMBER Xn)
% 114.25/114.51 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x21)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 114.25/114.51 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x21)) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 114.35/114.63 Found (and_rect40 (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x21))) as proof of (cNUMBER Xn)
% 114.35/114.63 Found ((and_rect4 (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x21))) as proof of (cNUMBER Xn)
% 114.35/114.63 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x21))) as proof of (cNUMBER Xn)
% 114.35/114.63 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x21)))) as proof of (cNUMBER Xn)
% 114.35/114.63 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x21)))) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 114.35/114.63 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x21)))) as proof of (((and ((and (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)))
% 114.35/114.63 Found x9:(cEVEN c0)
% 114.35/114.63 Instantiate: Xn0:=c0:fofType
% 114.35/114.63 Found x9 as proof of (cEVEN Xn0)
% 114.35/114.63 Found (or_introl00 x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 114.35/114.63 Found ((or_introl0 (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 114.35/114.63 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 114.35/114.63 Found (fun (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_introl (cEVEN Xn0)) (cODD Xn0)) x9)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 114.35/114.63 Found (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_introl (cEVEN Xn0)) (cODD Xn0)) x9)) as proof of ((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 114.35/114.63 Found (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_introl (cEVEN Xn0)) (cODD Xn0)) x9)) as proof of ((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0))))
% 114.35/114.63 Found (and_rect50 (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_introl (cEVEN Xn0)) (cODD Xn0)) x9))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 114.35/114.63 Found ((and_rect5 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_introl (cEVEN Xn0)) (cODD Xn0)) x9))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 114.96/115.21 Found (((fun (P:Type) (x9:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x9) x8)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_introl (cEVEN Xn0)) (cODD Xn0)) x9))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 114.96/115.21 Found (((fun (P:Type) (x9:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x9) x8)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_introl (cEVEN Xn0)) (cODD Xn0)) x9))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 114.96/115.21 Found x61:((or (cEVEN Xn0)) (cODD Xn0))
% 114.96/115.21 Found x61 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 114.96/115.21 Found (x7 x61) as proof of (cNUMBER Xn)
% 114.96/115.21 Found (x7 x61) as proof of (cNUMBER Xn)
% 114.96/115.21 Found (x7 x61) as proof of (cNUMBER Xn)
% 114.96/115.21 Found x41:((or (cEVEN Xn0)) (cODD Xn0))
% 114.96/115.21 Found x41 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 114.96/115.21 Found (x5 x41) as proof of (cNUMBER Xn)
% 114.96/115.21 Found (x5 x41) as proof of (cNUMBER Xn)
% 114.96/115.21 Found (fun (x9:(cODD (cS c0)))=> (x5 x41)) as proof of (cNUMBER Xn)
% 114.96/115.21 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x41)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 114.96/115.21 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x41)) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 114.96/115.21 Found x30:=(x3 x20):(cNUMBER Xn0)
% 114.96/115.21 Found (x3 x20) as proof of (cNUMBER Xn0)
% 114.96/115.21 Found (x3 x20) as proof of (cNUMBER Xn0)
% 114.96/115.21 Found x41:((or (cEVEN Xn0)) (cODD Xn0))
% 114.96/115.21 Found x41 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 114.96/115.21 Found (x5 x41) as proof of (cNUMBER Xn)
% 114.96/115.21 Found (x5 x41) as proof of (cNUMBER Xn)
% 114.96/115.21 Found (fun (x9:(cODD (cS c0)))=> (x5 x41)) as proof of (cNUMBER Xn)
% 114.96/115.21 Found (fun (x9:(cODD (cS c0)))=> (x5 x41)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 114.96/115.21 Found x70:(cNUMBER Xn00)
% 114.96/115.21 Found x70 as proof of (cNUMBER Xn00)
% 114.96/115.21 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 114.96/115.21 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 114.96/115.21 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 114.96/115.21 Found x30:=(x3 x20):(cNUMBER Xn0)
% 114.96/115.21 Instantiate: Xn0:=Xn:fofType
% 114.96/115.21 Found (x3 x20) as proof of (cNUMBER Xn)
% 114.96/115.21 Found (fun (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 114.96/115.21 Found (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 114.96/115.21 Found (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn)))
% 114.96/115.21 Found (and_rect30 (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 114.96/115.21 Found ((and_rect3 (cNUMBER Xn)) (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 114.96/115.21 Found (((fun (P:Type) (x6:(((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->P)))=> (((((and_rect ((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))) P) x6) x0)) (cNUMBER Xn)) (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 114.96/115.21 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (((fun (P:Type) (x6:(((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->P)))=> (((((and_rect ((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))) P) x6) x0)) (cNUMBER Xn)) (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)))) as proof of (cNUMBER Xn)
% 114.96/115.21 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (((fun (P:Type) (x6:(((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->P)))=> (((((and_rect ((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))) P) x6) x0)) (cNUMBER Xn)) (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)))) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 115.02/115.30 Found x41:((or (cEVEN Xn0)) (cODD Xn0))
% 115.02/115.30 Found x41 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 115.02/115.30 Found (x5 x41) as proof of (cNUMBER Xn)
% 115.02/115.30 Found (x5 x41) as proof of (cNUMBER Xn)
% 115.02/115.30 Found (x5 x41) as proof of (cNUMBER Xn)
% 115.02/115.30 Found x50:=(x5 x40):(cNUMBER Xn00)
% 115.02/115.30 Instantiate: Xn00:=Xn:fofType
% 115.02/115.30 Found (x5 x40) as proof of (cNUMBER Xn)
% 115.02/115.30 Found (fun (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 115.02/115.30 Found (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x5 x40)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 115.02/115.30 Found (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x5 x40)) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn)))
% 115.02/115.30 Found (and_rect30 (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 115.02/115.30 Found ((and_rect3 (cNUMBER Xn)) (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 115.02/115.30 Found (((fun (P:Type) (x6:(((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->P)))=> (((((and_rect ((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))) P) x6) x0)) (cNUMBER Xn)) (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 115.02/115.36 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (((fun (P:Type) (x6:(((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->P)))=> (((((and_rect ((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))) P) x6) x0)) (cNUMBER Xn)) (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x5 x40)))) as proof of (cNUMBER Xn)
% 115.02/115.36 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (((fun (P:Type) (x6:(((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->P)))=> (((((and_rect ((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))) P) x6) x0)) (cNUMBER Xn)) (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x5 x40)))) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 115.02/115.36 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 115.02/115.36 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 115.02/115.36 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 115.02/115.36 Found x31:(cNUMBER Xn0)
% 115.02/115.36 Instantiate: Xn0:=Xn:fofType
% 115.02/115.36 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x31) as proof of (cNUMBER Xn)
% 116.42/116.69 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))
% 116.42/116.69 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)))
% 116.42/116.69 Found x11:(cEVEN c0)
% 116.42/116.69 Instantiate: Xn0:=c0:fofType
% 116.42/116.69 Found x11 as proof of (cEVEN Xn0)
% 116.42/116.69 Found (or_introl00 x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 116.42/116.69 Found ((or_introl0 (cODD Xn0)) x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 116.42/116.69 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 116.42/116.69 Found (fun (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 116.42/116.69 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11)) as proof of ((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 116.42/116.69 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11)) as proof of ((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0))))
% 116.42/116.69 Found (and_rect50 (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 116.42/116.69 Found ((and_rect5 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 116.42/116.69 Found (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 116.42/116.69 Found (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 116.42/116.69 Found x70:(cNUMBER Xn00)
% 116.42/116.69 Instantiate: Xn00:=Xn:fofType
% 116.42/116.69 Found x70 as proof of (cNUMBER Xn)
% 116.42/116.69 Found x30:(cNUMBER Xn0)
% 116.42/116.69 Instantiate: Xn0:=Xn:fofType
% 116.42/116.69 Found x30 as proof of (cNUMBER Xn)
% 116.42/116.69 Found x40:=(x4 x50):((or (cEVEN Xn00)) (cODD Xn00))
% 116.42/116.69 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 116.42/116.69 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 116.42/116.69 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 116.42/116.69 Found x40:=(x4 x50):((or (cEVEN Xn00)) (cODD Xn00))
% 116.42/116.69 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 116.42/116.69 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 116.42/116.69 Found (fun (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x4 x50)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 116.42/116.69 Found (fun (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x4 x50)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 116.94/117.23 Found x80:((or (cEVEN Xn0)) (cODD Xn0))
% 116.94/117.23 Found x80 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 116.94/117.23 Found (x9 x80) as proof of (cNUMBER Xn)
% 116.94/117.23 Found (x9 x80) as proof of (cNUMBER Xn)
% 116.94/117.23 Found (x9 x80) as proof of (cNUMBER Xn)
% 116.94/117.23 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 116.94/117.23 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 116.94/117.23 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 116.94/117.23 Found (fun (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x2 x30)) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 116.94/117.23 Found (fun (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x2 x30)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->((or (cEVEN Xn00)) (cODD Xn00)))
% 116.94/117.23 Found x30:=(x3 x21):(cNUMBER Xn0)
% 116.94/117.23 Instantiate: Xn0:=Xn:fofType
% 116.94/117.23 Found (x3 x21) as proof of (cNUMBER Xn)
% 116.94/117.23 Found (fun (x9:(cODD (cS c0)))=> (x3 x21)) as proof of (cNUMBER Xn)
% 116.94/117.23 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x21)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 116.94/117.23 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x21)) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 116.94/117.23 Found (and_rect40 (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x21))) as proof of (cNUMBER Xn)
% 116.94/117.23 Found ((and_rect4 (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x21))) as proof of (cNUMBER Xn)
% 116.94/117.23 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x21))) as proof of (cNUMBER Xn)
% 116.94/117.23 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x21)))) as proof of (cNUMBER Xn)
% 116.94/117.23 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x21)))) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 116.94/117.23 Found x30:(cNUMBER Xn0)
% 116.94/117.23 Instantiate: Xn0:=Xn:fofType
% 116.94/117.23 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of (cNUMBER Xn)
% 116.94/117.23 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 116.94/117.23 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of (((and ((and (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)))
% 117.24/117.53 Found x50:(cNUMBER Xn00)
% 117.24/117.53 Instantiate: Xn00:=Xn:fofType
% 117.24/117.53 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of (cNUMBER Xn)
% 117.24/117.53 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 117.24/117.53 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of (((and ((and (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)))
% 117.24/117.53 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 117.24/117.53 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 117.24/117.53 Found (x3 x20) as proof of (cNUMBER Xn)
% 117.24/117.53 Found (x3 x20) as proof of (cNUMBER Xn)
% 117.24/117.53 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 117.24/117.53 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 117.24/117.53 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn)))
% 117.24/117.53 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 117.24/117.53 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 117.24/117.53 Found (x3 x20) as proof of (cNUMBER Xn)
% 117.24/117.53 Found (x3 x20) as proof of (cNUMBER Xn)
% 117.24/117.53 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 117.24/117.53 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 117.24/117.53 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 117.24/117.53 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 117.24/117.53 Found (x3 x20) as proof of (cNUMBER Xn)
% 117.24/117.53 Found (x3 x20) as proof of (cNUMBER Xn)
% 118.02/118.32 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 118.02/118.32 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 118.02/118.32 Found x30:=(x3 x21):(cNUMBER Xn0)
% 118.02/118.32 Instantiate: Xn0:=Xn:fofType
% 118.02/118.32 Found (x3 x21) as proof of (cNUMBER Xn)
% 118.02/118.32 Found (fun (x9:(cODD (cS c0)))=> (x3 x21)) as proof of (cNUMBER Xn)
% 118.02/118.32 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x21)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 118.02/118.32 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x21)) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 118.02/118.32 Found (and_rect40 (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x21))) as proof of (cNUMBER Xn)
% 118.02/118.32 Found ((and_rect4 (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x21))) as proof of (cNUMBER Xn)
% 118.02/118.32 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x21))) as proof of (cNUMBER Xn)
% 118.02/118.32 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x21))) as proof of (cNUMBER Xn)
% 118.02/118.32 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 118.02/118.32 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 118.02/118.32 Found (x3 x20) as proof of (cNUMBER Xn)
% 118.02/118.32 Found (x3 x20) as proof of (cNUMBER Xn)
% 118.02/118.32 Found (x3 x20) as proof of (cNUMBER Xn)
% 118.02/118.32 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 118.02/118.32 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 118.02/118.32 Found (x3 x20) as proof of (cNUMBER Xn)
% 118.02/118.32 Found (x3 x20) as proof of (cNUMBER Xn)
% 118.02/118.32 Found (x3 x20) as proof of (cNUMBER Xn)
% 118.02/118.32 Found x30:(cNUMBER Xn0)
% 118.02/118.32 Instantiate: Xn0:=Xn:fofType
% 118.02/118.32 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30) as proof of (cNUMBER Xn)
% 118.02/118.32 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 118.02/118.32 Found x30:(cNUMBER Xn0)
% 118.02/118.32 Instantiate: Xn0:=Xn:fofType
% 118.02/118.32 Found (fun (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30) as proof of (cNUMBER Xn)
% 118.02/118.32 Found (fun (x5:(cEVEN Xn0)) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 118.02/118.32 Found (fun (x5:(cEVEN Xn0)) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30) as proof of ((cEVEN Xn0)->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn)))
% 118.02/118.35 Found x30:(cNUMBER Xn0)
% 118.02/118.35 Instantiate: Xn0:=Xn:fofType
% 118.02/118.35 Found (fun (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30) as proof of (cNUMBER Xn)
% 118.02/118.35 Found (fun (x5:(cODD Xn0)) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 118.02/118.35 Found (fun (x5:(cODD Xn0)) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30) as proof of ((cODD Xn0)->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn)))
% 118.02/118.35 Found ((or_ind00 (fun (x5:(cEVEN Xn0)) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30)) (fun (x5:(cODD Xn0)) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 118.02/118.35 Found (((or_ind0 ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))) (fun (x5:(cEVEN Xn0)) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30)) (fun (x5:(cODD Xn0)) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 118.02/118.35 Found ((((fun (P:Prop) (x5:((cEVEN Xn0)->P)) (x6:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x5) x6) x20)) ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))) (fun (x5:(cEVEN Xn0)) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30)) (fun (x5:(cODD Xn0)) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 118.32/118.63 Found ((((fun (P:Prop) (x5:((cEVEN Xn0)->P)) (x6:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x5) x6) (x2 x31))) ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))) (fun (x5:(cEVEN Xn0)) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30)) (fun (x5:(cODD Xn0)) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 118.32/118.63 Found ((((fun (P:Prop) (x5:((cEVEN Xn0)->P)) (x6:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x5) x6) (x2 x31))) ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))) (fun (x5:(cEVEN Xn0)) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30)) (fun (x5:(cODD Xn0)) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 118.32/118.63 Found x50:(cNUMBER Xn00)
% 118.32/118.63 Found x50 as proof of (cNUMBER Xn00)
% 118.32/118.63 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 118.32/118.63 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 118.32/118.63 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 118.32/118.63 Found x30:(cNUMBER Xn0)
% 118.32/118.63 Found x30 as proof of (cNUMBER Xn0)
% 118.32/118.63 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 118.32/118.63 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 118.32/118.63 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 118.32/118.63 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 118.32/118.63 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 118.32/118.63 Found (x3 x20) as proof of (cNUMBER Xn)
% 118.32/118.63 Found (x3 x20) as proof of (cNUMBER Xn)
% 118.32/118.63 Found (x3 x20) as proof of (cNUMBER Xn)
% 118.32/118.63 Found x30:=(x3 x20):(cNUMBER Xn0)
% 118.32/118.63 Instantiate: Xn0:=Xn:fofType
% 118.32/118.63 Found (x3 x20) as proof of (cNUMBER Xn)
% 118.32/118.63 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 118.32/118.63 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))
% 118.32/118.63 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)))
% 118.32/118.63 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)
% 118.32/118.65 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)
% 118.32/118.65 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)
% 118.32/118.65 Found x30:(cNUMBER Xn0)
% 118.32/118.65 Instantiate: Xn0:=Xn:fofType
% 118.32/118.65 Found (fun (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30) as proof of (cNUMBER Xn)
% 118.32/118.65 Found (fun (x5:(cEVEN Xn0)) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 118.32/118.65 Found (fun (x5:(cEVEN Xn0)) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30) as proof of ((cEVEN Xn0)->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn)))
% 118.32/118.65 Found x30:(cNUMBER Xn0)
% 118.32/118.65 Instantiate: Xn0:=Xn:fofType
% 118.32/118.65 Found (fun (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30) as proof of (cNUMBER Xn)
% 118.32/118.65 Found (fun (x5:(cODD Xn0)) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 118.32/118.65 Found (fun (x5:(cODD Xn0)) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30) as proof of ((cODD Xn0)->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn)))
% 118.32/118.65 Found ((or_ind00 (fun (x5:(cEVEN Xn0)) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30)) (fun (x5:(cODD Xn0)) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 118.32/118.65 Found (((or_ind0 ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))) (fun (x5:(cEVEN Xn0)) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30)) (fun (x5:(cODD Xn0)) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 118.32/118.66 Found ((((fun (P:Prop) (x5:((cEVEN Xn0)->P)) (x6:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x5) x6) x20)) ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))) (fun (x5:(cEVEN Xn0)) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30)) (fun (x5:(cODD Xn0)) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 118.32/118.66 Found ((((fun (P:Prop) (x5:((cEVEN Xn0)->P)) (x6:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x5) x6) (x2 x31))) ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))) (fun (x5:(cEVEN Xn0)) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30)) (fun (x5:(cODD Xn0)) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 118.32/118.66 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))))=> ((((fun (P:Prop) (x5:((cEVEN Xn0)->P)) (x6:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x5) x6) (x2 x31))) ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))) (fun (x5:(cEVEN Xn0)) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30)) (fun (x5:(cODD Xn0)) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30))) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 119.78/120.05 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))))=> ((((fun (P:Prop) (x5:((cEVEN Xn0)->P)) (x6:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x5) x6) (x2 x31))) ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))) (fun (x5:(cEVEN Xn0)) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30)) (fun (x5:(cODD Xn0)) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30))) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn)))
% 119.78/120.05 Found x70:=(x7 x60):(cNUMBER Xn0)
% 119.78/120.05 Found (x7 x60) as proof of (cNUMBER Xn0)
% 119.78/120.05 Found (x7 x60) as proof of (cNUMBER Xn0)
% 119.78/120.05 Found x70:=(x7 x61):(cNUMBER Xn0)
% 119.78/120.05 Instantiate: Xn0:=Xn:fofType
% 119.78/120.05 Found (x7 x61) as proof of (cNUMBER Xn)
% 119.78/120.05 Found (x7 x61) as proof of (cNUMBER Xn)
% 119.78/120.05 Found x70:=(x7 x61):(cNUMBER Xn0)
% 119.78/120.05 Found (x7 x61) as proof of (cNUMBER Xn)
% 119.78/120.05 Found (x7 x61) as proof of (cNUMBER Xn)
% 119.78/120.05 Found (x7 x61) as proof of (cNUMBER Xn)
% 119.78/120.05 Found x30:=(x3 x22):(cNUMBER Xn0)
% 119.78/120.05 Found (x3 x22) as proof of (cNUMBER Xn)
% 119.78/120.05 Found (x3 x22) as proof of (cNUMBER Xn)
% 119.78/120.05 Found (fun (x3:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x3 x22)) as proof of (cNUMBER Xn)
% 119.78/120.05 Found (fun (x3:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x3 x22)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 119.78/120.05 Found x9:(cODD (cS c0))
% 119.78/120.05 Instantiate: Xn0:=(cS c0):fofType
% 119.78/120.05 Found x9 as proof of (cODD Xn0)
% 119.78/120.05 Found (or_intror00 x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 119.78/120.05 Found ((or_intror0 (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 119.78/120.05 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 119.78/120.05 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 119.78/120.05 Found (x7 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9)) as proof of (cNUMBER Xn0)
% 119.78/120.05 Found (x7 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9)) as proof of (cNUMBER Xn0)
% 119.78/120.05 Found x30:=(x3 x21):(cNUMBER Xn0)
% 119.78/120.05 Instantiate: Xn0:=Xn:fofType
% 119.78/120.05 Found (x3 x21) as proof of (cNUMBER Xn)
% 119.78/120.05 Found (fun (x9:(cODD (cS c0)))=> (x3 x21)) as proof of (cNUMBER Xn)
% 119.78/120.05 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x21)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 119.78/120.05 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x21)) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 119.78/120.05 Found (and_rect40 (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x21))) as proof of (cNUMBER Xn)
% 119.78/120.05 Found ((and_rect4 (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x21))) as proof of (cNUMBER Xn)
% 119.78/120.05 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x21))) as proof of (cNUMBER Xn)
% 120.12/120.36 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x21)))) as proof of (cNUMBER Xn)
% 120.12/120.36 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x21)))) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 120.12/120.36 Found x30:(cNUMBER Xn0)
% 120.12/120.36 Instantiate: Xn0:=Xn:fofType
% 120.12/120.36 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30) as proof of (cNUMBER Xn)
% 120.12/120.36 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 120.12/120.36 Found x30:(cNUMBER Xn0)
% 120.12/120.36 Instantiate: Xn0:=Xn:fofType
% 120.12/120.36 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30) as proof of (cNUMBER Xn)
% 120.12/120.36 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 120.12/120.36 Found x31:(cNUMBER Xn0)
% 120.12/120.36 Instantiate: Xn0:=Xn:fofType
% 120.12/120.36 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x31) as proof of (cNUMBER Xn)
% 120.12/120.36 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x31) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 120.12/120.36 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 120.12/120.36 Instantiate: Xn00:=Xn0:fofType
% 120.12/120.36 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 120.12/120.36 Found x50:(cNUMBER Xn00)
% 120.12/120.36 Instantiate: Xn00:=Xn:fofType
% 120.12/120.36 Found x50 as proof of (cNUMBER Xn)
% 120.12/120.36 Found x70:(cNUMBER Xn00)
% 120.12/120.36 Found x70 as proof of (cNUMBER Xn00)
% 120.12/120.36 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 120.12/120.36 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 120.12/120.36 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 120.12/120.36 Found x11:(cEVEN c0)
% 120.12/120.36 Instantiate: Xn0:=c0:fofType
% 120.12/120.36 Found x11 as proof of (cEVEN Xn0)
% 120.12/120.36 Found (or_introl00 x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 120.12/120.36 Found ((or_introl0 (cODD Xn0)) x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 120.12/120.36 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 120.12/120.36 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 120.12/120.36 Found (x9 (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11)) as proof of (cNUMBER Xn0)
% 120.12/120.36 Found (x9 (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11)) as proof of (cNUMBER Xn0)
% 120.12/120.36 Found x30:=(x3 x21):(cNUMBER Xn0)
% 120.12/120.36 Instantiate: Xn0:=Xn:fofType
% 120.12/120.36 Found (x3 x21) as proof of (cNUMBER Xn)
% 120.12/120.36 Found (fun (x9:(cODD (cS c0)))=> (x3 x21)) as proof of (cNUMBER Xn)
% 120.12/120.36 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x21)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 120.12/120.36 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x21)) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 120.12/120.36 Found (and_rect40 (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x21))) as proof of (cNUMBER Xn)
% 120.12/120.36 Found ((and_rect4 (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x21))) as proof of (cNUMBER Xn)
% 120.12/120.36 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x21))) as proof of (cNUMBER Xn)
% 123.54/123.83 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x21))) as proof of (cNUMBER Xn)
% 123.54/123.83 Found x90:(cNUMBER Xn00)
% 123.54/123.83 Instantiate: Xn00:=Xn:fofType
% 123.54/123.83 Found x90 as proof of (cNUMBER Xn)
% 123.54/123.83 Found x70:(cNUMBER Xn0)
% 123.54/123.83 Instantiate: Xn0:=Xn:fofType
% 123.54/123.83 Found x70 as proof of (cNUMBER Xn)
% 123.54/123.83 Found x61:((or (cEVEN Xn0)) (cODD Xn0))
% 123.54/123.83 Found x61 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 123.54/123.83 Found (x7 x61) as proof of (cNUMBER Xn)
% 123.54/123.83 Found (x7 x61) as proof of (cNUMBER Xn)
% 123.54/123.83 Found (fun (x9:(cODD (cS c0)))=> (x7 x61)) as proof of (cNUMBER Xn)
% 123.54/123.83 Found (fun (x9:(cODD (cS c0)))=> (x7 x61)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 123.54/123.83 Found x61:((or (cEVEN Xn0)) (cODD Xn0))
% 123.54/123.83 Found x61 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 123.54/123.83 Found (x7 x61) as proof of (cNUMBER Xn)
% 123.54/123.83 Found (x7 x61) as proof of (cNUMBER Xn)
% 123.54/123.83 Found (x7 x61) as proof of (cNUMBER Xn)
% 123.54/123.83 Found x30:=(x3 x20):(cNUMBER Xn0)
% 123.54/123.83 Instantiate: Xn0:=Xn:fofType
% 123.54/123.83 Found (x3 x20) as proof of (cNUMBER Xn)
% 123.54/123.83 Found (fun (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 123.54/123.83 Found (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 123.54/123.83 Found (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn)))
% 123.54/123.83 Found (and_rect30 (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 123.54/123.83 Found ((and_rect3 (cNUMBER Xn)) (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 123.54/123.84 Found (((fun (P:Type) (x6:(((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->P)))=> (((((and_rect ((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))) P) x6) x0)) (cNUMBER Xn)) (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 123.54/123.84 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (((fun (P:Type) (x6:(((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->P)))=> (((((and_rect ((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))) P) x6) x0)) (cNUMBER Xn)) (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)))) as proof of (cNUMBER Xn)
% 123.54/123.84 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 (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->P)))=> (((((and_rect ((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))) P) x6) x0)) (cNUMBER Xn)) (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)))) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 124.21/124.51 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 (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->P)))=> (((((and_rect ((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))) P) x6) x0)) (cNUMBER Xn)) (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x20)))) as proof of (((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))->((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn)))
% 124.21/124.51 Found x40:=(x4 x50):((or (cEVEN Xn00)) (cODD Xn00))
% 124.21/124.51 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 124.21/124.51 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 124.21/124.51 Found (fun (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x4 x50)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 124.21/124.51 Found (fun (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x4 x50)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 124.21/124.51 Found x30:(cNUMBER Xn0)
% 124.21/124.51 Instantiate: Xn0:=Xn:fofType
% 124.21/124.51 Found (fun (x11:(cODD (cS c0)))=> x30) as proof of (cNUMBER Xn)
% 124.21/124.51 Found (fun (x9:(cEVEN Xn0)) (x11:(cODD (cS c0)))=> x30) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 124.21/124.51 Found (fun (x9:(cEVEN Xn0)) (x11:(cODD (cS c0)))=> x30) as proof of ((cEVEN Xn0)->((cODD (cS c0))->(cNUMBER Xn)))
% 124.21/124.51 Found x30:(cNUMBER Xn0)
% 124.21/124.51 Instantiate: Xn0:=Xn:fofType
% 124.21/124.51 Found (fun (x11:(cODD (cS c0)))=> x30) as proof of (cNUMBER Xn)
% 124.21/124.51 Found (fun (x9:(cODD Xn0)) (x11:(cODD (cS c0)))=> x30) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 124.21/124.51 Found (fun (x9:(cODD Xn0)) (x11:(cODD (cS c0)))=> x30) as proof of ((cODD Xn0)->((cODD (cS c0))->(cNUMBER Xn)))
% 124.21/124.51 Found ((or_ind00 (fun (x9:(cEVEN Xn0)) (x11:(cODD (cS c0)))=> x30)) (fun (x9:(cODD Xn0)) (x11:(cODD (cS c0)))=> x30)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 124.21/124.51 Found (((or_ind0 ((cODD (cS c0))->(cNUMBER Xn))) (fun (x9:(cEVEN Xn0)) (x11:(cODD (cS c0)))=> x30)) (fun (x9:(cODD Xn0)) (x11:(cODD (cS c0)))=> x30)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 124.21/124.51 Found ((((fun (P:Prop) (x9:((cEVEN Xn0)->P)) (x11:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x9) x11) x20)) ((cODD (cS c0))->(cNUMBER Xn))) (fun (x9:(cEVEN Xn0)) (x11:(cODD (cS c0)))=> x30)) (fun (x9:(cODD Xn0)) (x11:(cODD (cS c0)))=> x30)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 124.21/124.51 Found ((((fun (P:Prop) (x9:((cEVEN Xn0)->P)) (x11:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x9) x11) (x2 x30))) ((cODD (cS c0))->(cNUMBER Xn))) (fun (x9:(cEVEN Xn0)) (x11:(cODD (cS c0)))=> x30)) (fun (x9:(cODD Xn0)) (x11:(cODD (cS c0)))=> x30)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 124.81/125.15 Found ((((fun (P:Prop) (x9:((cEVEN Xn0)->P)) (x11:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x9) x11) (x2 x30))) ((cODD (cS c0))->(cNUMBER Xn))) (fun (x9:(cEVEN Xn0)) (x11:(cODD (cS c0)))=> x30)) (fun (x9:(cODD Xn0)) (x11:(cODD (cS c0)))=> x30)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 124.81/125.15 Found x30:=(x3 x21):(cNUMBER Xn0)
% 124.81/125.15 Instantiate: Xn0:=Xn:fofType
% 124.81/125.15 Found (x3 x21) as proof of (cNUMBER Xn)
% 124.81/125.15 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x21)) as proof of (cNUMBER Xn)
% 124.81/125.15 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))
% 124.81/125.15 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)))
% 124.81/125.15 Found x30:(cNUMBER Xn0)
% 124.81/125.15 Instantiate: Xn0:=Xn:fofType
% 124.81/125.15 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of (cNUMBER Xn)
% 124.81/125.15 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 124.81/125.15 Found x70:(cNUMBER Xn00)
% 124.81/125.15 Instantiate: Xn00:=Xn:fofType
% 124.81/125.15 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x70) as proof of (cNUMBER Xn)
% 124.81/125.15 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x70) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 124.81/125.15 Found x30:=(x3 x20):(cNUMBER Xn0)
% 124.81/125.15 Found (x3 x20) as proof of (cNUMBER Xn0)
% 124.81/125.15 Found (x3 x20) as proof of (cNUMBER Xn0)
% 124.81/125.15 Found x30:=(x3 x21):(cNUMBER Xn0)
% 124.81/125.15 Instantiate: Xn0:=Xn:fofType
% 124.81/125.15 Found (x3 x21) as proof of (cNUMBER Xn)
% 124.81/125.15 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x21)) as proof of (cNUMBER Xn)
% 124.81/125.15 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x21)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 124.81/125.15 Found x30:=(x3 x20):(cNUMBER Xn0)
% 124.81/125.15 Instantiate: Xn00:=Xn0:fofType
% 124.81/125.15 Found (x3 x20) as proof of (cNUMBER Xn00)
% 124.81/125.15 Found (x3 x20) as proof of (cNUMBER Xn00)
% 124.81/125.15 Found x30:(cNUMBER Xn0)
% 124.81/125.15 Instantiate: Xn0:=Xn:fofType
% 124.81/125.15 Found (fun (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30) as proof of (cNUMBER Xn)
% 124.81/125.15 Found (fun (x5:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 124.81/125.15 Found (fun (x4:(cODD Xn0)) (x5:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn)))
% 124.91/125.19 Found (fun (x4:(cODD Xn0)) (x5:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30) as proof of ((cODD Xn0)->(((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))))
% 124.91/125.19 Found x30:(cNUMBER Xn0)
% 124.91/125.19 Instantiate: Xn0:=Xn:fofType
% 124.91/125.19 Found (fun (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30) as proof of (cNUMBER Xn)
% 124.91/125.19 Found (fun (x5:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 124.91/125.19 Found (fun (x4:(cEVEN Xn0)) (x5:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn)))
% 124.91/125.19 Found (fun (x4:(cEVEN Xn0)) (x5:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30) as proof of ((cEVEN Xn0)->(((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))))
% 124.91/125.19 Found ((or_ind00 (fun (x4:(cEVEN Xn0)) (x5:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30)) (fun (x4:(cODD Xn0)) (x5:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30)) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn)))
% 124.91/125.19 Found (((or_ind0 (((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn)))) (fun (x4:(cEVEN Xn0)) (x5:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30)) (fun (x4:(cODD Xn0)) (x5:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30)) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn)))
% 124.91/125.19 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 (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn)))) (fun (x4:(cEVEN Xn0)) (x5:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30)) (fun (x4:(cODD Xn0)) (x5:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30)) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn)))
% 124.91/125.19 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 (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn)))) (fun (x4:(cEVEN Xn0)) (x5:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30)) (fun (x4:(cODD Xn0)) (x5:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30)) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn)))
% 124.99/125.26 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 (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn)))) (fun (x4:(cEVEN Xn0)) (x5:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30)) (fun (x4:(cODD Xn0)) (x5:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x6:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> x30)) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn)))
% 124.99/125.26 Found x30:=(x3 x20):(cNUMBER Xn0)
% 124.99/125.26 Instantiate: Xn0:=Xn:fofType
% 124.99/125.26 Found (x3 x20) as proof of (cNUMBER Xn)
% 124.99/125.26 Found (fun (x4:(cEVEN Xn0))=> (x3 x20)) as proof of (cNUMBER Xn)
% 124.99/125.26 Found (fun (x4:(cEVEN Xn0))=> (x3 x20)) as proof of ((cEVEN Xn0)->(cNUMBER Xn))
% 124.99/125.26 Found x30:=(x3 x20):(cNUMBER Xn0)
% 124.99/125.26 Instantiate: Xn0:=Xn:fofType
% 124.99/125.26 Found (x3 x20) as proof of (cNUMBER Xn)
% 124.99/125.26 Found (fun (x4:(cODD Xn0))=> (x3 x20)) as proof of (cNUMBER Xn)
% 124.99/125.26 Found (fun (x4:(cODD Xn0))=> (x3 x20)) as proof of ((cODD Xn0)->(cNUMBER Xn))
% 124.99/125.26 Found ((or_ind00 (fun (x4:(cEVEN Xn0))=> (x3 x20))) (fun (x4:(cODD Xn0))=> (x3 x20))) as proof of (cNUMBER Xn)
% 125.78/126.08 Found (((or_ind0 (cNUMBER Xn)) (fun (x4:(cEVEN Xn0))=> (x3 x20))) (fun (x4:(cODD Xn0))=> (x3 x20))) as proof of (cNUMBER Xn)
% 125.78/126.08 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 x20))) (fun (x4:(cODD Xn0))=> (x3 x20))) as proof of (cNUMBER Xn)
% 125.78/126.08 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 x20))) (fun (x4:(cODD Xn0))=> (x3 x20)))) as proof of (cNUMBER Xn)
% 125.78/126.08 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 x20))) (fun (x4:(cODD Xn0))=> (x3 x20)))) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 125.78/126.08 Found x30:=(x3 x20):(cNUMBER Xn0)
% 125.78/126.08 Instantiate: Xn00:=Xn0:fofType
% 125.78/126.08 Found (x3 x20) as proof of (cNUMBER Xn00)
% 125.78/126.08 Found (x3 x20) as proof of (cNUMBER Xn00)
% 125.78/126.08 Found x9:(cEVEN c0)
% 125.78/126.08 Instantiate: Xn0:=c0:fofType
% 125.78/126.08 Found (fun (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x9) as proof of (cEVEN Xn0)
% 125.78/126.08 Found (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x9) as proof of ((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->(cEVEN Xn0))
% 125.78/126.08 Found (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x9) as proof of ((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->(cEVEN Xn0)))
% 125.78/126.08 Found (and_rect50 (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x9)) as proof of (cEVEN Xn0)
% 125.78/126.08 Found ((and_rect5 (cEVEN Xn0)) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x9)) as proof of (cEVEN Xn0)
% 125.78/126.08 Found (((fun (P:Type) (x9:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x9) x8)) (cEVEN Xn0)) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x9)) as proof of (cEVEN Xn0)
% 125.78/126.08 Found (((fun (P:Type) (x9:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x9) x8)) (cEVEN Xn0)) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x9)) as proof of (cEVEN Xn0)
% 125.78/126.08 Found (or_introl00 (((fun (P:Type) (x9:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x9) x8)) (cEVEN Xn0)) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x9))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 125.78/126.08 Found ((or_introl0 (cODD Xn0)) (((fun (P:Type) (x9:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x9) x8)) (cEVEN Xn0)) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x9))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 125.78/126.08 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) (((fun (P:Type) (x9:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x9) x8)) (cEVEN Xn0)) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x9))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 125.78/126.08 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) (((fun (P:Type) (x9:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x9) x8)) (cEVEN Xn0)) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x9))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 126.23/126.48 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 126.23/126.48 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 126.23/126.48 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 126.23/126.48 Found x50:=(x5 x40):(cNUMBER Xn0)
% 126.23/126.48 Instantiate: Xn0:=Xn:fofType
% 126.23/126.48 Found (x5 x40) as proof of (cNUMBER Xn)
% 126.23/126.48 Found (fun (x9:(cODD (cS c0)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 126.23/126.48 Found (fun (x8:((and (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))
% 126.23/126.48 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x40)) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 126.23/126.48 Found (and_rect40 (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x40))) as proof of (cNUMBER Xn)
% 126.23/126.48 Found ((and_rect4 (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x40))) as proof of (cNUMBER Xn)
% 126.23/126.48 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x40))) as proof of (cNUMBER Xn)
% 126.23/126.48 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x40))) as proof of (cNUMBER Xn)
% 126.23/126.48 Found x40:=(x4 x50):((or (cEVEN Xn00)) (cODD Xn00))
% 126.23/126.48 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 126.23/126.48 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 126.23/126.48 Found (fun (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x4 x50)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 126.23/126.48 Found (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x4 x50)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 126.23/126.48 Found (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x4 x50)) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->((or (cEVEN Xn0)) (cODD Xn0))))
% 127.39/127.72 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 127.39/127.72 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 127.39/127.72 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 127.39/127.72 Found (fun (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x2 x30)) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 127.39/127.72 Found (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x2 x30)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->((or (cEVEN Xn00)) (cODD Xn00)))
% 127.39/127.72 Found (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x2 x30)) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->((or (cEVEN Xn00)) (cODD Xn00))))
% 127.39/127.72 Found x50:(cNUMBER Xn00)
% 127.39/127.72 Found x50 as proof of (cNUMBER Xn00)
% 127.39/127.72 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 127.39/127.72 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 127.39/127.72 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 127.39/127.72 Found x30:(cNUMBER Xn0)
% 127.39/127.72 Found x30 as proof of (cNUMBER Xn0)
% 127.39/127.72 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 127.39/127.72 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 127.39/127.72 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 127.39/127.72 Found x70:=(x7 (cS c0)):((cODD (cS c0))->(cODD (cS (cS (cS c0)))))
% 127.39/127.72 Found (x7 (cS c0)) as proof of ((cODD (cS c0))->(cODD Xn0))
% 127.39/127.72 Found (x7 (cS c0)) as proof of ((cODD (cS c0))->(cODD Xn0))
% 127.39/127.72 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x7 (cS c0))) as proof of ((cODD (cS c0))->(cODD Xn0))
% 127.39/127.72 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x7 (cS c0))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->(cODD Xn0)))
% 127.39/127.72 Found (and_rect40 (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x7 (cS c0)))) as proof of (cODD Xn0)
% 127.39/127.72 Found ((and_rect4 (cODD Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x7 (cS c0)))) as proof of (cODD Xn0)
% 127.39/127.72 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) (cODD Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x7 (cS c0)))) as proof of (cODD Xn0)
% 127.39/127.72 Found (fun (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) (cODD Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x7 (cS c0))))) as proof of (cODD Xn0)
% 127.39/127.72 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) (cODD Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x7 (cS c0))))) as proof of ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->(cODD Xn0))
% 127.39/127.72 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) (cODD Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x7 (cS c0))))) as proof of (((and ((and (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)))
% 127.39/127.72 Found (and_rect30 (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) (cODD Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x7 (cS c0)))))) as proof of (cODD Xn0)
% 127.39/127.72 Found ((and_rect3 (cODD Xn0)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) (cODD Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x7 (cS c0)))))) as proof of (cODD Xn0)
% 127.39/127.72 Found (((fun (P:Type) (x6:(((and ((and (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 (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x4)) (cODD Xn0)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) (cODD Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x7 (cS c0)))))) as proof of (cODD Xn0)
% 127.39/127.72 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (((fun (P:Type) (x6:(((and ((and (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 (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x4)) (cODD Xn0)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) (cODD Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x7 (cS c0))))))) as proof of (cODD Xn0)
% 127.39/127.73 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (((fun (P:Type) (x6:(((and ((and (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 (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x4)) (cODD Xn0)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) (cODD Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x7 (cS c0))))))) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cODD Xn0))
% 127.39/127.73 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (((fun (P:Type) (x6:(((and ((and (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 (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x4)) (cODD Xn0)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) (cODD Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x7 (cS c0))))))) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cODD Xn0)))
% 127.48/127.73 Found (and_rect20 (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (((fun (P:Type) (x6:(((and ((and (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 (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x4)) (cODD Xn0)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) (cODD Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x7 (cS c0)))))))) as proof of (cODD Xn0)
% 127.48/127.73 Found ((and_rect2 (cODD Xn0)) (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (((fun (P:Type) (x6:(((and ((and (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 (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x4)) (cODD Xn0)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) (cODD Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x7 (cS c0)))))))) as proof of (cODD Xn0)
% 127.48/127.73 Found (((fun (P:Type) (x4:(((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->P)))=> (((((and_rect ((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))) P) x4) x0)) (cODD Xn0)) (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (((fun (P:Type) (x6:(((and ((and (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 (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x4)) (cODD Xn0)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) (cODD Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x7 (cS c0)))))))) as proof of (cODD Xn0)
% 127.48/127.75 Found (((fun (P:Type) (x4:(((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->P)))=> (((((and_rect ((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))) P) x4) x0)) (cODD Xn0)) (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (((fun (P:Type) (x6:(((and ((and (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 (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x4)) (cODD Xn0)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) (cODD Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x7 (cS c0)))))))) as proof of (cODD Xn0)
% 127.48/127.75 Found (or_intror00 (((fun (P:Type) (x4:(((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->P)))=> (((((and_rect ((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))) P) x4) x0)) (cODD Xn0)) (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (((fun (P:Type) (x6:(((and ((and (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 (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x4)) (cODD Xn0)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) (cODD Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x7 (cS c0))))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 127.48/127.75 Found ((or_intror0 (cODD Xn0)) (((fun (P:Type) (x4:(((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->P)))=> (((((and_rect ((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))) P) x4) x0)) (cODD Xn0)) (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (((fun (P:Type) (x6:(((and ((and (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 (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x4)) (cODD Xn0)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) (cODD Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x7 (cS c0))))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 127.48/127.75 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) (((fun (P:Type) (x4:(((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->P)))=> (((((and_rect ((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))) P) x4) x0)) (cODD Xn0)) (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (((fun (P:Type) (x6:(((and ((and (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 (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x4)) (cODD Xn0)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) (cODD Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x7 (cS c0))))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 127.48/127.75 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) (((fun (P:Type) (x4:(((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->P)))=> (((((and_rect ((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))) P) x4) x0)) (cODD Xn0)) (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (((fun (P:Type) (x6:(((and ((and (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 (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x4)) (cODD Xn0)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) (cODD Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x7 (cS c0))))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 128.15/128.44 Found x11:(cEVEN c0)
% 128.15/128.44 Instantiate: Xn0:=c0:fofType
% 128.15/128.44 Found (fun (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11) as proof of (cEVEN Xn0)
% 128.15/128.44 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11) as proof of ((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->(cEVEN Xn0))
% 128.15/128.44 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11) as proof of ((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->(cEVEN Xn0)))
% 128.15/128.44 Found (and_rect50 (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11)) as proof of (cEVEN Xn0)
% 128.15/128.44 Found ((and_rect5 (cEVEN Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11)) as proof of (cEVEN Xn0)
% 128.15/128.44 Found (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cEVEN Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11)) as proof of (cEVEN Xn0)
% 128.15/128.44 Found (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cEVEN Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11)) as proof of (cEVEN Xn0)
% 128.15/128.44 Found (or_introl00 (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cEVEN Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 128.15/128.44 Found ((or_introl0 (cODD Xn0)) (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x11) x8)) (cEVEN Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 128.15/128.44 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x11) x8)) (cEVEN Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 128.15/128.44 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x11) x8)) (cEVEN Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 128.15/128.44 Found x50:(cNUMBER Xn0)
% 128.15/128.44 Instantiate: Xn0:=Xn:fofType
% 128.15/128.44 Found x50 as proof of (cNUMBER Xn)
% 128.15/128.44 Found x90:(cNUMBER Xn00)
% 128.15/128.44 Instantiate: Xn00:=Xn:fofType
% 128.15/128.44 Found x90 as proof of (cNUMBER Xn)
% 128.15/128.44 Found x30:(cNUMBER Xn0)
% 128.15/128.44 Instantiate: Xn0:=Xn:fofType
% 128.15/128.44 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30) as proof of (cNUMBER Xn)
% 128.15/128.44 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))
% 128.15/128.44 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)))
% 129.36/129.63 Found x30:=(x3 x20):(cNUMBER Xn0)
% 129.36/129.63 Instantiate: Xn0:=Xn:fofType
% 129.36/129.63 Found (x3 x20) as proof of (cNUMBER Xn)
% 129.36/129.63 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 129.36/129.63 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))
% 129.36/129.63 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)))
% 129.36/129.63 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)
% 129.36/129.63 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)
% 129.36/129.63 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)
% 129.36/129.63 Found x50:=(x5 x40):(cNUMBER Xn00)
% 129.36/129.63 Instantiate: Xn00:=Xn:fofType
% 129.36/129.63 Found (x5 x40) as proof of (cNUMBER Xn)
% 129.36/129.63 Found (x5 x40) as proof of (cNUMBER Xn)
% 129.36/129.63 Found x30:=(x3 x20):(cNUMBER Xn0)
% 129.36/129.63 Instantiate: Xn0:=Xn:fofType
% 129.36/129.63 Found (x3 x20) as proof of (cNUMBER Xn)
% 129.36/129.63 Found (x3 x20) as proof of (cNUMBER Xn)
% 129.36/129.63 Found or_introl00:=(or_introl0 (cEVEN Xn0)):((cODD (cS c0))->((or (cODD (cS c0))) (cEVEN Xn0)))
% 129.36/129.63 Found (or_introl0 (cEVEN Xn0)) as proof of ((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0)))
% 129.36/129.63 Found ((or_introl (cODD (cS c0))) (cEVEN Xn0)) as proof of ((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0)))
% 129.36/129.63 Found ((or_introl (cODD (cS c0))) (cEVEN Xn0)) as proof of ((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0)))
% 129.36/129.63 Found (fun (x8:((and (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)))
% 129.36/129.63 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0))))
% 129.36/129.63 Found (and_rect40 (fun (x8:((and (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))
% 129.36/129.63 Found ((and_rect4 ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x8:((and (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))
% 129.36/129.63 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x8:((and (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))
% 129.36/129.63 Found (fun (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x8:((and (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))
% 129.36/129.63 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x8:((and (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)))
% 129.36/129.63 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0))))) as proof of (((and ((and (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))))
% 129.36/129.63 Found (and_rect30 (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x8:((and (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))
% 129.36/129.63 Found ((and_rect3 ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x8:((and (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))
% 129.36/129.63 Found (((fun (P:Type) (x6:(((and ((and (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 (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x4)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x8:((and (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))
% 129.36/129.63 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (((fun (P:Type) (x6:(((and ((and (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 (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x4)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x8:((and (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))
% 129.36/129.63 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (((fun (P:Type) (x6:(((and ((and (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 (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x4)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0))))))) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->((or (cODD Xn0)) (cEVEN Xn0)))
% 129.36/129.63 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (((fun (P:Type) (x6:(((and ((and (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 (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x4)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0))))))) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->((or (cODD Xn0)) (cEVEN Xn0))))
% 129.36/129.64 Found (and_rect20 (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (((fun (P:Type) (x6:(((and ((and (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 (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x4)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x8:((and (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))
% 129.36/129.64 Found ((and_rect2 ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (((fun (P:Type) (x6:(((and ((and (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 (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x4)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x8:((and (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))
% 129.36/129.64 Found (((fun (P:Type) (x4:(((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->P)))=> (((((and_rect ((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))) P) x4) x0)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (((fun (P:Type) (x6:(((and ((and (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 (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x4)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x8:((and (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))
% 129.36/129.64 Found (((fun (P:Type) (x4:(((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->P)))=> (((((and_rect ((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))) P) x4) x0)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (((fun (P:Type) (x6:(((and ((and (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 (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x4)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x8:((and (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))
% 129.36/129.65 Found (or_comm_i00 (((fun (P:Type) (x4:(((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->P)))=> (((((and_rect ((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))) P) x4) x0)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (((fun (P:Type) (x6:(((and ((and (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 (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x4)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x8:((and (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))
% 129.36/129.65 Found ((or_comm_i0 (cEVEN Xn0)) (((fun (P:Type) (x4:(((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->P)))=> (((((and_rect ((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))) P) x4) x0)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (((fun (P:Type) (x6:(((and ((and (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 (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x4)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x8:((and (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))
% 129.36/129.65 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((fun (P:Type) (x4:(((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->P)))=> (((((and_rect ((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))) P) x4) x0)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (((fun (P:Type) (x6:(((and ((and (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 (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x4)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x8:((and (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))
% 129.36/129.65 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((fun (P:Type) (x4:(((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->P)))=> (((((and_rect ((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))) P) x4) x0)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (((fun (P:Type) (x6:(((and ((and (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 (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x4)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x8:((and (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))
% 129.87/130.13 Found x70:(cNUMBER Xn00)
% 129.87/130.13 Found x70 as proof of (cNUMBER Xn00)
% 129.87/130.13 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 129.87/130.13 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 129.87/130.13 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 129.87/130.13 Found x9:(cEVEN c0)
% 129.87/130.13 Instantiate: Xn0:=c0:fofType
% 129.87/130.13 Found x9 as proof of (cEVEN Xn0)
% 129.87/130.13 Found (or_introl00 x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 129.87/130.13 Found ((or_introl0 (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 129.87/130.13 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 129.87/130.13 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 129.87/130.13 Found (x3 (((or_introl (cEVEN Xn0)) (cODD Xn0)) x9)) as proof of (cNUMBER Xn0)
% 129.87/130.13 Found (fun (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (x3 (((or_introl (cEVEN Xn0)) (cODD Xn0)) x9))) as proof of (cNUMBER Xn0)
% 129.87/130.13 Found (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (x3 (((or_introl (cEVEN Xn0)) (cODD Xn0)) x9))) as proof of ((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->(cNUMBER Xn0))
% 129.87/130.13 Found (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (x3 (((or_introl (cEVEN Xn0)) (cODD Xn0)) x9))) as proof of ((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->(cNUMBER Xn0)))
% 129.87/130.13 Found (and_rect50 (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (x3 (((or_introl (cEVEN Xn0)) (cODD Xn0)) x9)))) as proof of (cNUMBER Xn0)
% 129.87/130.13 Found ((and_rect5 (cNUMBER Xn0)) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (x3 (((or_introl (cEVEN Xn0)) (cODD Xn0)) x9)))) as proof of (cNUMBER Xn0)
% 129.87/130.13 Found (((fun (P:Type) (x9:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x9) x8)) (cNUMBER Xn0)) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (x3 (((or_introl (cEVEN Xn0)) (cODD Xn0)) x9)))) as proof of (cNUMBER Xn0)
% 129.87/130.13 Found (((fun (P:Type) (x9:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x9) x8)) (cNUMBER Xn0)) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (x3 (((or_introl (cEVEN Xn0)) (cODD Xn0)) x9)))) as proof of (cNUMBER Xn0)
% 131.04/131.31 Found x30:(cNUMBER Xn0)
% 131.04/131.31 Instantiate: Xn0:=Xn:fofType
% 131.04/131.31 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30) as proof of (cNUMBER Xn)
% 131.04/131.31 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 131.04/131.31 Found x31:(cNUMBER Xn0)
% 131.04/131.31 Instantiate: Xn0:=Xn:fofType
% 131.04/131.31 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x31) as proof of (cNUMBER Xn)
% 131.04/131.31 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x31) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 131.04/131.31 Found x70:(cNUMBER Xn0)
% 131.04/131.31 Instantiate: Xn0:=Xn:fofType
% 131.04/131.31 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x70) as proof of (cNUMBER Xn)
% 131.04/131.31 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x70) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 131.04/131.31 Found x30:=(x3 x20):(cNUMBER Xn0)
% 131.04/131.31 Found (x3 x20) as proof of (cNUMBER Xn0)
% 131.04/131.31 Found (x3 x20) as proof of (cNUMBER Xn0)
% 131.04/131.31 Found x50:=(x5 x40):(cNUMBER Xn0)
% 131.04/131.31 Instantiate: Xn0:=Xn:fofType
% 131.04/131.31 Found (x5 x40) as proof of (cNUMBER Xn)
% 131.04/131.31 Found (fun (x9:(cODD (cS c0)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 131.04/131.31 Found (fun (x8:((and (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))
% 131.04/131.31 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x40)) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 131.04/131.31 Found (and_rect40 (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x40))) as proof of (cNUMBER Xn)
% 131.04/131.31 Found ((and_rect4 (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x40))) as proof of (cNUMBER Xn)
% 131.04/131.31 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x40))) as proof of (cNUMBER Xn)
% 131.04/131.31 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x40)))) as proof of (cNUMBER Xn)
% 131.04/131.31 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x40)))) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 131.04/131.31 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x40)))) as proof of (((and ((and (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)))
% 132.41/132.68 Found x9:(cODD (cS c0))
% 132.41/132.68 Instantiate: Xn0:=(cS c0):fofType
% 132.41/132.68 Found x9 as proof of (cODD Xn0)
% 132.41/132.68 Found (or_introl00 x9) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 132.41/132.68 Found ((or_introl0 (cEVEN Xn0)) x9) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 132.41/132.68 Found (((or_introl (cODD Xn0)) (cEVEN Xn0)) x9) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 132.41/132.68 Found (((or_introl (cODD Xn0)) (cEVEN Xn0)) x9) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 132.41/132.68 Found (or_comm_i00 (((or_introl (cODD Xn0)) (cEVEN Xn0)) x9)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 132.41/132.68 Found ((or_comm_i0 (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x9)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 132.41/132.68 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x9)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 132.41/132.68 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x9)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 132.41/132.68 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 132.41/132.68 Instantiate: Xn0:=Xn00:fofType
% 132.41/132.68 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 132.41/132.68 Found x8:(cEVEN c0)
% 132.41/132.68 Instantiate: Xn0:=c0:fofType
% 132.41/132.68 Found x8 as proof of (cEVEN Xn0)
% 132.41/132.68 Found (or_introl00 x8) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 132.41/132.68 Found ((or_introl0 (cODD Xn0)) x8) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 132.41/132.68 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x8) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 132.41/132.68 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x8) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 132.41/132.68 Found (x12 (((or_introl (cEVEN Xn0)) (cODD Xn0)) x8)) as proof of (cNUMBER Xn0)
% 132.41/132.68 Found (x12 (((or_introl (cEVEN Xn0)) (cODD Xn0)) x8)) as proof of (cNUMBER Xn0)
% 132.41/132.68 Found x61:((or (cEVEN Xn0)) (cODD Xn0))
% 132.41/132.68 Found x61 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 132.41/132.68 Found (x7 x61) as proof of (cNUMBER Xn)
% 132.41/132.68 Found (x7 x61) as proof of (cNUMBER Xn)
% 132.41/132.68 Found (fun (x9:(cODD (cS c0)))=> (x7 x61)) as proof of (cNUMBER Xn)
% 132.41/132.68 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x7 x61)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 132.41/132.68 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x7 x61)) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 132.41/132.68 Found x61:((or (cEVEN Xn0)) (cODD Xn0))
% 132.41/132.68 Found x61 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 132.41/132.68 Found (x7 x61) as proof of (cNUMBER Xn)
% 132.41/132.68 Found (x7 x61) as proof of (cNUMBER Xn)
% 132.41/132.68 Found (fun (x9:(cODD (cS c0)))=> (x7 x61)) as proof of (cNUMBER Xn)
% 132.41/132.68 Found (fun (x9:(cODD (cS c0)))=> (x7 x61)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 132.41/132.68 Found x61:((or (cEVEN Xn0)) (cODD Xn0))
% 132.41/132.68 Found x61 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 132.41/132.68 Found (x7 x61) as proof of (cNUMBER Xn)
% 132.41/132.68 Found (x7 x61) as proof of (cNUMBER Xn)
% 132.41/132.68 Found (x7 x61) as proof of (cNUMBER Xn)
% 132.41/132.68 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 132.41/132.68 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 132.41/132.68 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 132.41/132.68 Found x31:(cNUMBER Xn0)
% 132.41/132.68 Instantiate: Xn0:=Xn:fofType
% 132.41/132.68 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x31) as proof of (cNUMBER Xn)
% 132.41/132.68 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x31) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 132.41/132.68 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x31) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 132.41/132.68 Found x11:(cEVEN c0)
% 132.41/132.68 Instantiate: Xn0:=c0:fofType
% 132.41/132.68 Found x11 as proof of (cEVEN Xn0)
% 132.41/132.68 Found (or_introl00 x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 132.41/132.68 Found ((or_introl0 (cODD Xn0)) x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 132.41/132.68 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 134.43/134.72 Found (fun (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 134.43/134.72 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11)) as proof of ((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 134.43/134.72 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11)) as proof of ((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0))))
% 134.43/134.72 Found (and_rect50 (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 134.43/134.72 Found ((and_rect5 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 134.43/134.72 Found (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 134.43/134.72 Found (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 134.43/134.72 Found x70:(cNUMBER Xn00)
% 134.43/134.72 Instantiate: Xn00:=Xn:fofType
% 134.43/134.72 Found x70 as proof of (cNUMBER Xn)
% 134.43/134.72 Found x50:(cNUMBER Xn0)
% 134.43/134.72 Instantiate: Xn0:=Xn:fofType
% 134.43/134.72 Found x50 as proof of (cNUMBER Xn)
% 134.43/134.72 Found x30:=(x3 x20):(cNUMBER Xn0)
% 134.43/134.72 Instantiate: Xn00:=Xn0:fofType
% 134.43/134.72 Found (x3 x20) as proof of (cNUMBER Xn00)
% 134.43/134.72 Found (x3 x20) as proof of (cNUMBER Xn00)
% 134.43/134.72 Found x30:=(x3 x20):(cNUMBER Xn0)
% 134.43/134.72 Found (x3 x20) as proof of (cNUMBER Xn0)
% 134.43/134.72 Found (x3 x20) as proof of (cNUMBER Xn0)
% 134.43/134.72 Found x30:=(x3 x21):(cNUMBER Xn0)
% 134.43/134.72 Instantiate: Xn0:=Xn:fofType
% 134.43/134.72 Found (x3 x21) as proof of (cNUMBER Xn)
% 134.43/134.72 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x21)) as proof of (cNUMBER Xn)
% 134.43/134.72 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x21)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 134.43/134.72 Found x40:=(x4 x50):((or (cEVEN Xn00)) (cODD Xn00))
% 134.43/134.72 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 134.43/134.72 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 134.43/134.72 Found (fun (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x4 x50)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 134.43/134.72 Found (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x4 x50)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 134.43/134.72 Found (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x4 x50)) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->((or (cEVEN Xn0)) (cODD Xn0))))
% 134.58/134.90 Found x30:(cNUMBER Xn0)
% 134.58/134.90 Instantiate: Xn0:=Xn:fofType
% 134.58/134.90 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of (cNUMBER Xn)
% 134.58/134.90 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 134.58/134.90 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of (((and ((and (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)))
% 134.58/134.90 Found x70:(cNUMBER Xn00)
% 134.58/134.90 Instantiate: Xn00:=Xn:fofType
% 134.58/134.90 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x70) as proof of (cNUMBER Xn)
% 134.58/134.90 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x70) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 134.58/134.90 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x70) as proof of (((and ((and (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)))
% 134.58/134.90 Found x30:(cNUMBER Xn0)
% 134.58/134.90 Instantiate: Xn0:=Xn:fofType
% 134.58/134.90 Found (fun (x11:(cODD (cS c0)))=> x30) as proof of (cNUMBER Xn)
% 134.58/134.90 Found (fun (x9:(cEVEN Xn0)) (x11:(cODD (cS c0)))=> x30) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 134.58/134.90 Found (fun (x9:(cEVEN Xn0)) (x11:(cODD (cS c0)))=> x30) as proof of ((cEVEN Xn0)->((cODD (cS c0))->(cNUMBER Xn)))
% 134.58/134.90 Found x30:(cNUMBER Xn0)
% 134.58/134.90 Instantiate: Xn0:=Xn:fofType
% 134.58/134.90 Found (fun (x11:(cODD (cS c0)))=> x30) as proof of (cNUMBER Xn)
% 134.58/134.90 Found (fun (x9:(cODD Xn0)) (x11:(cODD (cS c0)))=> x30) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 134.58/134.90 Found (fun (x9:(cODD Xn0)) (x11:(cODD (cS c0)))=> x30) as proof of ((cODD Xn0)->((cODD (cS c0))->(cNUMBER Xn)))
% 134.58/134.90 Found ((or_ind00 (fun (x9:(cEVEN Xn0)) (x11:(cODD (cS c0)))=> x30)) (fun (x9:(cODD Xn0)) (x11:(cODD (cS c0)))=> x30)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 134.58/134.90 Found (((or_ind0 ((cODD (cS c0))->(cNUMBER Xn))) (fun (x9:(cEVEN Xn0)) (x11:(cODD (cS c0)))=> x30)) (fun (x9:(cODD Xn0)) (x11:(cODD (cS c0)))=> x30)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 134.58/134.90 Found ((((fun (P:Prop) (x9:((cEVEN Xn0)->P)) (x11:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x9) x11) x20)) ((cODD (cS c0))->(cNUMBER Xn))) (fun (x9:(cEVEN Xn0)) (x11:(cODD (cS c0)))=> x30)) (fun (x9:(cODD Xn0)) (x11:(cODD (cS c0)))=> x30)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 134.58/134.90 Found ((((fun (P:Prop) (x9:((cEVEN Xn0)->P)) (x11:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x9) x11) (x2 x30))) ((cODD (cS c0))->(cNUMBER Xn))) (fun (x9:(cEVEN Xn0)) (x11:(cODD (cS c0)))=> x30)) (fun (x9:(cODD Xn0)) (x11:(cODD (cS c0)))=> x30)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 134.58/134.90 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))))=> ((((fun (P:Prop) (x9:((cEVEN Xn0)->P)) (x11:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x9) x11) (x2 x30))) ((cODD (cS c0))->(cNUMBER Xn))) (fun (x9:(cEVEN Xn0)) (x11:(cODD (cS c0)))=> x30)) (fun (x9:(cODD Xn0)) (x11:(cODD (cS c0)))=> x30))) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 134.90/135.20 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))))=> ((((fun (P:Prop) (x9:((cEVEN Xn0)->P)) (x11:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x9) x11) (x2 x30))) ((cODD (cS c0))->(cNUMBER Xn))) (fun (x9:(cEVEN Xn0)) (x11:(cODD (cS c0)))=> x30)) (fun (x9:(cODD Xn0)) (x11:(cODD (cS c0)))=> x30))) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 134.90/135.20 Found x50:=(x5 x40):(cNUMBER Xn0)
% 134.90/135.20 Instantiate: Xn0:=Xn:fofType
% 134.90/135.20 Found (x5 x40) as proof of (cNUMBER Xn)
% 134.90/135.20 Found (fun (x9:(cODD (cS c0)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 134.90/135.20 Found (fun (x8:((and (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))
% 134.90/135.20 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x40)) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 134.90/135.20 Found (and_rect40 (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x40))) as proof of (cNUMBER Xn)
% 134.90/135.20 Found ((and_rect4 (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x40))) as proof of (cNUMBER Xn)
% 134.90/135.20 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x40))) as proof of (cNUMBER Xn)
% 134.90/135.20 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x40)))) as proof of (cNUMBER Xn)
% 134.90/135.20 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x40)))) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 134.90/135.20 Found x50:(cNUMBER Xn00)
% 134.90/135.20 Found x50 as proof of (cNUMBER Xn00)
% 134.90/135.20 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 134.90/135.20 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 134.90/135.20 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 134.90/135.20 Found x30:(cNUMBER Xn0)
% 134.90/135.20 Found x30 as proof of (cNUMBER Xn0)
% 134.90/135.20 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 134.90/135.20 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 134.90/135.20 Found (fun (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x2 x30)) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 134.90/135.20 Found (fun (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x2 x30)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->((or (cEVEN Xn00)) (cODD Xn00)))
% 135.59/135.89 Found x50:(cNUMBER Xn00)
% 135.59/135.89 Found x50 as proof of (cNUMBER Xn00)
% 135.59/135.89 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 135.59/135.89 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 135.59/135.89 Found (fun (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x4 x50)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 135.59/135.89 Found (fun (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x4 x50)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 135.59/135.89 Found x50:=(x5 x40):(cNUMBER Xn0)
% 135.59/135.89 Instantiate: Xn0:=Xn:fofType
% 135.59/135.89 Found (x5 x40) as proof of (cNUMBER Xn)
% 135.59/135.89 Found (fun (x9:(cODD (cS c0)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 135.59/135.89 Found (fun (x8:((and (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))
% 135.59/135.89 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x40)) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 135.59/135.89 Found (and_rect40 (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x40))) as proof of (cNUMBER Xn)
% 135.59/135.89 Found ((and_rect4 (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x40))) as proof of (cNUMBER Xn)
% 135.59/135.89 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x40))) as proof of (cNUMBER Xn)
% 135.59/135.89 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x40))) as proof of (cNUMBER Xn)
% 135.59/135.89 Found x30:=(x3 x21):(cNUMBER Xn0)
% 135.59/135.89 Found (x3 x21) as proof of (cNUMBER Xn)
% 135.59/135.89 Found (x3 x21) as proof of (cNUMBER Xn)
% 135.59/135.89 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x21)) as proof of (cNUMBER Xn)
% 135.59/135.89 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x21)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 135.59/135.89 Found x9:(cEVEN c0)
% 135.59/135.89 Instantiate: Xn0:=c0:fofType
% 135.59/135.89 Found x9 as proof of (cEVEN Xn0)
% 135.59/135.89 Found (or_introl00 x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 135.59/135.89 Found ((or_introl0 (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 135.59/135.89 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 135.59/135.89 Found (fun (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_introl (cEVEN Xn0)) (cODD Xn0)) x9)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 135.59/135.89 Found (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_introl (cEVEN Xn0)) (cODD Xn0)) x9)) as proof of ((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 135.59/135.89 Found (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_introl (cEVEN Xn0)) (cODD Xn0)) x9)) as proof of ((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0))))
% 137.57/137.85 Found (and_rect50 (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_introl (cEVEN Xn0)) (cODD Xn0)) x9))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 137.57/137.85 Found ((and_rect5 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_introl (cEVEN Xn0)) (cODD Xn0)) x9))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 137.57/137.85 Found (((fun (P:Type) (x9:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x9) x8)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_introl (cEVEN Xn0)) (cODD Xn0)) x9))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 137.57/137.85 Found (((fun (P:Type) (x9:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x9) x8)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_introl (cEVEN Xn0)) (cODD Xn0)) x9))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 137.57/137.85 Found (x3 (((fun (P:Type) (x9:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x9) x8)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_introl (cEVEN Xn0)) (cODD Xn0)) x9)))) as proof of (cNUMBER Xn0)
% 137.57/137.85 Found (x3 (((fun (P:Type) (x9:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x9) x8)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_introl (cEVEN Xn0)) (cODD Xn0)) x9)))) as proof of (cNUMBER Xn0)
% 137.57/137.85 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 137.57/137.85 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 137.57/137.85 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 137.57/137.85 Found x50:(cNUMBER Xn0)
% 137.57/137.85 Instantiate: Xn0:=Xn:fofType
% 137.57/137.85 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x50) as proof of (cNUMBER Xn)
% 137.57/137.85 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x50) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 137.57/137.85 Found x50:=(x5 x40):(cNUMBER Xn00)
% 137.57/137.85 Instantiate: Xn00:=Xn:fofType
% 137.57/137.85 Found (x5 x40) as proof of (cNUMBER Xn)
% 137.57/137.85 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 137.57/137.85 Found (fun (x9:(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))
% 137.57/137.85 Found x30:=(x3 x20):(cNUMBER Xn0)
% 137.57/137.85 Instantiate: Xn0:=Xn:fofType
% 137.57/137.85 Found (x3 x20) as proof of (cNUMBER Xn)
% 137.57/137.85 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 137.57/137.85 Found (fun (x9:(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))
% 137.57/137.85 Found x11:(cEVEN c0)
% 137.57/137.85 Instantiate: Xn0:=c0:fofType
% 137.57/137.85 Found x11 as proof of (cEVEN Xn0)
% 137.57/137.85 Found (or_introl00 x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 137.57/137.85 Found ((or_introl0 (cODD Xn0)) x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 137.57/137.85 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 137.57/137.85 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 137.57/137.85 Found (x9 (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11)) as proof of (cNUMBER Xn0)
% 137.57/137.85 Found (x9 (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11)) as proof of (cNUMBER Xn0)
% 138.75/139.03 Found x50:=(x5 x40):(cNUMBER Xn00)
% 138.75/139.03 Instantiate: Xn0:=Xn00:fofType
% 138.75/139.03 Found (x5 x40) as proof of (cNUMBER Xn0)
% 138.75/139.03 Found (x5 x40) as proof of (cNUMBER Xn0)
% 138.75/139.03 Found x50:=(x5 x40):(cNUMBER Xn00)
% 138.75/139.03 Instantiate: Xn0:=Xn00:fofType
% 138.75/139.03 Found (x5 x40) as proof of (cNUMBER Xn0)
% 138.75/139.03 Found (x5 x40) as proof of (cNUMBER Xn0)
% 138.75/139.03 Found x50:=(x5 x40):(cNUMBER Xn0)
% 138.75/139.03 Instantiate: Xn0:=Xn:fofType
% 138.75/139.03 Found (x5 x40) as proof of (cNUMBER Xn)
% 138.75/139.03 Found (fun (x9:(cODD (cS c0)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 138.75/139.03 Found (fun (x8:((and (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))
% 138.75/139.03 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x40)) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 138.75/139.03 Found (and_rect40 (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x40))) as proof of (cNUMBER Xn)
% 138.75/139.03 Found ((and_rect4 (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x40))) as proof of (cNUMBER Xn)
% 138.75/139.03 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x40))) as proof of (cNUMBER Xn)
% 138.75/139.03 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x40)))) as proof of (cNUMBER Xn)
% 138.75/139.03 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x40)))) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 138.75/139.03 Found x30:=(x3 x20):(cNUMBER Xn0)
% 138.75/139.03 Instantiate: Xn00:=Xn0:fofType
% 138.75/139.03 Found (x3 x20) as proof of (cNUMBER Xn00)
% 138.75/139.03 Found (x3 x20) as proof of (cNUMBER Xn00)
% 138.75/139.03 Found x30:=(x3 x20):(cNUMBER Xn0)
% 138.75/139.03 Found (x3 x20) as proof of (cNUMBER Xn0)
% 138.75/139.03 Found (x3 x20) as proof of (cNUMBER Xn0)
% 138.75/139.03 Found x30:=(x3 x21):(cNUMBER Xn0)
% 138.75/139.03 Instantiate: Xn0:=Xn:fofType
% 138.75/139.03 Found (x3 x21) as proof of (cNUMBER Xn)
% 138.75/139.03 Found (x3 x21) as proof of (cNUMBER Xn)
% 138.75/139.03 Found x30:=(x3 x21):(cNUMBER Xn0)
% 138.75/139.03 Found (x3 x21) as proof of (cNUMBER Xn)
% 138.75/139.03 Found (x3 x21) as proof of (cNUMBER Xn)
% 138.75/139.03 Found (x3 x21) as proof of (cNUMBER Xn)
% 138.75/139.03 Found x30:=(x3 x20):(cNUMBER Xn0)
% 138.75/139.03 Instantiate: Xn00:=Xn0:fofType
% 138.75/139.03 Found (x3 x20) as proof of (cNUMBER Xn00)
% 138.75/139.03 Found (x3 x20) as proof of (cNUMBER Xn00)
% 138.75/139.03 Found x50:=(x5 x40):(cNUMBER Xn0)
% 138.75/139.03 Instantiate: Xn0:=Xn:fofType
% 138.75/139.03 Found (x5 x40) as proof of (cNUMBER Xn)
% 138.75/139.03 Found (fun (x9:(cODD (cS c0)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 138.75/139.03 Found (fun (x8:((and (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))
% 138.75/139.03 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x40)) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 138.75/139.03 Found (and_rect40 (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x40))) as proof of (cNUMBER Xn)
% 141.71/141.97 Found ((and_rect4 (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x40))) as proof of (cNUMBER Xn)
% 141.71/141.97 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x40))) as proof of (cNUMBER Xn)
% 141.71/141.97 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x40))) as proof of (cNUMBER Xn)
% 141.71/141.97 Found x50:=(x5 x40):(cNUMBER Xn00)
% 141.71/141.97 Found (x5 x40) as proof of (cNUMBER Xn00)
% 141.71/141.97 Found (x5 x40) as proof of (cNUMBER Xn00)
% 141.71/141.97 Found x50:=(x5 x41):(cNUMBER Xn00)
% 141.71/141.97 Instantiate: Xn00:=Xn:fofType
% 141.71/141.97 Found (x5 x41) as proof of (cNUMBER Xn)
% 141.71/141.97 Found (x5 x41) as proof of (cNUMBER Xn)
% 141.71/141.97 Found x50:=(x5 x41):(cNUMBER Xn00)
% 141.71/141.97 Found (x5 x41) as proof of (cNUMBER Xn)
% 141.71/141.97 Found (x5 x41) as proof of (cNUMBER Xn)
% 141.71/141.97 Found (x5 x41) as proof of (cNUMBER Xn)
% 141.71/141.97 Found x30:=(x3 x20):(cNUMBER Xn0)
% 141.71/141.97 Instantiate: Xn0:=Xn:fofType
% 141.71/141.97 Found (x3 x20) as proof of (cNUMBER Xn)
% 141.71/141.97 Found (x3 x20) as proof of (cNUMBER Xn)
% 141.71/141.97 Found x50:=(x5 x40):(cNUMBER Xn00)
% 141.71/141.97 Instantiate: Xn00:=Xn:fofType
% 141.71/141.97 Found (x5 x40) as proof of (cNUMBER Xn)
% 141.71/141.97 Found (x5 x40) as proof of (cNUMBER Xn)
% 141.71/141.97 Found x30:=(x3 x20):(cNUMBER Xn0)
% 141.71/141.97 Instantiate: Xn0:=Xn:fofType
% 141.71/141.97 Found (x3 x20) as proof of (cNUMBER Xn)
% 141.71/141.97 Found (x3 x20) as proof of (cNUMBER Xn)
% 141.71/141.97 Found x50:=(x5 x40):(cNUMBER Xn00)
% 141.71/141.97 Instantiate: Xn00:=Xn:fofType
% 141.71/141.97 Found (x5 x40) as proof of (cNUMBER Xn)
% 141.71/141.97 Found (x5 x40) as proof of (cNUMBER Xn)
% 141.71/141.97 Found x40:=(x4 x50):((or (cEVEN Xn00)) (cODD Xn00))
% 141.71/141.97 Instantiate: Xn0:=Xn00:fofType
% 141.71/141.97 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 141.71/141.97 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 141.71/141.97 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 141.71/141.97 Instantiate: Xn00:=Xn0:fofType
% 141.71/141.97 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 141.71/141.97 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 141.71/141.97 Found x70:(cNUMBER Xn0)
% 141.71/141.97 Instantiate: Xn0:=Xn:fofType
% 141.71/141.97 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x70) as proof of (cNUMBER Xn)
% 141.71/141.97 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))
% 141.71/141.97 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)))
% 141.71/141.97 Found x30:=(x3 x20):(cNUMBER Xn0)
% 141.71/141.97 Instantiate: Xn0:=Xn:fofType
% 141.71/141.97 Found (x3 x20) as proof of (cNUMBER Xn)
% 141.71/141.97 Found (x3 x20) as proof of (cNUMBER Xn)
% 141.71/141.97 Found x90:=(x9 x80):(cNUMBER Xn00)
% 141.71/141.97 Instantiate: Xn00:=Xn:fofType
% 141.71/141.97 Found (x9 x80) as proof of (cNUMBER Xn)
% 141.71/141.97 Found (x9 x80) as proof of (cNUMBER Xn)
% 141.71/141.97 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 141.71/141.97 Instantiate: Xn00:=Xn:fofType
% 141.71/141.97 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 141.71/141.97 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 141.71/141.97 Instantiate: Xn0:=Xn:fofType
% 141.71/141.97 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 141.71/141.97 Found x30:(cNUMBER Xn0)
% 141.71/141.97 Instantiate: Xn0:=Xn:fofType
% 141.71/141.97 Found (fun (x11:(cODD (cS c0)))=> x30) as proof of (cNUMBER Xn)
% 141.71/141.97 Found (fun (x9:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x11:(cODD (cS c0)))=> x30) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 141.71/141.97 Found (fun (x8:(cODD Xn0)) (x9:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x11:(cODD (cS c0)))=> x30) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 141.89/142.18 Found (fun (x8:(cODD Xn0)) (x9:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x11:(cODD (cS c0)))=> x30) as proof of ((cODD Xn0)->(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn))))
% 141.89/142.18 Found x30:(cNUMBER Xn0)
% 141.89/142.18 Instantiate: Xn0:=Xn:fofType
% 141.89/142.18 Found (fun (x11:(cODD (cS c0)))=> x30) as proof of (cNUMBER Xn)
% 141.89/142.18 Found (fun (x9:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x11:(cODD (cS c0)))=> x30) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 141.89/142.18 Found (fun (x8:(cEVEN Xn0)) (x9:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x11:(cODD (cS c0)))=> x30) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 141.89/142.18 Found (fun (x8:(cEVEN Xn0)) (x9:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x11:(cODD (cS c0)))=> x30) as proof of ((cEVEN Xn0)->(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn))))
% 141.89/142.18 Found ((or_ind00 (fun (x8:(cEVEN Xn0)) (x9:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x11:(cODD (cS c0)))=> x30)) (fun (x8:(cODD Xn0)) (x9:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x11:(cODD (cS c0)))=> x30)) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 141.89/142.18 Found (((or_ind0 (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))) (fun (x8:(cEVEN Xn0)) (x9:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x11:(cODD (cS c0)))=> x30)) (fun (x8:(cODD Xn0)) (x9:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x11:(cODD (cS c0)))=> x30)) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 141.89/142.18 Found ((((fun (P:Prop) (x8:((cEVEN Xn0)->P)) (x9:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x8) x9) x20)) (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->(cNUMBER Xn)))) (fun (x8:(cEVEN Xn0)) (x9:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x11:(cODD (cS c0)))=> x30)) (fun (x8:(cODD Xn0)) (x9:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x11:(cODD (cS c0)))=> x30)) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 141.89/142.18 Found ((((fun (P:Prop) (x8:((cEVEN Xn0)->P)) (x9:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x8) x9) (x2 x30))) (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->(cNUMBER Xn)))) (fun (x8:(cEVEN Xn0)) (x9:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x11:(cODD (cS c0)))=> x30)) (fun (x8:(cODD Xn0)) (x9:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x11:(cODD (cS c0)))=> x30)) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 141.89/142.18 Found ((((fun (P:Prop) (x8:((cEVEN Xn0)->P)) (x9:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x8) x9) (x2 x30))) (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->(cNUMBER Xn)))) (fun (x8:(cEVEN Xn0)) (x9:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x11:(cODD (cS c0)))=> x30)) (fun (x8:(cODD Xn0)) (x9:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x11:(cODD (cS c0)))=> x30)) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 141.89/142.18 Found x31:(cNUMBER Xn0)
% 144.01/144.30 Instantiate: Xn0:=Xn:fofType
% 144.01/144.30 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x31) as proof of (cNUMBER Xn)
% 144.01/144.30 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x31) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 144.01/144.30 Found x50:(cNUMBER Xn0)
% 144.01/144.30 Instantiate: Xn0:=Xn:fofType
% 144.01/144.30 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of (cNUMBER Xn)
% 144.01/144.30 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 144.01/144.30 Found x70:(cNUMBER Xn00)
% 144.01/144.30 Instantiate: Xn00:=Xn:fofType
% 144.01/144.30 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x70) as proof of (cNUMBER Xn)
% 144.01/144.30 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x70) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 144.01/144.30 Found x50:(cNUMBER Xn0)
% 144.01/144.30 Instantiate: Xn0:=Xn:fofType
% 144.01/144.30 Found (fun (x11:(cODD (cS c0)))=> x50) as proof of (cNUMBER Xn)
% 144.01/144.30 Found (fun (x9:(cODD Xn0)) (x11:(cODD (cS c0)))=> x50) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 144.01/144.30 Found (fun (x9:(cODD Xn0)) (x11:(cODD (cS c0)))=> x50) as proof of ((cODD Xn0)->((cODD (cS c0))->(cNUMBER Xn)))
% 144.01/144.30 Found x50:(cNUMBER Xn0)
% 144.01/144.30 Instantiate: Xn0:=Xn:fofType
% 144.01/144.30 Found (fun (x11:(cODD (cS c0)))=> x50) as proof of (cNUMBER Xn)
% 144.01/144.30 Found (fun (x9:(cEVEN Xn0)) (x11:(cODD (cS c0)))=> x50) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 144.01/144.30 Found (fun (x9:(cEVEN Xn0)) (x11:(cODD (cS c0)))=> x50) as proof of ((cEVEN Xn0)->((cODD (cS c0))->(cNUMBER Xn)))
% 144.01/144.30 Found ((or_ind00 (fun (x9:(cEVEN Xn0)) (x11:(cODD (cS c0)))=> x50)) (fun (x9:(cODD Xn0)) (x11:(cODD (cS c0)))=> x50)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 144.01/144.30 Found (((or_ind0 ((cODD (cS c0))->(cNUMBER Xn))) (fun (x9:(cEVEN Xn0)) (x11:(cODD (cS c0)))=> x50)) (fun (x9:(cODD Xn0)) (x11:(cODD (cS c0)))=> x50)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 144.01/144.30 Found ((((fun (P:Prop) (x9:((cEVEN Xn0)->P)) (x11:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x9) x11) x40)) ((cODD (cS c0))->(cNUMBER Xn))) (fun (x9:(cEVEN Xn0)) (x11:(cODD (cS c0)))=> x50)) (fun (x9:(cODD Xn0)) (x11:(cODD (cS c0)))=> x50)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 144.01/144.30 Found ((((fun (P:Prop) (x9:((cEVEN Xn0)->P)) (x11:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x9) x11) (x4 x50))) ((cODD (cS c0))->(cNUMBER Xn))) (fun (x9:(cEVEN Xn0)) (x11:(cODD (cS c0)))=> x50)) (fun (x9:(cODD Xn0)) (x11:(cODD (cS c0)))=> x50)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 144.01/144.30 Found ((((fun (P:Prop) (x9:((cEVEN Xn0)->P)) (x11:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x9) x11) (x4 x50))) ((cODD (cS c0))->(cNUMBER Xn))) (fun (x9:(cEVEN Xn0)) (x11:(cODD (cS c0)))=> x50)) (fun (x9:(cODD Xn0)) (x11:(cODD (cS c0)))=> x50)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 144.01/144.30 Found x50:(cNUMBER Xn00)
% 144.01/144.30 Found x50 as proof of (cNUMBER Xn00)
% 144.01/144.30 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 144.01/144.30 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 144.01/144.30 Found (fun (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x4 x50)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 144.01/144.30 Found (fun (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x4 x50)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 144.01/144.30 Found x30:=(x3 x21):(cNUMBER Xn0)
% 144.01/144.30 Instantiate: Xn0:=Xn:fofType
% 144.01/144.30 Found (x3 x21) as proof of (cNUMBER Xn)
% 144.01/144.30 Found (fun (x6:(cEVEN Xn0))=> (x3 x21)) as proof of (cNUMBER Xn)
% 144.01/144.30 Found (fun (x6:(cEVEN Xn0))=> (x3 x21)) as proof of ((cEVEN Xn0)->(cNUMBER Xn))
% 144.46/144.74 Found x30:=(x3 x21):(cNUMBER Xn0)
% 144.46/144.74 Instantiate: Xn0:=Xn:fofType
% 144.46/144.74 Found (x3 x21) as proof of (cNUMBER Xn)
% 144.46/144.74 Found (fun (x6:(cODD Xn0))=> (x3 x21)) as proof of (cNUMBER Xn)
% 144.46/144.74 Found (fun (x6:(cODD Xn0))=> (x3 x21)) as proof of ((cODD Xn0)->(cNUMBER Xn))
% 144.46/144.74 Found ((or_ind00 (fun (x6:(cEVEN Xn0))=> (x3 x21))) (fun (x6:(cODD Xn0))=> (x3 x21))) as proof of (cNUMBER Xn)
% 144.46/144.74 Found (((or_ind0 (cNUMBER Xn)) (fun (x6:(cEVEN Xn0))=> (x3 x21))) (fun (x6:(cODD Xn0))=> (x3 x21))) as proof of (cNUMBER Xn)
% 144.46/144.74 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)
% 144.46/144.74 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)
% 144.46/144.74 Found x30:=(x3 x21):(cNUMBER Xn0)
% 144.46/144.74 Instantiate: Xn0:=Xn:fofType
% 144.46/144.74 Found (x3 x21) as proof of (cNUMBER Xn)
% 144.46/144.74 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x21)) as proof of (cNUMBER Xn)
% 144.46/144.74 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x21)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 144.46/144.74 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x21)) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn)))
% 144.46/144.74 Found (and_rect20 (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x21))) as proof of (cNUMBER Xn)
% 144.46/144.74 Found ((and_rect2 (cNUMBER Xn)) (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x21))) as proof of (cNUMBER Xn)
% 144.46/144.74 Found (((fun (P:Type) (x4:(((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->P)))=> (((((and_rect ((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))) P) x4) x0)) (cNUMBER Xn)) (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x21))) as proof of (cNUMBER Xn)
% 145.38/145.70 Found (((fun (P:Type) (x4:(((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->P)))=> (((((and_rect ((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))) P) x4) x0)) (cNUMBER Xn)) (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x21))) as proof of (cNUMBER Xn)
% 145.38/145.70 Found x41:((or (cEVEN Xn00)) (cODD Xn00))
% 145.38/145.70 Instantiate: Xn00:=Xn:fofType
% 145.38/145.70 Found x41 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 145.38/145.70 Found (x3 x41) as proof of (cNUMBER Xn)
% 145.38/145.70 Found (x3 x41) as proof of (cNUMBER Xn)
% 145.38/145.70 Found (x3 x41) as proof of (cNUMBER Xn)
% 145.38/145.70 Found x41:((or (cEVEN Xn00)) (cODD Xn00))
% 145.38/145.70 Found x41 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 145.38/145.70 Found (x5 x41) as proof of (cNUMBER Xn)
% 145.38/145.70 Found (x5 x41) as proof of (cNUMBER Xn)
% 145.38/145.70 Found (x5 x41) as proof of (cNUMBER Xn)
% 145.38/145.70 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 145.38/145.70 Instantiate: Xn0:=Xn00:fofType
% 145.38/145.70 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 145.38/145.70 Found x21:((or (cEVEN Xn0)) (cODD Xn0))
% 145.38/145.70 Instantiate: Xn0:=Xn:fofType
% 145.38/145.70 Found x21 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 145.38/145.70 Found (x5 x21) as proof of (cNUMBER Xn)
% 145.38/145.70 Found (x5 x21) as proof of (cNUMBER Xn)
% 145.38/145.70 Found (x5 x21) as proof of (cNUMBER Xn)
% 145.38/145.70 Found x50:(cNUMBER Xn00)
% 145.38/145.70 Instantiate: Xn0:=Xn00:fofType
% 145.38/145.70 Found x50 as proof of (cNUMBER Xn0)
% 145.38/145.70 Found x21:((or (cEVEN Xn0)) (cODD Xn0))
% 145.38/145.70 Found x21 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 145.38/145.70 Found (x3 x21) as proof of (cNUMBER Xn)
% 145.38/145.70 Found (x3 x21) as proof of (cNUMBER Xn)
% 145.38/145.70 Found (x3 x21) as proof of (cNUMBER Xn)
% 145.38/145.70 Found x30:(cNUMBER Xn0)
% 145.38/145.70 Instantiate: Xn00:=Xn0:fofType
% 145.38/145.70 Found x30 as proof of (cNUMBER Xn00)
% 145.38/145.70 Found x70:=(x7 x61):(cNUMBER Xn0)
% 145.38/145.70 Instantiate: Xn0:=Xn:fofType
% 145.38/145.70 Found (x7 x61) as proof of (cNUMBER Xn)
% 145.38/145.70 Found (fun (x9:(cODD (cS c0)))=> (x7 x61)) as proof of (cNUMBER Xn)
% 145.38/145.70 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x7 x61)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 145.38/145.70 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x7 x61)) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 145.38/145.70 Found (and_rect40 (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x7 x61))) as proof of (cNUMBER Xn)
% 146.61/146.88 Found ((and_rect4 (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x7 x61))) as proof of (cNUMBER Xn)
% 146.61/146.88 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x4)) (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x7 x61))) as proof of (cNUMBER Xn)
% 146.61/146.88 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x4)) (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x7 x61))) as proof of (cNUMBER Xn)
% 146.61/146.88 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 146.61/146.88 Instantiate: Xn00:=Xn0:fofType
% 146.61/146.88 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 146.61/146.88 Found x30:=(x3 x21):(cNUMBER Xn0)
% 146.61/146.88 Found (x3 x21) as proof of (cNUMBER Xn)
% 146.61/146.88 Found (x3 x21) as proof of (cNUMBER Xn)
% 146.61/146.88 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x21)) as proof of (cNUMBER Xn)
% 146.61/146.88 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))
% 146.61/146.88 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)))
% 146.61/146.88 Found x50:(cNUMBER Xn00)
% 146.61/146.88 Found x50 as proof of (cNUMBER Xn00)
% 146.61/146.88 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 146.61/146.88 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 146.61/146.88 Found (fun (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x4 x50)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 146.61/146.88 Found (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x4 x50)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 146.61/146.88 Found (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x4 x50)) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->((or (cEVEN Xn0)) (cODD Xn0))))
% 146.61/146.88 Found x30:=(x3 x21):(cNUMBER Xn0)
% 146.61/146.88 Found (x3 x21) as proof of (cNUMBER Xn)
% 146.61/146.88 Found (x3 x21) as proof of (cNUMBER Xn)
% 146.61/146.88 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x21)) as proof of (cNUMBER Xn)
% 146.61/146.88 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x21)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 147.17/147.45 Found x30:(cNUMBER Xn0)
% 147.17/147.45 Found x30 as proof of (cNUMBER Xn0)
% 147.17/147.45 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 147.17/147.45 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 147.17/147.45 Found (fun (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x2 x30)) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 147.17/147.45 Found (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x2 x30)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->((or (cEVEN Xn00)) (cODD Xn00)))
% 147.17/147.45 Found (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x2 x30)) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->((or (cEVEN Xn00)) (cODD Xn00))))
% 147.17/147.45 Found x30:=(x3 x21):(cNUMBER Xn0)
% 147.17/147.45 Found (x3 x21) as proof of (cNUMBER Xn0)
% 147.17/147.45 Found (x3 x21) as proof of (cNUMBER Xn0)
% 147.17/147.45 Found x11:(cEVEN c0)
% 147.17/147.45 Instantiate: Xn0:=c0:fofType
% 147.17/147.45 Found (fun (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11) as proof of (cEVEN Xn0)
% 147.17/147.45 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11) as proof of ((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->(cEVEN Xn0))
% 147.17/147.45 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11) as proof of ((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->(cEVEN Xn0)))
% 147.17/147.45 Found (and_rect50 (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11)) as proof of (cEVEN Xn0)
% 147.17/147.45 Found ((and_rect5 (cEVEN Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11)) as proof of (cEVEN Xn0)
% 147.17/147.45 Found (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cEVEN Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11)) as proof of (cEVEN Xn0)
% 147.17/147.45 Found (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cEVEN Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11)) as proof of (cEVEN Xn0)
% 147.17/147.45 Found (or_introl00 (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cEVEN Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 148.22/148.51 Found ((or_introl0 (cODD Xn0)) (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x11) x8)) (cEVEN Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 148.22/148.51 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x11) x8)) (cEVEN Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 148.22/148.51 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x11) x8)) (cEVEN Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 148.22/148.51 Found x50:(cNUMBER Xn0)
% 148.22/148.51 Instantiate: Xn0:=Xn:fofType
% 148.22/148.51 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x50) as proof of (cNUMBER Xn)
% 148.22/148.51 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))
% 148.22/148.51 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)))
% 148.22/148.51 Found x30:=(x3 x20):(cNUMBER Xn0)
% 148.22/148.51 Instantiate: Xn0:=Xn:fofType
% 148.22/148.51 Found (x3 x20) as proof of (cNUMBER Xn)
% 148.22/148.51 Found (x3 x20) as proof of (cNUMBER Xn)
% 148.22/148.51 Found x70:=(x7 x60):(cNUMBER Xn00)
% 148.22/148.51 Instantiate: Xn00:=Xn:fofType
% 148.22/148.51 Found (x7 x60) as proof of (cNUMBER Xn)
% 148.22/148.51 Found (x7 x60) as proof of (cNUMBER Xn)
% 148.22/148.51 Found x30:=(x3 x20):(cNUMBER Xn0)
% 148.22/148.51 Found (x3 x20) as proof of (cNUMBER Xn0)
% 148.22/148.51 Found (x3 x20) as proof of (cNUMBER Xn0)
% 148.22/148.51 Found x30:=(x3 x21):(cNUMBER Xn0)
% 148.22/148.51 Instantiate: Xn0:=Xn:fofType
% 148.22/148.51 Found (x3 x21) as proof of (cNUMBER Xn)
% 148.22/148.51 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x21)) as proof of (cNUMBER Xn)
% 148.22/148.51 Found (fun (x12:(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))
% 148.22/148.51 Found x50:=(x5 x40):(cNUMBER Xn00)
% 148.22/148.51 Instantiate: Xn00:=Xn:fofType
% 148.22/148.51 Found (x5 x40) as proof of (cNUMBER Xn)
% 148.22/148.51 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 148.22/148.51 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(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))
% 148.22/148.51 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (((and ((and (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)))
% 148.22/148.51 Found x30:=(x3 x20):(cNUMBER Xn0)
% 148.22/148.51 Instantiate: Xn0:=Xn:fofType
% 148.22/148.51 Found (x3 x20) as proof of (cNUMBER Xn)
% 148.22/148.51 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 148.22/148.51 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(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))
% 148.22/148.51 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (((and ((and (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)))
% 148.51/148.82 Found x30:=(x3 x20):(cNUMBER Xn0)
% 148.51/148.82 Instantiate: Xn00:=Xn0:fofType
% 148.51/148.82 Found (x3 x20) as proof of (cNUMBER Xn00)
% 148.51/148.82 Found (x3 x20) as proof of (cNUMBER Xn00)
% 148.51/148.82 Found x20:=(x2 x31):((or (cEVEN Xn0)) (cODD Xn0))
% 148.51/148.82 Found (x2 x31) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 148.51/148.82 Found (x2 x31) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 148.51/148.82 Found x32:(cNUMBER Xn0)
% 148.51/148.82 Instantiate: Xn0:=Xn:fofType
% 148.51/148.82 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x32) as proof of (cNUMBER Xn)
% 148.51/148.82 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x32) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 148.51/148.82 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x32) as proof of (((and ((and (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)))
% 148.51/148.82 Found x50:=(x5 x40):(cNUMBER Xn00)
% 148.51/148.82 Instantiate: Xn0:=Xn00:fofType
% 148.51/148.82 Found (x5 x40) as proof of (cNUMBER Xn0)
% 148.51/148.82 Found (x5 x40) as proof of (cNUMBER Xn0)
% 148.51/148.82 Found x30:=(x3 x20):(cNUMBER Xn0)
% 148.51/148.82 Found (x3 x20) as proof of (cNUMBER Xn0)
% 148.51/148.82 Found (x3 x20) as proof of (cNUMBER Xn0)
% 148.51/148.82 Found x30:=(x3 x21):(cNUMBER Xn0)
% 148.51/148.82 Instantiate: Xn0:=Xn:fofType
% 148.51/148.82 Found (x3 x21) as proof of (cNUMBER Xn)
% 148.51/148.82 Found (x3 x21) as proof of (cNUMBER Xn)
% 148.51/148.82 Found x30:=(x3 x21):(cNUMBER Xn0)
% 148.51/148.82 Found (x3 x21) as proof of (cNUMBER Xn)
% 148.51/148.82 Found (x3 x21) as proof of (cNUMBER Xn)
% 148.51/148.82 Found (x3 x21) as proof of (cNUMBER Xn)
% 148.51/148.82 Found x9:(cEVEN c0)
% 148.51/148.82 Instantiate: Xn0:=c0:fofType
% 148.51/148.82 Found x9 as proof of (cEVEN Xn0)
% 148.51/148.82 Found (or_introl00 x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 148.51/148.82 Found ((or_introl0 (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 148.51/148.82 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 148.51/148.82 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 148.51/148.82 Found (x5 (((or_introl (cEVEN Xn0)) (cODD Xn0)) x9)) as proof of (cNUMBER Xn0)
% 148.51/148.82 Found (fun (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (x5 (((or_introl (cEVEN Xn0)) (cODD Xn0)) x9))) as proof of (cNUMBER Xn0)
% 148.51/148.82 Found (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (x5 (((or_introl (cEVEN Xn0)) (cODD Xn0)) x9))) as proof of ((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->(cNUMBER Xn0))
% 148.51/148.82 Found (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (x5 (((or_introl (cEVEN Xn0)) (cODD Xn0)) x9))) as proof of ((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->(cNUMBER Xn0)))
% 148.51/148.82 Found (and_rect50 (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (x5 (((or_introl (cEVEN Xn0)) (cODD Xn0)) x9)))) as proof of (cNUMBER Xn0)
% 148.51/148.82 Found ((and_rect5 (cNUMBER Xn0)) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (x5 (((or_introl (cEVEN Xn0)) (cODD Xn0)) x9)))) as proof of (cNUMBER Xn0)
% 148.51/148.82 Found (((fun (P:Type) (x9:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x9) x8)) (cNUMBER Xn0)) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (x5 (((or_introl (cEVEN Xn0)) (cODD Xn0)) x9)))) as proof of (cNUMBER Xn0)
% 148.51/148.82 Found (((fun (P:Type) (x9:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x9) x8)) (cNUMBER Xn0)) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (x5 (((or_introl (cEVEN Xn0)) (cODD Xn0)) x9)))) as proof of (cNUMBER Xn0)
% 149.90/150.24 Found x30:=(x3 x20):(cNUMBER Xn0)
% 149.90/150.24 Instantiate: Xn0:=Xn:fofType
% 149.90/150.24 Found (x3 x20) as proof of (cNUMBER Xn)
% 149.90/150.24 Found (x3 x20) as proof of (cNUMBER Xn)
% 149.90/150.24 Found x50:=(x5 x40):(cNUMBER Xn00)
% 149.90/150.24 Found (x5 x40) as proof of (cNUMBER Xn00)
% 149.90/150.24 Found (x5 x40) as proof of (cNUMBER Xn00)
% 149.90/150.24 Found x50:=(x5 x41):(cNUMBER Xn00)
% 149.90/150.24 Instantiate: Xn00:=Xn:fofType
% 149.90/150.24 Found (x5 x41) as proof of (cNUMBER Xn)
% 149.90/150.24 Found (x5 x41) as proof of (cNUMBER Xn)
% 149.90/150.24 Found x50:=(x5 x41):(cNUMBER Xn00)
% 149.90/150.24 Found (x5 x41) as proof of (cNUMBER Xn)
% 149.90/150.24 Found (x5 x41) as proof of (cNUMBER Xn)
% 149.90/150.24 Found (x5 x41) as proof of (cNUMBER Xn)
% 149.90/150.24 Found x90:=(x9 x80):(cNUMBER Xn0)
% 149.90/150.24 Found (x9 x80) as proof of (cNUMBER Xn)
% 149.90/150.24 Found (x9 x80) as proof of (cNUMBER Xn)
% 149.90/150.24 Found (fun (x9:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x9 x80)) as proof of (cNUMBER Xn)
% 149.90/150.24 Found (fun (x9:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x9 x80)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 149.90/150.24 Found x50:=(x5 x40):(cNUMBER Xn00)
% 149.90/150.24 Instantiate: Xn00:=Xn:fofType
% 149.90/150.24 Found (x5 x40) as proof of (cNUMBER Xn)
% 149.90/150.24 Found (x5 x40) as proof of (cNUMBER Xn)
% 149.90/150.24 Found x50:=(x5 x40):(cNUMBER Xn00)
% 149.90/150.24 Instantiate: Xn00:=Xn:fofType
% 149.90/150.24 Found (x5 x40) as proof of (cNUMBER Xn)
% 149.90/150.24 Found (x5 x40) as proof of (cNUMBER Xn)
% 149.90/150.24 Found x30:=(x3 x20):(cNUMBER Xn0)
% 149.90/150.24 Instantiate: Xn0:=Xn:fofType
% 149.90/150.24 Found (x3 x20) as proof of (cNUMBER Xn)
% 149.90/150.24 Found (x3 x20) as proof of (cNUMBER Xn)
% 149.90/150.24 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 149.90/150.24 Instantiate: Xn00:=Xn:fofType
% 149.90/150.24 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 149.90/150.24 Found x50:=(x5 x41):(cNUMBER Xn0)
% 149.90/150.24 Instantiate: Xn0:=Xn:fofType
% 149.90/150.24 Found (x5 x41) as proof of (cNUMBER Xn)
% 149.90/150.24 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x41)) as proof of (cNUMBER Xn)
% 149.90/150.24 Found (fun (x6:((and ((and (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 x41)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 149.90/150.24 Found (fun (x6:((and ((and (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 x41)) as proof of (((and ((and (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)))
% 149.90/150.24 Found (and_rect30 (fun (x6:((and ((and (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 x41))) as proof of (cNUMBER Xn)
% 149.90/150.24 Found ((and_rect3 (cNUMBER Xn)) (fun (x6:((and ((and (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 x41))) as proof of (cNUMBER Xn)
% 149.90/150.24 Found (((fun (P:Type) (x6:(((and ((and (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 (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) x2)) (cNUMBER Xn)) (fun (x6:((and ((and (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 x41))) as proof of (cNUMBER Xn)
% 149.90/150.24 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (((fun (P:Type) (x6:(((and ((and (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 (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) x2)) (cNUMBER Xn)) (fun (x6:((and ((and (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 x41)))) as proof of (cNUMBER Xn)
% 151.01/151.30 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (((fun (P:Type) (x6:(((and ((and (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 (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) x2)) (cNUMBER Xn)) (fun (x6:((and ((and (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 x41)))) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 151.01/151.30 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 151.01/151.30 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 151.01/151.30 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 151.01/151.30 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 151.01/151.30 Instantiate: Xn0:=Xn:fofType
% 151.01/151.30 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 151.01/151.30 Found x9:(cODD (cS c0))
% 151.01/151.30 Instantiate: Xn0:=(cS c0):fofType
% 151.01/151.30 Found x9 as proof of (cODD Xn0)
% 151.01/151.30 Found (or_introl00 x9) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 151.01/151.30 Found ((or_introl0 (cEVEN Xn0)) x9) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 151.01/151.30 Found (((or_introl (cODD Xn0)) (cEVEN Xn0)) x9) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 151.01/151.30 Found (((or_introl (cODD Xn0)) (cEVEN Xn0)) x9) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 151.01/151.30 Found (or_comm_i00 (((or_introl (cODD Xn0)) (cEVEN Xn0)) x9)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 151.01/151.30 Found ((or_comm_i0 (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x9)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 151.01/151.30 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x9)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 151.01/151.30 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x9)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 151.01/151.30 Found x30:=(x3 x20):(cNUMBER Xn0)
% 151.01/151.30 Instantiate: Xn0:=Xn:fofType
% 151.01/151.30 Found (x3 x20) as proof of (cNUMBER Xn)
% 151.01/151.30 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 151.01/151.30 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 151.01/151.30 Found x90:=(x9 x80):(cNUMBER Xn00)
% 151.01/151.30 Instantiate: Xn00:=Xn:fofType
% 151.01/151.30 Found (x9 x80) as proof of (cNUMBER Xn)
% 151.01/151.30 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x9 x80)) as proof of (cNUMBER Xn)
% 151.01/151.30 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x9 x80)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 151.01/151.30 Found x9:(cODD (cS c0))
% 151.01/151.30 Instantiate: Xn0:=(cS c0):fofType
% 151.01/151.30 Found x9 as proof of (cODD Xn0)
% 151.01/151.30 Found (or_introl00 x9) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 151.01/151.30 Found ((or_introl0 (cEVEN Xn0)) x9) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 151.01/151.30 Found (((or_introl (cODD Xn0)) (cEVEN Xn0)) x9) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 151.01/151.30 Found (((or_introl (cODD Xn0)) (cEVEN Xn0)) x9) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 151.01/151.30 Found (or_comm_i00 (((or_introl (cODD Xn0)) (cEVEN Xn0)) x9)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 151.01/151.30 Found ((or_comm_i0 (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x9)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 151.01/151.30 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x9)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 151.01/151.30 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x9)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 151.01/151.30 Found x9:(cEVEN c0)
% 151.01/151.30 Instantiate: Xn0:=c0:fofType
% 151.01/151.30 Found (fun (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x9) as proof of (cEVEN Xn0)
% 151.01/151.30 Found (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x9) as proof of ((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->(cEVEN Xn0))
% 151.01/151.30 Found (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x9) as proof of ((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->(cEVEN Xn0)))
% 151.01/151.30 Found (and_rect50 (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x9)) as proof of (cEVEN Xn0)
% 151.01/151.30 Found ((and_rect5 (cEVEN Xn0)) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x9)) as proof of (cEVEN Xn0)
% 151.01/151.30 Found (((fun (P:Type) (x9:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x9) x7)) (cEVEN Xn0)) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x9)) as proof of (cEVEN Xn0)
% 151.01/151.30 Found (fun (x8:(cODD (cS c0)))=> (((fun (P:Type) (x9:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x9) x7)) (cEVEN Xn0)) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x9))) as proof of (cEVEN Xn0)
% 151.01/151.30 Found (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> (((fun (P:Type) (x9:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x9) x7)) (cEVEN Xn0)) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x9))) as proof of ((cODD (cS c0))->(cEVEN Xn0))
% 151.01/151.30 Found (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> (((fun (P:Type) (x9:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x9) x7)) (cEVEN Xn0)) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x9))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->(cEVEN Xn0)))
% 151.01/151.30 Found (and_rect40 (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> (((fun (P:Type) (x9:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x9) x7)) (cEVEN Xn0)) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x9)))) as proof of (cEVEN Xn0)
% 151.01/151.30 Found ((and_rect4 (cEVEN Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> (((fun (P:Type) (x9:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x9) x7)) (cEVEN Xn0)) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x9)))) as proof of (cEVEN Xn0)
% 151.01/151.30 Found (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x7) x6)) (cEVEN Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> (((fun (P:Type) (x9:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x9) x7)) (cEVEN Xn0)) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x9)))) as proof of (cEVEN Xn0)
% 151.01/151.30 Found (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x7) x6)) (cEVEN Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> (((fun (P:Type) (x9:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x9) x7)) (cEVEN Xn0)) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x9)))) as proof of (cEVEN Xn0)
% 151.71/151.99 Found (or_introl00 (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x7) x6)) (cEVEN Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> (((fun (P:Type) (x9:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x9) x7)) (cEVEN Xn0)) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x9))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 151.71/151.99 Found ((or_introl0 (cODD Xn0)) (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x6)) (cEVEN Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> (((fun (P:Type) (x9:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x9) x7)) (cEVEN Xn0)) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x9))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 151.71/151.99 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x6)) (cEVEN Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> (((fun (P:Type) (x9:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x9) x7)) (cEVEN Xn0)) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x9))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 151.71/151.99 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x6)) (cEVEN Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> (((fun (P:Type) (x9:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x9) x7)) (cEVEN Xn0)) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x9))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 151.71/151.99 Found x50:=(x5 x40):(cNUMBER Xn0)
% 151.71/151.99 Found (x5 x40) as proof of (cNUMBER Xn0)
% 151.71/151.99 Found (x5 x40) as proof of (cNUMBER Xn0)
% 151.71/151.99 Found x30:(cNUMBER Xn0)
% 151.71/151.99 Instantiate: Xn0:=Xn:fofType
% 151.71/151.99 Found (fun (x6:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30) as proof of (cNUMBER Xn)
% 151.71/151.99 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))
% 152.35/152.61 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)))
% 152.35/152.61 Found x30:(cNUMBER Xn0)
% 152.35/152.61 Instantiate: Xn0:=Xn:fofType
% 152.35/152.61 Found (fun (x6:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30) as proof of (cNUMBER Xn)
% 152.35/152.61 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))
% 152.35/152.61 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)))
% 152.35/152.61 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))
% 152.35/152.61 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))
% 152.35/152.61 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))
% 152.35/152.61 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))
% 152.35/152.61 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))
% 152.35/152.61 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 152.35/152.61 Instantiate: Xn00:=Xn:fofType
% 152.35/152.61 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 152.35/152.61 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 152.35/152.61 Instantiate: Xn0:=Xn:fofType
% 152.35/152.61 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 152.35/152.61 Found x11:(cEVEN c0)
% 152.35/152.61 Instantiate: Xn0:=c0:fofType
% 152.35/152.61 Found x11 as proof of (cEVEN Xn0)
% 152.35/152.61 Found (or_introl00 x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 152.35/152.61 Found ((or_introl0 (cODD Xn0)) x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 152.35/152.61 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 152.35/152.61 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 152.35/152.61 Found (x3 (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11)) as proof of (cNUMBER Xn0)
% 152.35/152.61 Found (fun (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (x3 (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11))) as proof of (cNUMBER Xn0)
% 152.35/152.61 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (x3 (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11))) as proof of ((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->(cNUMBER Xn0))
% 152.35/152.61 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (x3 (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11))) as proof of ((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->(cNUMBER Xn0)))
% 153.46/153.74 Found (and_rect50 (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (x3 (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11)))) as proof of (cNUMBER Xn0)
% 153.46/153.74 Found ((and_rect5 (cNUMBER Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (x3 (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11)))) as proof of (cNUMBER Xn0)
% 153.46/153.74 Found (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (x3 (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11)))) as proof of (cNUMBER Xn0)
% 153.46/153.74 Found (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (x3 (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11)))) as proof of (cNUMBER Xn0)
% 153.46/153.74 Found x40:=(x4 x50):((or (cEVEN Xn0)) (cODD Xn0))
% 153.46/153.74 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 153.46/153.74 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 153.46/153.74 Found x51:(cNUMBER Xn0)
% 153.46/153.74 Instantiate: Xn0:=Xn:fofType
% 153.46/153.74 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x51) as proof of (cNUMBER Xn)
% 153.46/153.74 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x51) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 153.46/153.74 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x51) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 153.46/153.74 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 153.46/153.74 Instantiate: Xn0:=Xn00:fofType
% 153.46/153.74 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 153.46/153.74 Found (x3 x40) as proof of (cNUMBER Xn0)
% 153.46/153.74 Found (x3 x40) as proof of (cNUMBER Xn0)
% 153.46/153.74 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 153.46/153.74 Instantiate: Xn0:=Xn00:fofType
% 153.46/153.74 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 153.46/153.74 Found (x3 x40) as proof of (cNUMBER Xn0)
% 153.46/153.74 Found (x3 x40) as proof of (cNUMBER Xn0)
% 153.46/153.74 Found x7:(cODD (cS c0))
% 153.46/153.74 Instantiate: Xn0:=(cS c0):fofType
% 153.46/153.74 Found x7 as proof of (cODD Xn0)
% 153.46/153.74 Found (or_intror00 x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 153.46/153.74 Found ((or_intror0 (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 153.46/153.74 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 153.46/153.74 Found (fun (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 153.46/153.74 Found (fun (x11:(cEVEN c0)) (x12:(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)))
% 153.46/153.75 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7)) as proof of ((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0))))
% 153.46/153.75 Found (and_rect50 (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 153.46/153.75 Found ((and_rect5 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 153.46/153.75 Found (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 154.41/154.72 Found (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 154.41/154.72 Found x21:((or (cEVEN Xn0)) (cODD Xn0))
% 154.41/154.72 Instantiate: Xn0:=Xn:fofType
% 154.41/154.72 Found x21 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 154.41/154.72 Found (x5 x21) as proof of (cNUMBER Xn)
% 154.41/154.72 Found (x5 x21) as proof of (cNUMBER Xn)
% 154.41/154.72 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x21)) as proof of (cNUMBER Xn)
% 154.41/154.72 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x21)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 154.41/154.72 Found x21:((or (cEVEN Xn0)) (cODD Xn0))
% 154.41/154.72 Found x21 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 154.41/154.72 Found (x3 x21) as proof of (cNUMBER Xn)
% 154.41/154.72 Found (x3 x21) as proof of (cNUMBER Xn)
% 154.41/154.72 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x21)) as proof of (cNUMBER Xn)
% 154.41/154.72 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x21)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 154.41/154.72 Found x30:=(x3 x21):(cNUMBER Xn0)
% 154.41/154.72 Instantiate: Xn0:=Xn:fofType
% 154.41/154.72 Found (x3 x21) as proof of (cNUMBER Xn)
% 154.41/154.72 Found (fun (x6:(cODD Xn0))=> (x3 x21)) as proof of (cNUMBER Xn)
% 154.41/154.72 Found (fun (x6:(cODD Xn0))=> (x3 x21)) as proof of ((cODD Xn0)->(cNUMBER Xn))
% 154.41/154.72 Found x30:=(x3 x21):(cNUMBER Xn0)
% 154.41/154.72 Instantiate: Xn0:=Xn:fofType
% 154.41/154.72 Found (x3 x21) as proof of (cNUMBER Xn)
% 154.41/154.72 Found (fun (x6:(cEVEN Xn0))=> (x3 x21)) as proof of (cNUMBER Xn)
% 154.41/154.72 Found (fun (x6:(cEVEN Xn0))=> (x3 x21)) as proof of ((cEVEN Xn0)->(cNUMBER Xn))
% 154.41/154.72 Found ((or_ind00 (fun (x6:(cEVEN Xn0))=> (x3 x21))) (fun (x6:(cODD Xn0))=> (x3 x21))) as proof of (cNUMBER Xn)
% 154.41/154.72 Found (((or_ind0 (cNUMBER Xn)) (fun (x6:(cEVEN Xn0))=> (x3 x21))) (fun (x6:(cODD Xn0))=> (x3 x21))) as proof of (cNUMBER Xn)
% 154.41/154.72 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)
% 154.41/154.72 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> ((((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)
% 154.41/154.72 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> ((((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 (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 154.41/154.72 Found x30:=(x3 x21):(cNUMBER Xn0)
% 154.41/154.72 Instantiate: Xn0:=Xn:fofType
% 154.41/154.72 Found (x3 x21) as proof of (cNUMBER Xn)
% 154.41/154.72 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x21)) as proof of (cNUMBER Xn)
% 154.41/154.72 Found (fun (x11:(cEVEN c0)) (x12:(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))
% 154.41/154.72 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x21)) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 155.56/155.86 Found x50:=(x5 x40):(cNUMBER Xn00)
% 155.56/155.86 Found (x5 x40) as proof of (cNUMBER Xn)
% 155.56/155.86 Found (x5 x40) as proof of (cNUMBER Xn)
% 155.56/155.86 Found (x5 x40) as proof of (cNUMBER Xn)
% 155.56/155.86 Found x30:=(x3 x20):(cNUMBER Xn0)
% 155.56/155.86 Found (x3 x20) as proof of (cNUMBER Xn)
% 155.56/155.86 Found (x3 x20) as proof of (cNUMBER Xn)
% 155.56/155.86 Found (x3 x20) as proof of (cNUMBER Xn)
% 155.56/155.86 Found x31:(cNUMBER Xn0)
% 155.56/155.86 Instantiate: Xn0:=Xn:fofType
% 155.56/155.86 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x31) as proof of (cNUMBER Xn)
% 155.56/155.86 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x31) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 155.56/155.86 Found x90:=(x9 x80):(cNUMBER Xn00)
% 155.56/155.86 Instantiate: Xn00:=Xn:fofType
% 155.56/155.86 Found (x9 x80) as proof of (cNUMBER Xn)
% 155.56/155.86 Found (x9 x80) as proof of (cNUMBER Xn)
% 155.56/155.86 Found x70:=(x7 x60):(cNUMBER Xn0)
% 155.56/155.86 Instantiate: Xn0:=Xn:fofType
% 155.56/155.86 Found (x7 x60) as proof of (cNUMBER Xn)
% 155.56/155.86 Found (x7 x60) as proof of (cNUMBER Xn)
% 155.56/155.86 Found x30:=(x3 x21):(cNUMBER Xn0)
% 155.56/155.86 Instantiate: Xn0:=Xn:fofType
% 155.56/155.86 Found (x3 x21) as proof of (cNUMBER Xn)
% 155.56/155.86 Found (fun (x6:(cODD Xn0))=> (x3 x21)) as proof of (cNUMBER Xn)
% 155.56/155.86 Found (fun (x6:(cODD Xn0))=> (x3 x21)) as proof of ((cODD Xn0)->(cNUMBER Xn))
% 155.56/155.86 Found x30:=(x3 x21):(cNUMBER Xn0)
% 155.56/155.86 Instantiate: Xn0:=Xn:fofType
% 155.56/155.86 Found (x3 x21) as proof of (cNUMBER Xn)
% 155.56/155.86 Found (fun (x6:(cEVEN Xn0))=> (x3 x21)) as proof of (cNUMBER Xn)
% 155.56/155.86 Found (fun (x6:(cEVEN Xn0))=> (x3 x21)) as proof of ((cEVEN Xn0)->(cNUMBER Xn))
% 155.56/155.86 Found ((or_ind00 (fun (x6:(cEVEN Xn0))=> (x3 x21))) (fun (x6:(cODD Xn0))=> (x3 x21))) as proof of (cNUMBER Xn)
% 155.56/155.86 Found (((or_ind0 (cNUMBER Xn)) (fun (x6:(cEVEN Xn0))=> (x3 x21))) (fun (x6:(cODD Xn0))=> (x3 x21))) as proof of (cNUMBER Xn)
% 155.56/155.86 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)
% 155.56/155.86 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)
% 155.56/155.86 Found x21:((or (cEVEN Xn0)) (cODD Xn0))
% 155.56/155.86 Instantiate: Xn0:=Xn:fofType
% 155.56/155.86 Found x21 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 155.56/155.86 Found (x5 x21) as proof of (cNUMBER Xn)
% 155.56/155.86 Found (x5 x21) as proof of (cNUMBER Xn)
% 155.56/155.86 Found (x5 x21) as proof of (cNUMBER Xn)
% 155.56/155.86 Found x21:((or (cEVEN Xn0)) (cODD Xn0))
% 155.56/155.86 Found x21 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 155.56/155.86 Found (x3 x21) as proof of (cNUMBER Xn)
% 155.56/155.86 Found (x3 x21) as proof of (cNUMBER Xn)
% 155.56/155.86 Found (x3 x21) as proof of (cNUMBER Xn)
% 155.56/155.86 Found x80:((or (cEVEN Xn00)) (cODD Xn00))
% 155.56/155.86 Instantiate: Xn00:=Xn:fofType
% 155.56/155.86 Found x80 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 155.56/155.86 Found x70:(cNUMBER Xn00)
% 155.56/155.86 Instantiate: Xn00:=Xn:fofType
% 155.56/155.86 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x70) as proof of (cNUMBER Xn)
% 155.56/155.86 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x70) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 155.56/155.86 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x70) as proof of (((and ((and (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)))
% 155.56/155.86 Found x50:(cNUMBER Xn0)
% 155.56/155.86 Instantiate: Xn0:=Xn:fofType
% 155.56/155.86 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of (cNUMBER Xn)
% 155.56/155.86 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 155.56/155.86 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of (((and ((and (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)))
% 155.61/155.90 Found x30:=(x3 x21):(cNUMBER Xn0)
% 155.61/155.90 Instantiate: Xn0:=Xn:fofType
% 155.61/155.90 Found (x3 x21) as proof of (cNUMBER Xn)
% 155.61/155.90 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x21)) as proof of (cNUMBER Xn)
% 155.61/155.90 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x21)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 155.61/155.90 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x21)) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn)))
% 155.61/155.90 Found (and_rect20 (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x21))) as proof of (cNUMBER Xn)
% 155.61/155.90 Found ((and_rect2 (cNUMBER Xn)) (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x21))) as proof of (cNUMBER Xn)
% 155.61/155.90 Found (((fun (P:Type) (x4:(((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->P)))=> (((((and_rect ((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))) P) x4) x0)) (cNUMBER Xn)) (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x21))) as proof of (cNUMBER Xn)
% 155.77/156.07 Found (((fun (P:Type) (x4:(((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->P)))=> (((((and_rect ((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))) P) x4) x0)) (cNUMBER Xn)) (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x3 x21))) as proof of (cNUMBER Xn)
% 155.77/156.07 Found x50:(cNUMBER Xn0)
% 155.77/156.07 Instantiate: Xn0:=Xn:fofType
% 155.77/156.07 Found (fun (x11:(cODD (cS c0)))=> x50) as proof of (cNUMBER Xn)
% 155.77/156.07 Found (fun (x9:(cEVEN Xn0)) (x11:(cODD (cS c0)))=> x50) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 155.77/156.07 Found (fun (x9:(cEVEN Xn0)) (x11:(cODD (cS c0)))=> x50) as proof of ((cEVEN Xn0)->((cODD (cS c0))->(cNUMBER Xn)))
% 155.77/156.07 Found x50:(cNUMBER Xn0)
% 155.77/156.07 Instantiate: Xn0:=Xn:fofType
% 155.77/156.07 Found (fun (x11:(cODD (cS c0)))=> x50) as proof of (cNUMBER Xn)
% 155.77/156.07 Found (fun (x9:(cODD Xn0)) (x11:(cODD (cS c0)))=> x50) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 155.77/156.07 Found (fun (x9:(cODD Xn0)) (x11:(cODD (cS c0)))=> x50) as proof of ((cODD Xn0)->((cODD (cS c0))->(cNUMBER Xn)))
% 155.77/156.07 Found ((or_ind00 (fun (x9:(cEVEN Xn0)) (x11:(cODD (cS c0)))=> x50)) (fun (x9:(cODD Xn0)) (x11:(cODD (cS c0)))=> x50)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 155.77/156.07 Found (((or_ind0 ((cODD (cS c0))->(cNUMBER Xn))) (fun (x9:(cEVEN Xn0)) (x11:(cODD (cS c0)))=> x50)) (fun (x9:(cODD Xn0)) (x11:(cODD (cS c0)))=> x50)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 155.77/156.07 Found ((((fun (P:Prop) (x9:((cEVEN Xn0)->P)) (x11:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x9) x11) x40)) ((cODD (cS c0))->(cNUMBER Xn))) (fun (x9:(cEVEN Xn0)) (x11:(cODD (cS c0)))=> x50)) (fun (x9:(cODD Xn0)) (x11:(cODD (cS c0)))=> x50)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 155.77/156.07 Found ((((fun (P:Prop) (x9:((cEVEN Xn0)->P)) (x11:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x9) x11) (x4 x50))) ((cODD (cS c0))->(cNUMBER Xn))) (fun (x9:(cEVEN Xn0)) (x11:(cODD (cS c0)))=> x50)) (fun (x9:(cODD Xn0)) (x11:(cODD (cS c0)))=> x50)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 155.77/156.07 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))))=> ((((fun (P:Prop) (x9:((cEVEN Xn0)->P)) (x11:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x9) x11) (x4 x50))) ((cODD (cS c0))->(cNUMBER Xn))) (fun (x9:(cEVEN Xn0)) (x11:(cODD (cS c0)))=> x50)) (fun (x9:(cODD Xn0)) (x11:(cODD (cS c0)))=> x50))) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 155.77/156.07 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))))=> ((((fun (P:Prop) (x9:((cEVEN Xn0)->P)) (x11:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x9) x11) (x4 x50))) ((cODD (cS c0))->(cNUMBER Xn))) (fun (x9:(cEVEN Xn0)) (x11:(cODD (cS c0)))=> x50)) (fun (x9:(cODD Xn0)) (x11:(cODD (cS c0)))=> x50))) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 155.77/156.07 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 155.77/156.07 Instantiate: Xn0:=Xn:fofType
% 155.77/156.07 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 156.08/156.38 Found x32:(cNUMBER Xn0)
% 156.08/156.38 Instantiate: Xn0:=Xn:fofType
% 156.08/156.38 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x32) as proof of (cNUMBER Xn)
% 156.08/156.38 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x32) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 156.08/156.38 Found x41:((or (cEVEN Xn00)) (cODD Xn00))
% 156.08/156.38 Instantiate: Xn00:=Xn:fofType
% 156.08/156.38 Found x41 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 156.08/156.38 Found (x3 x41) as proof of (cNUMBER Xn)
% 156.08/156.38 Found (x3 x41) as proof of (cNUMBER Xn)
% 156.08/156.38 Found (x3 x41) as proof of (cNUMBER Xn)
% 156.08/156.38 Found x41:((or (cEVEN Xn00)) (cODD Xn00))
% 156.08/156.38 Found x41 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 156.08/156.38 Found (x5 x41) as proof of (cNUMBER Xn)
% 156.08/156.38 Found (x5 x41) as proof of (cNUMBER Xn)
% 156.08/156.38 Found (x5 x41) as proof of (cNUMBER Xn)
% 156.08/156.38 Found x50:(cNUMBER Xn00)
% 156.08/156.38 Found x50 as proof of (cNUMBER Xn00)
% 156.08/156.38 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 156.08/156.38 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 156.08/156.38 Found (fun (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x4 x50)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 156.08/156.38 Found (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x4 x50)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 156.08/156.38 Found (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x4 x50)) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->((or (cEVEN Xn0)) (cODD Xn0))))
% 156.08/156.38 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 156.08/156.38 Instantiate: Xn0:=Xn:fofType
% 156.08/156.38 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 156.08/156.38 Found (fun (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x2 x30)) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 156.08/156.38 Found (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x2 x30)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->((or (cEVEN Xn00)) (cODD Xn00)))
% 156.08/156.38 Found (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x2 x30)) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->((or (cEVEN Xn00)) (cODD Xn00))))
% 156.08/156.39 Found (and_rect30 (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x2 x30))) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 156.08/156.39 Found ((and_rect3 ((or (cEVEN Xn00)) (cODD Xn00))) (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x2 x30))) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 156.08/156.39 Found (((fun (P:Type) (x6:(((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->P)))=> (((((and_rect ((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))) P) x6) x0)) ((or (cEVEN Xn00)) (cODD Xn00))) (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x2 x30))) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 156.08/156.39 Found (((fun (P:Type) (x6:(((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->P)))=> (((((and_rect ((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))) P) x6) x0)) ((or (cEVEN Xn00)) (cODD Xn00))) (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x2 x30))) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 156.08/156.39 Found x40:=(x4 x50):((or (cEVEN Xn00)) (cODD Xn00))
% 156.08/156.39 Instantiate: Xn00:=Xn:fofType
% 156.08/156.39 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 156.08/156.39 Found (fun (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x4 x50)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 156.08/156.39 Found (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x4 x50)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 156.08/156.39 Found (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x4 x50)) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->((or (cEVEN Xn0)) (cODD Xn0))))
% 156.08/156.39 Found (and_rect30 (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x4 x50))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 156.08/156.39 Found ((and_rect3 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x4 x50))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 156.08/156.39 Found (((fun (P:Type) (x6:(((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->P)))=> (((((and_rect ((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))) P) x6) x0)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x4 x50))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 157.95/158.23 Found (((fun (P:Type) (x6:(((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->P)))=> (((((and_rect ((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))) P) x6) x0)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x4 x50))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 157.95/158.23 Found x70:=(x7 x61):(cNUMBER Xn0)
% 157.95/158.23 Instantiate: Xn0:=Xn:fofType
% 157.95/158.23 Found (x7 x61) as proof of (cNUMBER Xn)
% 157.95/158.23 Found (fun (x9:(cODD (cS c0)))=> (x7 x61)) as proof of (cNUMBER Xn)
% 157.95/158.23 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x7 x61)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 157.95/158.23 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x7 x61)) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 157.95/158.23 Found (and_rect40 (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x7 x61))) as proof of (cNUMBER Xn)
% 157.95/158.23 Found ((and_rect4 (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x7 x61))) as proof of (cNUMBER Xn)
% 157.95/158.23 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x4)) (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x7 x61))) as proof of (cNUMBER Xn)
% 157.95/158.23 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x4)) (cNUMBER Xn)) (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x7 x61))) as proof of (cNUMBER Xn)
% 157.95/158.23 Found x9:(cEVEN c0)
% 157.95/158.23 Instantiate: Xn0:=c0:fofType
% 157.95/158.23 Found x9 as proof of (cEVEN Xn0)
% 157.95/158.23 Found (or_introl00 x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 157.95/158.23 Found ((or_introl0 (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 157.95/158.23 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 157.95/158.23 Found (fun (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_introl (cEVEN Xn0)) (cODD Xn0)) x9)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 157.95/158.23 Found (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_introl (cEVEN Xn0)) (cODD Xn0)) x9)) as proof of ((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 157.95/158.23 Found (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_introl (cEVEN Xn0)) (cODD Xn0)) x9)) as proof of ((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0))))
% 160.74/161.04 Found (and_rect50 (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_introl (cEVEN Xn0)) (cODD Xn0)) x9))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 160.74/161.04 Found ((and_rect5 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_introl (cEVEN Xn0)) (cODD Xn0)) x9))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 160.74/161.04 Found (((fun (P:Type) (x9:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x9) x8)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_introl (cEVEN Xn0)) (cODD Xn0)) x9))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 160.74/161.04 Found (((fun (P:Type) (x9:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x9) x8)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_introl (cEVEN Xn0)) (cODD Xn0)) x9))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 160.74/161.04 Found (x5 (((fun (P:Type) (x9:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x9) x8)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_introl (cEVEN Xn0)) (cODD Xn0)) x9)))) as proof of (cNUMBER Xn0)
% 160.74/161.04 Found (x5 (((fun (P:Type) (x9:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x9) x8)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_introl (cEVEN Xn0)) (cODD Xn0)) x9)))) as proof of (cNUMBER Xn0)
% 160.74/161.04 Found x22:((or (cEVEN Xn0)) (cODD Xn0))
% 160.74/161.04 Found x22 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 160.74/161.04 Found (x3 x22) as proof of (cNUMBER Xn)
% 160.74/161.04 Found (x3 x22) as proof of (cNUMBER Xn)
% 160.74/161.04 Found (fun (x3:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x3 x22)) as proof of (cNUMBER Xn)
% 160.74/161.04 Found (fun (x3:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x3 x22)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 160.74/161.04 Found x30:=(x3 x20):(cNUMBER Xn0)
% 160.74/161.04 Instantiate: Xn0:=Xn:fofType
% 160.74/161.04 Found (x3 x20) as proof of (cNUMBER Xn)
% 160.74/161.04 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 160.74/161.04 Found (fun (x9:(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))
% 160.74/161.04 Found x70:=(x7 x60):(cNUMBER Xn00)
% 160.74/161.04 Instantiate: Xn00:=Xn:fofType
% 160.74/161.04 Found (x7 x60) as proof of (cNUMBER Xn)
% 160.74/161.04 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x7 x60)) as proof of (cNUMBER Xn)
% 160.74/161.04 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x7 x60)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 160.74/161.04 Found x30:=(x3 x20):(cNUMBER Xn0)
% 160.74/161.04 Found (x3 x20) as proof of (cNUMBER Xn00)
% 160.74/161.04 Found (x3 x20) as proof of (cNUMBER Xn00)
% 160.74/161.04 Found (x3 x20) as proof of (cNUMBER Xn00)
% 160.74/161.04 Found x30:=(x3 x40):(cNUMBER Xn0)
% 160.74/161.04 Found (x3 x40) as proof of (cNUMBER Xn00)
% 160.74/161.04 Found (x3 x40) as proof of (cNUMBER Xn00)
% 160.74/161.04 Found (x3 x40) as proof of (cNUMBER Xn00)
% 160.74/161.04 Found x30:=(x3 x20):(cNUMBER Xn0)
% 160.74/161.04 Found (x3 x20) as proof of (cNUMBER Xn0)
% 160.74/161.04 Found (x3 x20) as proof of (cNUMBER Xn0)
% 160.74/161.04 Found x30:=(x3 x20):(cNUMBER Xn0)
% 160.74/161.04 Found (x3 x20) as proof of (cNUMBER Xn00)
% 160.74/161.04 Found (x3 x20) as proof of (cNUMBER Xn00)
% 160.74/161.04 Found (x3 x20) as proof of (cNUMBER Xn00)
% 160.74/161.04 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 160.74/161.04 Instantiate: Xn00:=Xn:fofType
% 162.28/162.62 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 162.28/162.62 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 162.28/162.62 Instantiate: Xn00:=Xn:fofType
% 162.28/162.62 Found (fun (x9:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x40) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 162.28/162.62 Found (fun (x9:(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)))
% 162.28/162.62 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 162.28/162.62 Instantiate: Xn0:=Xn:fofType
% 162.28/162.62 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x20) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 162.28/162.62 Found (fun (x9:(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)))
% 162.28/162.62 Found x30:=(x3 x20):(cNUMBER Xn0)
% 162.28/162.62 Instantiate: Xn00:=Xn0:fofType
% 162.28/162.62 Found (x3 x20) as proof of (cNUMBER Xn00)
% 162.28/162.62 Found (x3 x20) as proof of (cNUMBER Xn00)
% 162.28/162.62 Found x30:=(x3 x20):(cNUMBER Xn0)
% 162.28/162.62 Found (x3 x20) as proof of (cNUMBER Xn0)
% 162.28/162.62 Found (x3 x20) as proof of (cNUMBER Xn0)
% 162.28/162.62 Found x30:=(x3 x21):(cNUMBER Xn0)
% 162.28/162.62 Instantiate: Xn0:=Xn:fofType
% 162.28/162.62 Found (x3 x21) as proof of (cNUMBER Xn)
% 162.28/162.62 Found (x3 x21) as proof of (cNUMBER Xn)
% 162.28/162.62 Found x30:=(x3 x21):(cNUMBER Xn0)
% 162.28/162.62 Found (x3 x21) as proof of (cNUMBER Xn)
% 162.28/162.62 Found (x3 x21) as proof of (cNUMBER Xn)
% 162.28/162.62 Found (x3 x21) as proof of (cNUMBER Xn)
% 162.28/162.62 Found x50:=(x5 x40):(cNUMBER Xn00)
% 162.28/162.62 Instantiate: Xn00:=Xn:fofType
% 162.28/162.62 Found (x5 x40) as proof of (cNUMBER Xn)
% 162.28/162.62 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 162.28/162.62 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 162.28/162.62 Found x30:=(x3 x20):(cNUMBER Xn0)
% 162.28/162.62 Instantiate: Xn0:=Xn:fofType
% 162.28/162.62 Found (x3 x20) as proof of (cNUMBER Xn)
% 162.28/162.62 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 162.28/162.62 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 162.28/162.62 Found x30:=(x3 x20):(cNUMBER Xn0)
% 162.28/162.62 Instantiate: Xn0:=Xn:fofType
% 162.28/162.62 Found (x3 x20) as proof of (cNUMBER Xn)
% 162.28/162.62 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 162.28/162.62 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 162.28/162.62 Found x30:=(x3 x20):(cNUMBER Xn0)
% 162.28/162.62 Found (x3 x20) as proof of (cNUMBER Xn0)
% 162.28/162.62 Found (x3 x20) as proof of (cNUMBER Xn0)
% 162.28/162.62 Found x30:=(x3 x21):(cNUMBER Xn0)
% 162.28/162.62 Instantiate: Xn0:=Xn:fofType
% 162.28/162.62 Found (x3 x21) as proof of (cNUMBER Xn)
% 162.28/162.62 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x21)) as proof of (cNUMBER Xn)
% 162.28/162.62 Found (fun (x12:(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))
% 162.28/162.62 Found x50:=(x5 x40):(cNUMBER Xn00)
% 162.28/162.62 Instantiate: Xn00:=Xn:fofType
% 162.28/162.62 Found (x5 x40) as proof of (cNUMBER Xn)
% 162.28/162.62 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 162.28/162.62 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 162.28/162.62 Found x50:=(x5 x41):(cNUMBER Xn0)
% 162.28/162.62 Found (x5 x41) as proof of (cNUMBER Xn0)
% 162.28/162.62 Found (x5 x41) as proof of (cNUMBER Xn0)
% 162.28/162.62 Found x50:=(x5 x42):(cNUMBER Xn0)
% 162.28/162.62 Instantiate: Xn0:=Xn:fofType
% 162.28/162.62 Found (x5 x42) as proof of (cNUMBER Xn)
% 162.28/162.62 Found (x5 x42) as proof of (cNUMBER Xn)
% 162.28/162.62 Found x50:=(x5 x40):(cNUMBER Xn00)
% 162.28/162.62 Instantiate: Xn00:=Xn:fofType
% 162.28/162.62 Found (x5 x40) as proof of (cNUMBER Xn)
% 162.28/162.62 Found (x5 x40) as proof of (cNUMBER Xn)
% 162.28/162.62 Found x30:=(x3 x20):(cNUMBER Xn0)
% 162.28/162.62 Instantiate: Xn0:=Xn:fofType
% 162.28/162.62 Found (x3 x20) as proof of (cNUMBER Xn)
% 162.28/162.62 Found (x3 x20) as proof of (cNUMBER Xn)
% 162.28/162.62 Found x50:=(x5 x41):(cNUMBER Xn00)
% 162.28/162.62 Instantiate: Xn00:=Xn:fofType
% 162.28/162.62 Found (x5 x41) as proof of (cNUMBER Xn)
% 162.28/162.62 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x41)) as proof of (cNUMBER Xn)
% 164.67/164.98 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x41)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 164.67/164.98 Found x50:=(x5 x40):(cNUMBER Xn0)
% 164.67/164.98 Found (x5 x40) as proof of (cNUMBER Xn)
% 164.67/164.98 Found (x5 x40) as proof of (cNUMBER Xn)
% 164.67/164.98 Found (x5 x40) as proof of (cNUMBER Xn)
% 164.67/164.98 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 164.67/164.98 Instantiate: Xn0:=Xn:fofType
% 164.67/164.98 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x20) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 164.67/164.98 Found (fun (x9:(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)))
% 164.67/164.98 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 164.67/164.98 Instantiate: Xn00:=Xn:fofType
% 164.67/164.98 Found (fun (x9:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x40) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 164.67/164.98 Found (fun (x9:(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)))
% 164.67/164.98 Found x30:=(x3 x20):(cNUMBER Xn0)
% 164.67/164.98 Instantiate: Xn0:=Xn:fofType
% 164.67/164.98 Found (x3 x20) as proof of (cNUMBER Xn)
% 164.67/164.98 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 164.67/164.98 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))
% 164.67/164.98 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)))
% 164.67/164.98 Found x50:=(x5 x40):(cNUMBER Xn0)
% 164.67/164.98 Instantiate: Xn0:=Xn:fofType
% 164.67/164.98 Found (x5 x40) as proof of (cNUMBER Xn)
% 164.67/164.98 Found (x5 x40) as proof of (cNUMBER Xn)
% 164.67/164.98 Found x90:=(x9 x80):(cNUMBER Xn00)
% 164.67/164.98 Instantiate: Xn00:=Xn:fofType
% 164.67/164.98 Found (x9 x80) as proof of (cNUMBER Xn)
% 164.67/164.98 Found (x9 x80) as proof of (cNUMBER Xn)
% 164.67/164.98 Found x30:=(x3 x21):(cNUMBER Xn0)
% 164.67/164.98 Found (x3 x21) as proof of (cNUMBER Xn0)
% 164.67/164.98 Found (x3 x21) as proof of (cNUMBER Xn0)
% 164.67/164.98 Found x30:=(x3 x22):(cNUMBER Xn0)
% 164.67/164.98 Instantiate: Xn0:=Xn:fofType
% 164.67/164.98 Found (x3 x22) as proof of (cNUMBER Xn)
% 164.67/164.98 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x22)) as proof of (cNUMBER Xn)
% 164.67/164.98 Found (fun (x7:(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))
% 164.67/164.98 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 164.67/164.98 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 164.67/164.98 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 164.67/164.98 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 164.67/164.98 Instantiate: Xn00:=Xn:fofType
% 164.67/164.98 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 164.67/164.98 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 164.67/164.98 Instantiate: Xn0:=Xn:fofType
% 164.67/164.98 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 164.67/164.98 Found x41:((or (cEVEN Xn00)) (cODD Xn00))
% 164.67/164.98 Instantiate: Xn00:=Xn:fofType
% 164.67/164.98 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x41) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 164.67/164.98 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)))
% 164.67/164.98 Found x30:(cNUMBER Xn0)
% 164.67/164.98 Instantiate: Xn0:=Xn:fofType
% 164.67/164.98 Found (fun (x6:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30) as proof of (cNUMBER Xn)
% 164.67/164.98 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))
% 164.67/164.98 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)))
% 164.67/164.98 Found x30:(cNUMBER Xn0)
% 164.67/164.98 Instantiate: Xn0:=Xn:fofType
% 164.67/164.98 Found (fun (x6:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30) as proof of (cNUMBER Xn)
% 164.67/164.98 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))
% 165.08/165.39 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)))
% 165.08/165.39 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))
% 165.08/165.39 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))
% 165.08/165.39 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))
% 165.08/165.39 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))
% 165.08/165.39 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))
% 165.08/165.39 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)))
% 165.08/165.39 Found x20:=(x2 x31):((or (cEVEN Xn0)) (cODD Xn0))
% 165.08/165.39 Found (x2 x31) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 165.08/165.39 Found (x2 x31) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 165.08/165.39 Found x50:(cNUMBER Xn0)
% 165.08/165.39 Instantiate: Xn0:=Xn:fofType
% 165.08/165.39 Found (fun (x11:(cODD (cS c0)))=> x50) as proof of (cNUMBER Xn)
% 165.08/165.39 Found (fun (x9:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x11:(cODD (cS c0)))=> x50) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 165.08/165.39 Found (fun (x8:(cEVEN Xn0)) (x9:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x11:(cODD (cS c0)))=> x50) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 165.08/165.39 Found (fun (x8:(cEVEN Xn0)) (x9:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x11:(cODD (cS c0)))=> x50) as proof of ((cEVEN Xn0)->(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn))))
% 165.08/165.39 Found x50:(cNUMBER Xn0)
% 165.08/165.39 Instantiate: Xn0:=Xn:fofType
% 165.08/165.39 Found (fun (x11:(cODD (cS c0)))=> x50) as proof of (cNUMBER Xn)
% 165.08/165.39 Found (fun (x9:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x11:(cODD (cS c0)))=> x50) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 165.08/165.39 Found (fun (x8:(cODD Xn0)) (x9:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x11:(cODD (cS c0)))=> x50) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 165.88/166.17 Found (fun (x8:(cODD Xn0)) (x9:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x11:(cODD (cS c0)))=> x50) as proof of ((cODD Xn0)->(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn))))
% 165.88/166.17 Found ((or_ind00 (fun (x8:(cEVEN Xn0)) (x9:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x11:(cODD (cS c0)))=> x50)) (fun (x8:(cODD Xn0)) (x9:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x11:(cODD (cS c0)))=> x50)) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 165.88/166.17 Found (((or_ind0 (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))) (fun (x8:(cEVEN Xn0)) (x9:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x11:(cODD (cS c0)))=> x50)) (fun (x8:(cODD Xn0)) (x9:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x11:(cODD (cS c0)))=> x50)) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 165.88/166.17 Found ((((fun (P:Prop) (x8:((cEVEN Xn0)->P)) (x9:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x8) x9) x40)) (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->(cNUMBER Xn)))) (fun (x8:(cEVEN Xn0)) (x9:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x11:(cODD (cS c0)))=> x50)) (fun (x8:(cODD Xn0)) (x9:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x11:(cODD (cS c0)))=> x50)) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 165.88/166.17 Found ((((fun (P:Prop) (x8:((cEVEN Xn0)->P)) (x9:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x8) x9) (x4 x50))) (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->(cNUMBER Xn)))) (fun (x8:(cEVEN Xn0)) (x9:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x11:(cODD (cS c0)))=> x50)) (fun (x8:(cODD Xn0)) (x9:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x11:(cODD (cS c0)))=> x50)) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 165.88/166.17 Found ((((fun (P:Prop) (x8:((cEVEN Xn0)->P)) (x9:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x8) x9) (x4 x50))) (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->(cNUMBER Xn)))) (fun (x8:(cEVEN Xn0)) (x9:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x11:(cODD (cS c0)))=> x50)) (fun (x8:(cODD Xn0)) (x9:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x11:(cODD (cS c0)))=> x50)) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 165.88/166.17 Found x51:(cNUMBER Xn0)
% 165.88/166.17 Instantiate: Xn0:=Xn:fofType
% 165.88/166.17 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x51) as proof of (cNUMBER Xn)
% 165.88/166.17 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x51) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 165.88/166.17 Found x30:=(x3 x22):(cNUMBER Xn0)
% 165.88/166.17 Instantiate: Xn0:=Xn:fofType
% 165.88/166.17 Found (x3 x22) as proof of (cNUMBER Xn)
% 165.88/166.17 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x22)) as proof of (cNUMBER Xn)
% 165.88/166.17 Found (fun (x6:((and ((and (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 x22)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 166.56/166.88 Found (fun (x6:((and ((and (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 x22)) as proof of (((and ((and (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)))
% 166.56/166.88 Found x80:((or (cEVEN Xn00)) (cODD Xn00))
% 166.56/166.88 Instantiate: Xn00:=Xn:fofType
% 166.56/166.88 Found x80 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 166.56/166.88 Found x50:=(x5 x40):(cNUMBER Xn00)
% 166.56/166.88 Found (x5 x40) as proof of (cNUMBER Xn)
% 166.56/166.88 Found (x5 x40) as proof of (cNUMBER Xn)
% 166.56/166.88 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 166.56/166.88 Found (fun (x9:(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))
% 166.56/166.88 Found x30:=(x3 x20):(cNUMBER Xn0)
% 166.56/166.88 Found (x3 x20) as proof of (cNUMBER Xn)
% 166.56/166.88 Found (x3 x20) as proof of (cNUMBER Xn)
% 166.56/166.88 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 166.56/166.88 Found (fun (x9:(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))
% 166.56/166.88 Found x70:(cNUMBER Xn0)
% 166.56/166.88 Instantiate: Xn0:=Xn:fofType
% 166.56/166.88 Found (fun (x11:(cODD (cS c0)))=> x70) as proof of (cNUMBER Xn)
% 166.56/166.88 Found (fun (x9:(cEVEN Xn0)) (x11:(cODD (cS c0)))=> x70) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 166.56/166.88 Found (fun (x9:(cEVEN Xn0)) (x11:(cODD (cS c0)))=> x70) as proof of ((cEVEN Xn0)->((cODD (cS c0))->(cNUMBER Xn)))
% 166.56/166.88 Found x70:(cNUMBER Xn0)
% 166.56/166.88 Instantiate: Xn0:=Xn:fofType
% 166.56/166.88 Found (fun (x11:(cODD (cS c0)))=> x70) as proof of (cNUMBER Xn)
% 166.56/166.88 Found (fun (x9:(cODD Xn0)) (x11:(cODD (cS c0)))=> x70) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 166.56/166.88 Found (fun (x9:(cODD Xn0)) (x11:(cODD (cS c0)))=> x70) as proof of ((cODD Xn0)->((cODD (cS c0))->(cNUMBER Xn)))
% 166.56/166.88 Found ((or_ind00 (fun (x9:(cEVEN Xn0)) (x11:(cODD (cS c0)))=> x70)) (fun (x9:(cODD Xn0)) (x11:(cODD (cS c0)))=> x70)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 166.56/166.88 Found (((or_ind0 ((cODD (cS c0))->(cNUMBER Xn))) (fun (x9:(cEVEN Xn0)) (x11:(cODD (cS c0)))=> x70)) (fun (x9:(cODD Xn0)) (x11:(cODD (cS c0)))=> x70)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 166.56/166.88 Found ((((fun (P:Prop) (x9:((cEVEN Xn0)->P)) (x11:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x9) x11) x60)) ((cODD (cS c0))->(cNUMBER Xn))) (fun (x9:(cEVEN Xn0)) (x11:(cODD (cS c0)))=> x70)) (fun (x9:(cODD Xn0)) (x11:(cODD (cS c0)))=> x70)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 166.56/166.88 Found ((((fun (P:Prop) (x9:((cEVEN Xn0)->P)) (x11:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x9) x11) (x6 x70))) ((cODD (cS c0))->(cNUMBER Xn))) (fun (x9:(cEVEN Xn0)) (x11:(cODD (cS c0)))=> x70)) (fun (x9:(cODD Xn0)) (x11:(cODD (cS c0)))=> x70)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 166.56/166.88 Found ((((fun (P:Prop) (x9:((cEVEN Xn0)->P)) (x11:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x9) x11) (x6 x70))) ((cODD (cS c0))->(cNUMBER Xn))) (fun (x9:(cEVEN Xn0)) (x11:(cODD (cS c0)))=> x70)) (fun (x9:(cODD Xn0)) (x11:(cODD (cS c0)))=> x70)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 166.56/166.88 Found x70:=(x7 x60):(cNUMBER Xn0)
% 166.56/166.88 Instantiate: Xn0:=Xn:fofType
% 166.56/166.88 Found (x7 x60) as proof of (cNUMBER Xn)
% 166.56/166.88 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x7 x60)) as proof of (cNUMBER Xn)
% 166.56/166.88 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x7 x60)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 166.56/166.88 Found x21:((or (cEVEN Xn0)) (cODD Xn0))
% 166.56/166.88 Instantiate: Xn0:=Xn:fofType
% 166.56/166.88 Found x21 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 166.56/166.88 Found (x5 x21) as proof of (cNUMBER Xn)
% 166.56/166.88 Found (x5 x21) as proof of (cNUMBER Xn)
% 166.56/166.88 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x21)) as proof of (cNUMBER Xn)
% 166.56/166.88 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))
% 166.61/166.91 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)))
% 166.61/166.91 Found x21:((or (cEVEN Xn0)) (cODD Xn0))
% 166.61/166.91 Found x21 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 166.61/166.91 Found (x3 x21) as proof of (cNUMBER Xn)
% 166.61/166.91 Found (x3 x21) as proof of (cNUMBER Xn)
% 166.61/166.91 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x21)) as proof of (cNUMBER Xn)
% 166.61/166.91 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))
% 166.61/166.91 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)))
% 166.61/166.91 Found x40:=(x4 x50):((or (cEVEN Xn00)) (cODD Xn00))
% 166.61/166.91 Instantiate: Xn00:=Xn:fofType
% 166.61/166.91 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 166.61/166.91 Found (fun (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x4 x50)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 166.61/166.91 Found (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x4 x50)) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 166.61/166.91 Found (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x4 x50)) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->((or (cEVEN Xn0)) (cODD Xn0))))
% 166.61/166.91 Found (and_rect30 (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x4 x50))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 166.61/166.91 Found ((and_rect3 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x4 x50))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 167.52/167.87 Found (((fun (P:Type) (x6:(((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->P)))=> (((((and_rect ((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))) P) x6) x0)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x4 x50))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 167.52/167.87 Found (((fun (P:Type) (x6:(((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->P)))=> (((((and_rect ((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))) P) x6) x0)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (x4 x50))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 167.52/167.87 Found x90:=(x9 x80):(cNUMBER Xn00)
% 167.52/167.87 Instantiate: Xn00:=Xn:fofType
% 167.52/167.87 Found (x9 x80) as proof of (cNUMBER Xn)
% 167.52/167.87 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x9 x80)) as proof of (cNUMBER Xn)
% 167.52/167.87 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x9 x80)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 167.52/167.87 Found x21:((or (cEVEN Xn0)) (cODD Xn0))
% 167.52/167.87 Instantiate: Xn0:=Xn:fofType
% 167.52/167.87 Found x21 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 167.52/167.87 Found (x5 x21) as proof of (cNUMBER Xn)
% 167.52/167.87 Found (x5 x21) as proof of (cNUMBER Xn)
% 167.52/167.87 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x21)) as proof of (cNUMBER Xn)
% 167.52/167.87 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x21)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 167.52/167.87 Found x21:((or (cEVEN Xn0)) (cODD Xn0))
% 167.52/167.87 Found x21 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 167.52/167.87 Found (x3 x21) as proof of (cNUMBER Xn)
% 167.52/167.87 Found (x3 x21) as proof of (cNUMBER Xn)
% 167.52/167.87 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x21)) as proof of (cNUMBER Xn)
% 167.52/167.87 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x21)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 167.52/167.87 Found or_comm_i100:=(or_comm_i10 x20):((or (cODD Xn0)) (cEVEN Xn0))
% 167.52/167.87 Found (or_comm_i10 x20) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 167.52/167.87 Found ((or_comm_i1 (cODD Xn0)) x20) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 167.52/167.87 Found (((or_comm_i (cEVEN Xn0)) (cODD Xn0)) x20) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 168.06/168.40 Found (((or_comm_i (cEVEN Xn0)) (cODD Xn0)) x20) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 168.06/168.40 Found x40:(cNUMBER Xn00)
% 168.06/168.40 Instantiate: Xn0:=Xn00:fofType
% 168.06/168.40 Found x40 as proof of (cNUMBER Xn0)
% 168.06/168.40 Found x30:=(x3 x21):(cNUMBER Xn0)
% 168.06/168.40 Instantiate: Xn0:=Xn:fofType
% 168.06/168.40 Found (x3 x21) as proof of (cNUMBER Xn)
% 168.06/168.40 Found (fun (x6:(cODD Xn0))=> (x3 x21)) as proof of (cNUMBER Xn)
% 168.06/168.40 Found (fun (x6:(cODD Xn0))=> (x3 x21)) as proof of ((cODD Xn0)->(cNUMBER Xn))
% 168.06/168.40 Found x30:=(x3 x21):(cNUMBER Xn0)
% 168.06/168.40 Instantiate: Xn0:=Xn:fofType
% 168.06/168.40 Found (x3 x21) as proof of (cNUMBER Xn)
% 168.06/168.40 Found (fun (x6:(cEVEN Xn0))=> (x3 x21)) as proof of (cNUMBER Xn)
% 168.06/168.40 Found (fun (x6:(cEVEN Xn0))=> (x3 x21)) as proof of ((cEVEN Xn0)->(cNUMBER Xn))
% 168.06/168.40 Found ((or_ind00 (fun (x6:(cEVEN Xn0))=> (x3 x21))) (fun (x6:(cODD Xn0))=> (x3 x21))) as proof of (cNUMBER Xn)
% 168.06/168.40 Found (((or_ind0 (cNUMBER Xn)) (fun (x6:(cEVEN Xn0))=> (x3 x21))) (fun (x6:(cODD Xn0))=> (x3 x21))) as proof of (cNUMBER Xn)
% 168.06/168.40 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)
% 168.06/168.40 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> ((((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)
% 168.06/168.40 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> ((((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 (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 168.06/168.40 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> ((((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 (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn)))
% 168.06/168.40 Found x30:=(x3 x21):(cNUMBER Xn0)
% 168.06/168.40 Instantiate: Xn0:=Xn:fofType
% 168.06/168.40 Found (x3 x21) as proof of (cNUMBER Xn)
% 168.06/168.40 Found (fun (x6:(cEVEN Xn0))=> (x3 x21)) as proof of (cNUMBER Xn)
% 168.06/168.40 Found (fun (x6:(cEVEN Xn0))=> (x3 x21)) as proof of ((cEVEN Xn0)->(cNUMBER Xn))
% 168.06/168.40 Found x30:=(x3 x21):(cNUMBER Xn0)
% 168.06/168.40 Instantiate: Xn0:=Xn:fofType
% 168.06/168.40 Found (x3 x21) as proof of (cNUMBER Xn)
% 168.06/168.40 Found (fun (x6:(cODD Xn0))=> (x3 x21)) as proof of (cNUMBER Xn)
% 168.06/168.40 Found (fun (x6:(cODD Xn0))=> (x3 x21)) as proof of ((cODD Xn0)->(cNUMBER Xn))
% 168.06/168.40 Found ((or_ind00 (fun (x6:(cEVEN Xn0))=> (x3 x21))) (fun (x6:(cODD Xn0))=> (x3 x21))) as proof of (cNUMBER Xn)
% 170.00/170.33 Found (((or_ind0 (cNUMBER Xn)) (fun (x6:(cEVEN Xn0))=> (x3 x21))) (fun (x6:(cODD Xn0))=> (x3 x21))) as proof of (cNUMBER Xn)
% 170.00/170.33 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)
% 170.00/170.33 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> ((((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)
% 170.00/170.33 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> ((((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 (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 170.00/170.33 Found x30:=(x3 x21):(cNUMBER Xn0)
% 170.00/170.33 Instantiate: Xn0:=Xn:fofType
% 170.00/170.33 Found (x3 x21) as proof of (cNUMBER Xn)
% 170.00/170.33 Found (fun (x6:(cODD Xn0))=> (x3 x21)) as proof of (cNUMBER Xn)
% 170.00/170.33 Found (fun (x6:(cODD Xn0))=> (x3 x21)) as proof of ((cODD Xn0)->(cNUMBER Xn))
% 170.00/170.33 Found x30:=(x3 x21):(cNUMBER Xn0)
% 170.00/170.33 Instantiate: Xn0:=Xn:fofType
% 170.00/170.33 Found (x3 x21) as proof of (cNUMBER Xn)
% 170.00/170.33 Found (fun (x6:(cEVEN Xn0))=> (x3 x21)) as proof of (cNUMBER Xn)
% 170.00/170.33 Found (fun (x6:(cEVEN Xn0))=> (x3 x21)) as proof of ((cEVEN Xn0)->(cNUMBER Xn))
% 170.00/170.33 Found ((or_ind00 (fun (x6:(cEVEN Xn0))=> (x3 x21))) (fun (x6:(cODD Xn0))=> (x3 x21))) as proof of (cNUMBER Xn)
% 170.00/170.33 Found (((or_ind0 (cNUMBER Xn)) (fun (x6:(cEVEN Xn0))=> (x3 x21))) (fun (x6:(cODD Xn0))=> (x3 x21))) as proof of (cNUMBER Xn)
% 170.00/170.33 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)
% 170.00/170.33 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)
% 170.00/170.33 Found x21:((or (cEVEN Xn0)) (cODD Xn0))
% 170.00/170.33 Instantiate: Xn0:=Xn:fofType
% 170.00/170.33 Found x21 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 170.00/170.33 Found (x5 x21) as proof of (cNUMBER Xn)
% 170.00/170.33 Found (x5 x21) as proof of (cNUMBER Xn)
% 170.00/170.33 Found (x5 x21) as proof of (cNUMBER Xn)
% 170.00/170.33 Found x21:((or (cEVEN Xn0)) (cODD Xn0))
% 170.00/170.33 Found x21 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 170.00/170.33 Found (x3 x21) as proof of (cNUMBER Xn)
% 170.00/170.33 Found (x3 x21) as proof of (cNUMBER Xn)
% 170.00/170.33 Found (x3 x21) as proof of (cNUMBER Xn)
% 170.00/170.33 Found x32:(cNUMBER Xn0)
% 170.00/170.33 Instantiate: Xn0:=Xn:fofType
% 170.00/170.33 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x32) as proof of (cNUMBER Xn)
% 170.00/170.33 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x32) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 170.00/170.33 Found x32:(cNUMBER Xn0)
% 170.00/170.33 Instantiate: Xn0:=Xn:fofType
% 170.00/170.33 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x32) as proof of (cNUMBER Xn)
% 170.00/170.33 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x32) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 170.00/170.33 Found x11:(cEVEN c0)
% 170.00/170.33 Instantiate: Xn0:=c0:fofType
% 170.00/170.33 Found (fun (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11) as proof of (cEVEN Xn0)
% 170.00/170.33 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11) as proof of ((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->(cEVEN Xn0))
% 170.71/171.01 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11) as proof of ((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->(cEVEN Xn0)))
% 170.71/171.01 Found (and_rect50 (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11)) as proof of (cEVEN Xn0)
% 170.71/171.01 Found ((and_rect5 (cEVEN Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11)) as proof of (cEVEN Xn0)
% 170.71/171.01 Found (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x6)) (cEVEN Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11)) as proof of (cEVEN Xn0)
% 170.71/171.01 Found (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x6)) (cEVEN Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11)) as proof of (cEVEN Xn0)
% 170.71/171.01 Found (or_introl00 (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x6)) (cEVEN Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 170.71/171.01 Found ((or_introl0 (cODD Xn0)) (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x11) x6)) (cEVEN Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 170.71/171.01 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x11) x6)) (cEVEN Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 170.71/171.01 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x11) x6)) (cEVEN Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 170.71/171.01 Found x50:=(x5 x41):(cNUMBER Xn0)
% 170.71/171.01 Found (x5 x41) as proof of (cNUMBER Xn0)
% 170.71/171.01 Found (x5 x41) as proof of (cNUMBER Xn0)
% 170.71/171.01 Found x30:=(x3 x20):(cNUMBER Xn0)
% 170.71/171.01 Found (x3 x20) as proof of (cNUMBER Xn0)
% 170.71/171.01 Found (x3 x20) as proof of (cNUMBER Xn0)
% 170.71/171.01 Found x30:=(x3 x21):(cNUMBER Xn0)
% 170.71/171.01 Instantiate: Xn0:=Xn:fofType
% 170.71/171.01 Found (x3 x21) as proof of (cNUMBER Xn)
% 170.71/171.01 Found (x3 x21) as proof of (cNUMBER Xn)
% 170.71/171.01 Found x30:=(x3 x21):(cNUMBER Xn0)
% 170.71/171.01 Found (x3 x21) as proof of (cNUMBER Xn)
% 170.71/171.01 Found (x3 x21) as proof of (cNUMBER Xn)
% 170.71/171.01 Found (x3 x21) as proof of (cNUMBER Xn)
% 170.71/171.01 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 170.71/171.01 Instantiate: Xn0:=Xn00:fofType
% 170.71/171.01 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 170.71/171.01 Found (x3 x40) as proof of (cNUMBER Xn0)
% 170.71/171.01 Found (x3 x40) as proof of (cNUMBER Xn0)
% 170.71/171.01 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 170.71/171.01 Instantiate: Xn00:=Xn:fofType
% 170.71/171.01 Found (fun (x9:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x40) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 170.71/171.01 Found (fun (x9:(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)))
% 170.71/171.01 Found x90:=(x9 x80):(cNUMBER Xn00)
% 170.71/171.01 Found (x9 x80) as proof of (cNUMBER Xn)
% 170.71/171.01 Found (x9 x80) as proof of (cNUMBER Xn)
% 171.46/171.81 Found (x9 x80) as proof of (cNUMBER Xn)
% 171.46/171.81 Found x30:=(x3 x20):(cNUMBER Xn0)
% 171.46/171.81 Found (x3 x20) as proof of (cNUMBER Xn)
% 171.46/171.81 Found (x3 x20) as proof of (cNUMBER Xn)
% 171.46/171.81 Found (x3 x20) as proof of (cNUMBER Xn)
% 171.46/171.81 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 171.46/171.81 Instantiate: Xn0:=Xn00:fofType
% 171.46/171.81 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 171.46/171.81 Found (x3 x40) as proof of (cNUMBER Xn0)
% 171.46/171.81 Found (x3 x40) as proof of (cNUMBER Xn0)
% 171.46/171.81 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 171.46/171.81 Instantiate: Xn00:=Xn0:fofType
% 171.46/171.81 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 171.46/171.81 Found (x5 x20) as proof of (cNUMBER Xn00)
% 171.46/171.81 Found (x5 x20) as proof of (cNUMBER Xn00)
% 171.46/171.81 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 171.46/171.81 Instantiate: Xn00:=Xn0:fofType
% 171.46/171.81 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 171.46/171.81 Found (x5 x20) as proof of (cNUMBER Xn00)
% 171.46/171.81 Found (x5 x20) as proof of (cNUMBER Xn00)
% 171.46/171.81 Found x70:=(x7 x60):(cNUMBER Xn00)
% 171.46/171.81 Instantiate: Xn00:=Xn:fofType
% 171.46/171.81 Found (x7 x60) as proof of (cNUMBER Xn)
% 171.46/171.81 Found (x7 x60) as proof of (cNUMBER Xn)
% 171.46/171.81 Found x50:=(x5 x40):(cNUMBER Xn0)
% 171.46/171.81 Instantiate: Xn0:=Xn:fofType
% 171.46/171.81 Found (x5 x40) as proof of (cNUMBER Xn)
% 171.46/171.81 Found (x5 x40) as proof of (cNUMBER Xn)
% 171.46/171.81 Found x70:=(x7 x60):(cNUMBER Xn00)
% 171.46/171.81 Instantiate: Xn00:=Xn:fofType
% 171.46/171.81 Found (x7 x60) as proof of (cNUMBER Xn)
% 171.46/171.81 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x7 x60)) as proof of (cNUMBER Xn)
% 171.46/171.81 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x7 x60)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 171.46/171.81 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x7 x60)) as proof of (((and ((and (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)))
% 171.46/171.81 Found x40:=(x4 x51):((or (cEVEN Xn0)) (cODD Xn0))
% 171.46/171.81 Found (x4 x51) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 171.46/171.81 Found (x4 x51) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 171.46/171.81 Found x52:(cNUMBER Xn0)
% 171.46/171.81 Instantiate: Xn0:=Xn:fofType
% 171.46/171.81 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x52) as proof of (cNUMBER Xn)
% 171.46/171.81 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x52) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 171.46/171.81 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x52) as proof of (((and ((and (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)))
% 171.46/171.81 Found x30:=(x3 x20):(cNUMBER Xn0)
% 171.46/171.81 Instantiate: Xn0:=Xn:fofType
% 171.46/171.81 Found (x3 x20) as proof of (cNUMBER Xn)
% 171.46/171.81 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 171.46/171.81 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(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))
% 171.46/171.81 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (((and ((and (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)))
% 171.46/171.81 Found x50:=(x5 x40):(cNUMBER Xn0)
% 171.46/171.81 Found (x5 x40) as proof of (cNUMBER Xn0)
% 171.46/171.81 Found (x5 x40) as proof of (cNUMBER Xn0)
% 171.46/171.81 Found x50:=(x5 x41):(cNUMBER Xn0)
% 171.46/171.81 Instantiate: Xn0:=Xn:fofType
% 171.46/171.81 Found (x5 x41) as proof of (cNUMBER Xn)
% 172.47/172.82 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x41)) as proof of (cNUMBER Xn)
% 172.47/172.82 Found (fun (x12:(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))
% 172.47/172.82 Found x30:=(x3 x20):(cNUMBER Xn0)
% 172.47/172.82 Found (x3 x20) as proof of (cNUMBER Xn00)
% 172.47/172.82 Found (x3 x20) as proof of (cNUMBER Xn00)
% 172.47/172.82 Found (x3 x20) as proof of (cNUMBER Xn00)
% 172.47/172.82 Found x80:((or (cEVEN Xn00)) (cODD Xn00))
% 172.47/172.82 Instantiate: Xn00:=Xn:fofType
% 172.47/172.82 Found x80 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 172.47/172.82 Found x60:((or (cEVEN Xn0)) (cODD Xn0))
% 172.47/172.82 Instantiate: Xn0:=Xn:fofType
% 172.47/172.82 Found x60 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 172.47/172.82 Found x30:(cNUMBER Xn0)
% 172.47/172.82 Instantiate: Xn0:=Xn:fofType
% 172.47/172.82 Found (fun (x6:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30) as proof of (cNUMBER Xn)
% 172.47/172.82 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))
% 172.47/172.82 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)))
% 172.47/172.82 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))))
% 172.47/172.82 Found x30:(cNUMBER Xn0)
% 172.47/172.82 Instantiate: Xn0:=Xn:fofType
% 172.47/172.82 Found (fun (x6:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30) as proof of (cNUMBER Xn)
% 172.47/172.82 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))
% 172.47/172.82 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)))
% 172.47/172.82 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))))
% 172.47/172.82 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)))
% 172.47/172.82 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)))
% 172.47/172.82 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)))
% 173.20/173.51 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)))
% 173.20/173.51 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)))
% 173.20/173.51 Found x9:(cEVEN c0)
% 173.20/173.51 Instantiate: Xn0:=c0:fofType
% 173.20/173.51 Found x9 as proof of (cEVEN Xn0)
% 173.20/173.51 Found (or_introl00 x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 173.20/173.51 Found ((or_introl0 (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 173.20/173.51 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 173.20/173.51 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 173.20/173.51 Found (x7 (((or_introl (cEVEN Xn0)) (cODD Xn0)) x9)) as proof of (cNUMBER Xn0)
% 173.20/173.51 Found (fun (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (x7 (((or_introl (cEVEN Xn0)) (cODD Xn0)) x9))) as proof of (cNUMBER Xn0)
% 173.20/173.51 Found (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (x7 (((or_introl (cEVEN Xn0)) (cODD Xn0)) x9))) as proof of ((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->(cNUMBER Xn0))
% 173.20/173.51 Found (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (x7 (((or_introl (cEVEN Xn0)) (cODD Xn0)) x9))) as proof of ((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->(cNUMBER Xn0)))
% 173.20/173.51 Found (and_rect50 (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (x7 (((or_introl (cEVEN Xn0)) (cODD Xn0)) x9)))) as proof of (cNUMBER Xn0)
% 173.20/173.51 Found ((and_rect5 (cNUMBER Xn0)) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (x7 (((or_introl (cEVEN Xn0)) (cODD Xn0)) x9)))) as proof of (cNUMBER Xn0)
% 173.20/173.51 Found (((fun (P:Type) (x9:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x9) x8)) (cNUMBER Xn0)) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (x7 (((or_introl (cEVEN Xn0)) (cODD Xn0)) x9)))) as proof of (cNUMBER Xn0)
% 173.20/173.51 Found (((fun (P:Type) (x9:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x9) x8)) (cNUMBER Xn0)) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (x7 (((or_introl (cEVEN Xn0)) (cODD Xn0)) x9)))) as proof of (cNUMBER Xn0)
% 173.20/173.51 Found x9:(cODD (cS c0))
% 173.20/173.51 Instantiate: Xn0:=(cS c0):fofType
% 173.20/173.51 Found x9 as proof of (cODD Xn0)
% 173.20/173.51 Found (or_introl00 x9) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 173.20/173.51 Found ((or_introl0 (cEVEN Xn0)) x9) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 173.20/173.51 Found (((or_introl (cODD Xn0)) (cEVEN Xn0)) x9) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 173.20/173.51 Found (((or_introl (cODD Xn0)) (cEVEN Xn0)) x9) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 173.55/173.87 Found (or_comm_i00 (((or_introl (cODD Xn0)) (cEVEN Xn0)) x9)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 173.55/173.87 Found ((or_comm_i0 (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x9)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 173.55/173.87 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x9)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 173.55/173.87 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x9)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 173.55/173.87 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 173.55/173.87 Instantiate: Xn00:=Xn:fofType
% 173.55/173.87 Found (fun (x9:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x40) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 173.55/173.87 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x9:(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)))
% 173.55/173.87 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x9:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x40) as proof of (((and ((and (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))))
% 173.55/173.87 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 173.55/173.87 Instantiate: Xn0:=Xn:fofType
% 173.55/173.87 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x20) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 173.55/173.87 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(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)))
% 173.55/173.87 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x20) as proof of (((and ((and (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))))
% 173.55/173.87 Found x50:=(x5 x40):(cNUMBER Xn00)
% 173.55/173.87 Instantiate: Xn00:=Xn:fofType
% 173.55/173.87 Found (x5 x40) as proof of (cNUMBER Xn)
% 173.55/173.87 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 173.55/173.87 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 173.55/173.87 Found x30:=(x3 x20):(cNUMBER Xn0)
% 173.55/173.87 Instantiate: Xn0:=Xn:fofType
% 173.55/173.87 Found (x3 x20) as proof of (cNUMBER Xn)
% 173.55/173.87 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 173.55/173.87 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 173.55/173.87 Found x40:=(x4 x50):((or (cEVEN Xn0)) (cODD Xn0))
% 173.55/173.87 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 173.55/173.87 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 173.55/173.87 Found x9:(cODD (cS c0))
% 173.55/173.87 Instantiate: Xn0:=(cS c0):fofType
% 173.55/173.87 Found x9 as proof of (cODD Xn0)
% 173.55/173.87 Found (or_introl00 x9) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 173.55/173.87 Found ((or_introl0 (cEVEN Xn0)) x9) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 173.55/173.87 Found (((or_introl (cODD Xn0)) (cEVEN Xn0)) x9) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 173.55/173.87 Found (((or_introl (cODD Xn0)) (cEVEN Xn0)) x9) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 173.55/173.87 Found (or_comm_i00 (((or_introl (cODD Xn0)) (cEVEN Xn0)) x9)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 173.55/173.87 Found ((or_comm_i0 (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x9)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 173.55/173.87 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x9)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 173.55/173.87 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x9)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 173.55/173.87 Found x50:(cNUMBER Xn00)
% 174.32/174.65 Instantiate: Xn0:=Xn00:fofType
% 174.32/174.65 Found x50 as proof of (cNUMBER Xn0)
% 174.32/174.65 Found (x2 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 174.32/174.65 Found (x2 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 174.32/174.65 Found x30:(cNUMBER Xn0)
% 174.32/174.65 Instantiate: Xn00:=Xn0:fofType
% 174.32/174.65 Found x30 as proof of (cNUMBER Xn00)
% 174.32/174.65 Found (x4 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 174.32/174.65 Found (x4 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 174.32/174.65 Found x50:=(x5 x40):(cNUMBER Xn0)
% 174.32/174.65 Instantiate: Xn0:=Xn:fofType
% 174.32/174.65 Found (x5 x40) as proof of (cNUMBER Xn)
% 174.32/174.65 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 174.32/174.65 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 174.32/174.65 Found x90:=(x9 x80):(cNUMBER Xn00)
% 174.32/174.65 Instantiate: Xn00:=Xn:fofType
% 174.32/174.65 Found (x9 x80) as proof of (cNUMBER Xn)
% 174.32/174.65 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x9 x80)) as proof of (cNUMBER Xn)
% 174.32/174.65 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x9 x80)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 174.32/174.65 Found x50:=(x5 x42):(cNUMBER Xn0)
% 174.32/174.65 Instantiate: Xn0:=Xn:fofType
% 174.32/174.65 Found (x5 x42) as proof of (cNUMBER Xn)
% 174.32/174.65 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x5 x42)) as proof of (cNUMBER Xn)
% 174.32/174.65 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x5 x42)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 174.32/174.65 Found x9:(cEVEN c0)
% 174.32/174.65 Instantiate: Xn0:=c0:fofType
% 174.32/174.65 Found (fun (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x9) as proof of (cEVEN Xn0)
% 174.32/174.65 Found (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x9) as proof of ((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->(cEVEN Xn0))
% 174.32/174.65 Found (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x9) as proof of ((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->(cEVEN Xn0)))
% 174.32/174.65 Found (and_rect50 (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x9)) as proof of (cEVEN Xn0)
% 174.32/174.65 Found ((and_rect5 (cEVEN Xn0)) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x9)) as proof of (cEVEN Xn0)
% 174.32/174.65 Found (((fun (P:Type) (x9:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x9) x7)) (cEVEN Xn0)) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x9)) as proof of (cEVEN Xn0)
% 174.32/174.65 Found (fun (x8:(cODD (cS c0)))=> (((fun (P:Type) (x9:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x9) x7)) (cEVEN Xn0)) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x9))) as proof of (cEVEN Xn0)
% 174.32/174.65 Found (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> (((fun (P:Type) (x9:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x9) x7)) (cEVEN Xn0)) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x9))) as proof of ((cODD (cS c0))->(cEVEN Xn0))
% 174.32/174.65 Found (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> (((fun (P:Type) (x9:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x9) x7)) (cEVEN Xn0)) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x9))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->(cEVEN Xn0)))
% 174.32/174.65 Found (and_rect40 (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> (((fun (P:Type) (x9:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x9) x7)) (cEVEN Xn0)) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x9)))) as proof of (cEVEN Xn0)
% 174.32/174.65 Found ((and_rect4 (cEVEN Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> (((fun (P:Type) (x9:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x9) x7)) (cEVEN Xn0)) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x9)))) as proof of (cEVEN Xn0)
% 174.32/174.65 Found (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x7) x6)) (cEVEN Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> (((fun (P:Type) (x9:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x9) x7)) (cEVEN Xn0)) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x9)))) as proof of (cEVEN Xn0)
% 174.32/174.65 Found (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x7) x6)) (cEVEN Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> (((fun (P:Type) (x9:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x9) x7)) (cEVEN Xn0)) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x9)))) as proof of (cEVEN Xn0)
% 174.32/174.65 Found (or_introl00 (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x7) x6)) (cEVEN Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> (((fun (P:Type) (x9:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x9) x7)) (cEVEN Xn0)) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x9))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 174.32/174.65 Found ((or_introl0 (cODD Xn0)) (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x6)) (cEVEN Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> (((fun (P:Type) (x9:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x9) x7)) (cEVEN Xn0)) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x9))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 174.32/174.65 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x6)) (cEVEN Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> (((fun (P:Type) (x9:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x9) x7)) (cEVEN Xn0)) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x9))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 175.86/176.17 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x6)) (cEVEN Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> (((fun (P:Type) (x9:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x9) x7)) (cEVEN Xn0)) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x9))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 175.86/176.17 Found x70:=(x7 x60):(cNUMBER Xn0)
% 175.86/176.17 Found (x7 x60) as proof of (cNUMBER Xn0)
% 175.86/176.17 Found (x7 x60) as proof of (cNUMBER Xn0)
% 175.86/176.17 Found x9:(cODD (cS c0))
% 175.86/176.17 Instantiate: Xn0:=(cS c0):fofType
% 175.86/176.17 Found x9 as proof of (cODD Xn0)
% 175.86/176.17 Found (or_introl00 x9) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 175.86/176.17 Found ((or_introl0 (cEVEN Xn0)) x9) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 175.86/176.17 Found (((or_introl (cODD Xn0)) (cEVEN Xn0)) x9) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 175.86/176.17 Found (((or_introl (cODD Xn0)) (cEVEN Xn0)) x9) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 175.86/176.17 Found (or_comm_i00 (((or_introl (cODD Xn0)) (cEVEN Xn0)) x9)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 175.86/176.17 Found ((or_comm_i0 (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x9)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 175.86/176.17 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x9)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 175.86/176.17 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x9)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 175.86/176.17 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 175.86/176.17 Instantiate: Xn0:=Xn:fofType
% 175.86/176.17 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 175.86/176.17 Found x80:((or (cEVEN Xn00)) (cODD Xn00))
% 175.86/176.17 Instantiate: Xn00:=Xn:fofType
% 175.86/176.17 Found x80 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 175.86/176.17 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 175.86/176.17 Instantiate: Xn00:=Xn:fofType
% 175.86/176.17 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 175.86/176.17 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 175.86/176.17 Instantiate: Xn00:=Xn:fofType
% 175.86/176.17 Found (fun (x9:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x40) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 175.86/176.17 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x9:(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)))
% 175.86/176.17 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x9:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x40) as proof of (((and ((and (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))))
% 175.86/176.17 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 175.86/176.17 Instantiate: Xn0:=Xn:fofType
% 175.86/176.17 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x20) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 175.86/176.17 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(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)))
% 176.28/176.60 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x20) as proof of (((and ((and (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))))
% 176.28/176.60 Found x50:=(x5 x40):(cNUMBER Xn00)
% 176.28/176.60 Found (x5 x40) as proof of (cNUMBER Xn0)
% 176.28/176.60 Found (x5 x40) as proof of (cNUMBER Xn0)
% 176.28/176.60 Found (x5 x40) as proof of (cNUMBER Xn0)
% 176.28/176.60 Found x80:((or (cEVEN Xn00)) (cODD Xn00))
% 176.28/176.60 Instantiate: Xn00:=Xn:fofType
% 176.28/176.60 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x80) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 176.28/176.60 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)))
% 176.28/176.60 Found x9:(cODD (cS c0))
% 176.28/176.60 Instantiate: Xn0:=(cS c0):fofType
% 176.28/176.60 Found x9 as proof of (cODD Xn0)
% 176.28/176.60 Found (or_intror00 x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 176.28/176.60 Found ((or_intror0 (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 176.28/176.60 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 176.28/176.60 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 176.28/176.60 Found (x5 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9)) as proof of (cNUMBER Xn0)
% 176.28/176.60 Found (fun (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (x5 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9))) as proof of (cNUMBER Xn0)
% 176.28/176.60 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (x5 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9))) as proof of ((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->(cNUMBER Xn0))
% 176.28/176.60 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (x5 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9))) as proof of ((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->(cNUMBER Xn0)))
% 176.28/176.60 Found (and_rect50 (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (x5 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9)))) as proof of (cNUMBER Xn0)
% 176.28/176.60 Found ((and_rect5 (cNUMBER Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (x5 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9)))) as proof of (cNUMBER Xn0)
% 176.28/176.60 Found (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (x5 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9)))) as proof of (cNUMBER Xn0)
% 176.28/176.60 Found (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (x5 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9)))) as proof of (cNUMBER Xn0)
% 176.28/176.60 Found x30:=(x3 x21):(cNUMBER Xn0)
% 176.28/176.60 Found (x3 x21) as proof of (cNUMBER Xn0)
% 176.28/176.60 Found (x3 x21) as proof of (cNUMBER Xn0)
% 176.28/176.60 Found x30:=(x3 x22):(cNUMBER Xn0)
% 176.28/176.60 Instantiate: Xn0:=Xn:fofType
% 176.28/176.60 Found (x3 x22) as proof of (cNUMBER Xn)
% 176.28/176.60 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x22)) as proof of (cNUMBER Xn)
% 176.28/176.60 Found (fun (x7:(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))
% 176.28/176.60 Found x50:=(x5 x40):(cNUMBER Xn00)
% 176.28/176.60 Found (x5 x40) as proof of (cNUMBER Xn0)
% 176.28/176.60 Found (x5 x40) as proof of (cNUMBER Xn0)
% 176.28/176.60 Found (x5 x40) as proof of (cNUMBER Xn0)
% 176.28/176.60 Found x30:=(x3 x20):(cNUMBER Xn0)
% 178.16/178.47 Found (x3 x20) as proof of (cNUMBER Xn00)
% 178.16/178.47 Found (x3 x20) as proof of (cNUMBER Xn00)
% 178.16/178.47 Found (x3 x20) as proof of (cNUMBER Xn00)
% 178.16/178.47 Found x30:=(x3 x20):(cNUMBER Xn0)
% 178.16/178.47 Found (x3 x20) as proof of (cNUMBER Xn00)
% 178.16/178.47 Found (x3 x20) as proof of (cNUMBER Xn00)
% 178.16/178.47 Found (x3 x20) as proof of (cNUMBER Xn00)
% 178.16/178.47 Found x30:=(x3 x21):(cNUMBER Xn0)
% 178.16/178.47 Found (x3 x21) as proof of (cNUMBER Xn)
% 178.16/178.47 Found (x3 x21) as proof of (cNUMBER Xn)
% 178.16/178.47 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x21)) as proof of (cNUMBER Xn)
% 178.16/178.47 Found (fun (x12:(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))
% 178.16/178.47 Found x30:=(x3 x21):(cNUMBER Xn0)
% 178.16/178.47 Found (x3 x21) as proof of (cNUMBER Xn0)
% 178.16/178.47 Found (x3 x21) as proof of (cNUMBER Xn0)
% 178.16/178.47 Found x30:=(x3 x22):(cNUMBER Xn0)
% 178.16/178.47 Instantiate: Xn0:=Xn:fofType
% 178.16/178.47 Found (x3 x22) as proof of (cNUMBER Xn)
% 178.16/178.47 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x22)) as proof of (cNUMBER Xn)
% 178.16/178.47 Found (fun (x7:(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))
% 178.16/178.47 Found x60:=(x6 x70):((or (cEVEN Xn0)) (cODD Xn0))
% 178.16/178.47 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 178.16/178.47 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 178.16/178.47 Found x71:(cNUMBER Xn0)
% 178.16/178.47 Instantiate: Xn0:=Xn:fofType
% 178.16/178.47 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x71) as proof of (cNUMBER Xn)
% 178.16/178.47 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x71) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 178.16/178.47 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x71) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 178.16/178.47 Found x80:((or (cEVEN Xn00)) (cODD Xn00))
% 178.16/178.47 Instantiate: Xn00:=Xn:fofType
% 178.16/178.47 Found x80 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 178.16/178.47 Found x20:=(x2 x31):((or (cEVEN Xn0)) (cODD Xn0))
% 178.16/178.47 Found (x2 x31) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 178.16/178.47 Found (x2 x31) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 178.16/178.47 Found x30:=(x3 x20):(cNUMBER Xn0)
% 178.16/178.47 Found (x3 x20) as proof of (cNUMBER Xn)
% 178.16/178.47 Found (x3 x20) as proof of (cNUMBER Xn)
% 178.16/178.47 Found (x3 x20) as proof of (cNUMBER Xn)
% 178.16/178.47 Found x50:=(x5 x40):(cNUMBER Xn00)
% 178.16/178.47 Found (x5 x40) as proof of (cNUMBER Xn)
% 178.16/178.47 Found (x5 x40) as proof of (cNUMBER Xn)
% 178.16/178.47 Found (x5 x40) as proof of (cNUMBER Xn)
% 178.16/178.47 Found x30:=(x3 x20):(cNUMBER Xn0)
% 178.16/178.47 Found (x3 x20) as proof of (cNUMBER Xn)
% 178.16/178.47 Found (x3 x20) as proof of (cNUMBER Xn)
% 178.16/178.47 Found (x3 x20) as proof of (cNUMBER Xn)
% 178.16/178.47 Found x11:(cEVEN c0)
% 178.16/178.47 Instantiate: Xn0:=c0:fofType
% 178.16/178.47 Found (fun (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11) as proof of (cEVEN Xn0)
% 178.16/178.47 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11) as proof of ((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->(cEVEN Xn0))
% 178.16/178.47 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11) as proof of ((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->(cEVEN Xn0)))
% 178.16/178.47 Found (and_rect50 (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11)) as proof of (cEVEN Xn0)
% 178.16/178.47 Found ((and_rect5 (cEVEN Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11)) as proof of (cEVEN Xn0)
% 178.16/178.47 Found (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x11) x8)) (cEVEN Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11)) as proof of (cEVEN Xn0)
% 178.16/178.47 Found (fun (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x11) x8)) (cEVEN Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11))) as proof of (cEVEN Xn0)
% 178.16/178.48 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x11) x8)) (cEVEN Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11))) as proof of ((cODD (cS c0))->(cEVEN Xn0))
% 178.16/178.48 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x11) x8)) (cEVEN Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->(cEVEN Xn0)))
% 178.16/178.48 Found (and_rect40 (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x11) x8)) (cEVEN Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11)))) as proof of (cEVEN Xn0)
% 178.16/178.48 Found ((and_rect4 (cEVEN Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x11) x8)) (cEVEN Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11)))) as proof of (cEVEN Xn0)
% 178.16/178.48 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cEVEN Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x11) x8)) (cEVEN Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11)))) as proof of (cEVEN Xn0)
% 178.16/178.48 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cEVEN Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x11) x8)) (cEVEN Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11)))) as proof of (cEVEN Xn0)
% 178.16/178.48 Found (or_introl00 (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cEVEN Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x11) x8)) (cEVEN Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 178.85/179.22 Found ((or_introl0 (cODD Xn0)) (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) (cEVEN Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x11) x8)) (cEVEN Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 178.85/179.22 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) (cEVEN Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x11) x8)) (cEVEN Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 178.85/179.22 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) (cEVEN Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x11) x8)) (cEVEN Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 178.85/179.22 Found x50:=(x5 x40):(cNUMBER Xn00)
% 178.85/179.22 Found (x5 x40) as proof of (cNUMBER Xn)
% 178.85/179.22 Found (x5 x40) as proof of (cNUMBER Xn)
% 178.85/179.22 Found (x5 x40) as proof of (cNUMBER Xn)
% 178.85/179.22 Found x20:=(x2 x31):((or (cEVEN Xn0)) (cODD Xn0))
% 178.85/179.22 Found (x2 x31) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 178.85/179.22 Found (x2 x31) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 178.85/179.22 Found x50:=(x5 x41):(cNUMBER Xn0)
% 178.85/179.22 Instantiate: Xn0:=Xn:fofType
% 178.85/179.22 Found (x5 x41) as proof of (cNUMBER Xn)
% 178.85/179.22 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x41)) as proof of (cNUMBER Xn)
% 178.85/179.22 Found (fun (x11:(cEVEN c0)) (x12:(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))
% 178.85/179.22 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x41)) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 178.85/179.22 Found x30:=(x3 x20):(cNUMBER Xn0)
% 178.85/179.22 Found (x3 x20) as proof of (cNUMBER Xn)
% 178.85/179.22 Found (x3 x20) as proof of (cNUMBER Xn)
% 178.85/179.22 Found (x3 x20) as proof of (cNUMBER Xn)
% 178.85/179.22 Found x70:=(x7 x60):(cNUMBER Xn0)
% 178.85/179.22 Instantiate: Xn0:=Xn:fofType
% 178.85/179.22 Found (x7 x60) as proof of (cNUMBER Xn)
% 178.85/179.22 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x7 x60)) as proof of (cNUMBER Xn)
% 178.85/179.22 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))
% 179.83/180.20 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)))
% 179.83/180.20 Found x70:=(x7 x60):(cNUMBER Xn00)
% 179.83/180.20 Found (x7 x60) as proof of (cNUMBER Xn)
% 179.83/180.20 Found (x7 x60) as proof of (cNUMBER Xn)
% 179.83/180.20 Found (x7 x60) as proof of (cNUMBER Xn)
% 179.83/180.20 Found x40:=(x4 x50):((or (cEVEN Xn00)) (cODD Xn00))
% 179.83/180.20 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 179.83/180.20 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 179.83/180.20 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 179.83/180.20 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 179.83/180.20 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 179.83/180.20 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 179.83/180.20 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 179.83/180.20 Found x51:(cNUMBER Xn0)
% 179.83/180.20 Instantiate: Xn0:=Xn:fofType
% 179.83/180.20 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x51) as proof of (cNUMBER Xn)
% 179.83/180.20 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x51) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 179.83/180.20 Found x50:=(x5 x40):(cNUMBER Xn00)
% 179.83/180.20 Found (x5 x40) as proof of (cNUMBER Xn)
% 179.83/180.20 Found (x5 x40) as proof of (cNUMBER Xn)
% 179.83/180.20 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 179.83/180.20 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(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))
% 179.83/180.20 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (((and ((and (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)))
% 179.83/180.20 Found x30:=(x3 x20):(cNUMBER Xn0)
% 179.83/180.20 Found (x3 x20) as proof of (cNUMBER Xn)
% 179.83/180.20 Found (x3 x20) as proof of (cNUMBER Xn)
% 179.83/180.20 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 179.83/180.20 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(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))
% 179.83/180.20 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (((and ((and (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)))
% 179.83/180.20 Found x52:(cNUMBER Xn0)
% 179.83/180.20 Instantiate: Xn0:=Xn:fofType
% 179.83/180.20 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x52) as proof of (cNUMBER Xn)
% 179.83/180.20 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x52) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 179.83/180.20 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 179.83/180.20 Instantiate: Xn0:=Xn:fofType
% 179.83/180.20 Found x40 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 179.83/180.20 Found x70:(cNUMBER Xn0)
% 179.83/180.20 Instantiate: Xn0:=Xn:fofType
% 179.83/180.20 Found (fun (x11:(cODD (cS c0)))=> x70) as proof of (cNUMBER Xn)
% 179.83/180.20 Found (fun (x9:(cODD Xn0)) (x11:(cODD (cS c0)))=> x70) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 179.83/180.20 Found (fun (x9:(cODD Xn0)) (x11:(cODD (cS c0)))=> x70) as proof of ((cODD Xn0)->((cODD (cS c0))->(cNUMBER Xn)))
% 179.83/180.20 Found x70:(cNUMBER Xn0)
% 179.83/180.20 Instantiate: Xn0:=Xn:fofType
% 179.83/180.20 Found (fun (x11:(cODD (cS c0)))=> x70) as proof of (cNUMBER Xn)
% 179.83/180.20 Found (fun (x9:(cEVEN Xn0)) (x11:(cODD (cS c0)))=> x70) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 181.53/181.83 Found (fun (x9:(cEVEN Xn0)) (x11:(cODD (cS c0)))=> x70) as proof of ((cEVEN Xn0)->((cODD (cS c0))->(cNUMBER Xn)))
% 181.53/181.83 Found ((or_ind00 (fun (x9:(cEVEN Xn0)) (x11:(cODD (cS c0)))=> x70)) (fun (x9:(cODD Xn0)) (x11:(cODD (cS c0)))=> x70)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 181.53/181.83 Found (((or_ind0 ((cODD (cS c0))->(cNUMBER Xn))) (fun (x9:(cEVEN Xn0)) (x11:(cODD (cS c0)))=> x70)) (fun (x9:(cODD Xn0)) (x11:(cODD (cS c0)))=> x70)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 181.53/181.83 Found ((((fun (P:Prop) (x9:((cEVEN Xn0)->P)) (x11:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x9) x11) x60)) ((cODD (cS c0))->(cNUMBER Xn))) (fun (x9:(cEVEN Xn0)) (x11:(cODD (cS c0)))=> x70)) (fun (x9:(cODD Xn0)) (x11:(cODD (cS c0)))=> x70)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 181.53/181.83 Found ((((fun (P:Prop) (x9:((cEVEN Xn0)->P)) (x11:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x9) x11) (x6 x70))) ((cODD (cS c0))->(cNUMBER Xn))) (fun (x9:(cEVEN Xn0)) (x11:(cODD (cS c0)))=> x70)) (fun (x9:(cODD Xn0)) (x11:(cODD (cS c0)))=> x70)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 181.53/181.83 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))))=> ((((fun (P:Prop) (x9:((cEVEN Xn0)->P)) (x11:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x9) x11) (x6 x70))) ((cODD (cS c0))->(cNUMBER Xn))) (fun (x9:(cEVEN Xn0)) (x11:(cODD (cS c0)))=> x70)) (fun (x9:(cODD Xn0)) (x11:(cODD (cS c0)))=> x70))) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 181.53/181.83 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))))=> ((((fun (P:Prop) (x9:((cEVEN Xn0)->P)) (x11:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x9) x11) (x6 x70))) ((cODD (cS c0))->(cNUMBER Xn))) (fun (x9:(cEVEN Xn0)) (x11:(cODD (cS c0)))=> x70)) (fun (x9:(cODD Xn0)) (x11:(cODD (cS c0)))=> x70))) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 181.53/181.83 Found x80:((or (cEVEN Xn00)) (cODD Xn00))
% 181.53/181.83 Instantiate: Xn00:=Xn:fofType
% 181.53/181.83 Found x80 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 181.53/181.83 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 181.53/181.83 Instantiate: Xn0:=Xn:fofType
% 181.53/181.83 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 181.53/181.83 Found (x5 x20) as proof of (cNUMBER Xn)
% 181.53/181.83 Found (x5 x20) as proof of (cNUMBER Xn)
% 181.53/181.83 Found (x5 x20) as proof of (cNUMBER Xn)
% 181.53/181.83 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 181.53/181.83 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 181.53/181.83 Found (x3 x20) as proof of (cNUMBER Xn)
% 181.53/181.83 Found (x3 x20) as proof of (cNUMBER Xn)
% 181.53/181.83 Found (x3 x20) as proof of (cNUMBER Xn)
% 181.53/181.83 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 181.53/181.83 Instantiate: Xn00:=Xn:fofType
% 181.53/181.83 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 181.53/181.83 Found (x3 x40) as proof of (cNUMBER Xn)
% 181.53/181.83 Found (x3 x40) as proof of (cNUMBER Xn)
% 181.53/181.83 Found (x3 x40) as proof of (cNUMBER Xn)
% 181.53/181.83 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 181.53/181.83 Found x40 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 181.53/181.83 Found (x5 x40) as proof of (cNUMBER Xn)
% 181.53/181.83 Found (x5 x40) as proof of (cNUMBER Xn)
% 181.53/181.83 Found (x5 x40) as proof of (cNUMBER Xn)
% 181.53/181.83 Found x9:(cEVEN c0)
% 181.53/181.83 Instantiate: Xn0:=c0:fofType
% 181.53/181.83 Found x9 as proof of (cEVEN Xn0)
% 181.53/181.83 Found (or_introl00 x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 181.53/181.83 Found ((or_introl0 (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 181.53/181.83 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 181.53/181.83 Found (fun (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_introl (cEVEN Xn0)) (cODD Xn0)) x9)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 181.53/181.83 Found (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_introl (cEVEN Xn0)) (cODD Xn0)) x9)) as proof of ((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 181.53/181.83 Found (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_introl (cEVEN Xn0)) (cODD Xn0)) x9)) as proof of ((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0))))
% 181.53/181.83 Found (and_rect50 (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_introl (cEVEN Xn0)) (cODD Xn0)) x9))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 182.37/182.74 Found ((and_rect5 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_introl (cEVEN Xn0)) (cODD Xn0)) x9))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 182.37/182.74 Found (((fun (P:Type) (x9:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x9) x8)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_introl (cEVEN Xn0)) (cODD Xn0)) x9))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 182.37/182.74 Found (((fun (P:Type) (x9:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x9) x8)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_introl (cEVEN Xn0)) (cODD Xn0)) x9))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 182.37/182.74 Found (x7 (((fun (P:Type) (x9:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x9) x8)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_introl (cEVEN Xn0)) (cODD Xn0)) x9)))) as proof of (cNUMBER Xn0)
% 182.37/182.74 Found (x7 (((fun (P:Type) (x9:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x9) x8)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_introl (cEVEN Xn0)) (cODD Xn0)) x9)))) as proof of (cNUMBER Xn0)
% 182.37/182.74 Found x30:=(x3 x20):(cNUMBER Xn0)
% 182.37/182.74 Found (x3 x20) as proof of (cNUMBER Xn)
% 182.37/182.74 Found (x3 x20) as proof of (cNUMBER Xn)
% 182.37/182.74 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 182.37/182.74 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 182.37/182.74 Found x90:=(x9 x80):(cNUMBER Xn00)
% 182.37/182.74 Found (x9 x80) as proof of (cNUMBER Xn)
% 182.37/182.74 Found (x9 x80) as proof of (cNUMBER Xn)
% 182.37/182.74 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x9 x80)) as proof of (cNUMBER Xn)
% 182.37/182.74 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x9 x80)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 182.37/182.74 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 182.37/182.74 Instantiate: Xn0:=Xn:fofType
% 182.37/182.74 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 182.37/182.74 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 182.37/182.74 Found x40:=(x4 x50):((or (cEVEN Xn00)) (cODD Xn00))
% 182.37/182.74 Instantiate: Xn00:=Xn:fofType
% 182.37/182.74 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 182.37/182.74 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 182.37/182.74 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 182.37/182.74 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 182.37/182.74 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 182.37/182.74 Found x20:=(x2 x31):((or (cEVEN Xn0)) (cODD Xn0))
% 182.37/182.74 Instantiate: Xn0:=Xn:fofType
% 182.37/182.74 Found (x2 x31) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 182.37/182.74 Found (x2 x31) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 182.37/182.74 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 182.37/182.74 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 182.37/182.74 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 182.37/182.74 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 182.37/182.74 Found x40:=(x4 x51):((or (cEVEN Xn00)) (cODD Xn00))
% 182.37/182.74 Instantiate: Xn00:=Xn:fofType
% 182.37/182.74 Found (x4 x51) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 182.37/182.74 Found (x4 x51) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 182.37/182.74 Found x40:=(x4 x50):((or (cEVEN Xn00)) (cODD Xn00))
% 182.37/182.74 Found (x4 x50) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 182.37/182.74 Found (x4 x50) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 185.07/185.43 Found x40:=(x4 x50):((or (cEVEN Xn00)) (cODD Xn00))
% 185.07/185.43 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 185.07/185.43 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 185.07/185.43 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 185.07/185.43 Found x80:((or (cEVEN Xn00)) (cODD Xn00))
% 185.07/185.43 Instantiate: Xn00:=Xn:fofType
% 185.07/185.43 Found x80 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 185.07/185.43 Found x30:=(x3 x21):(cNUMBER Xn0)
% 185.07/185.43 Found (x3 x21) as proof of (cNUMBER Xn0)
% 185.07/185.43 Found (x3 x21) as proof of (cNUMBER Xn0)
% 185.07/185.43 Found x30:=(x3 x22):(cNUMBER Xn0)
% 185.07/185.43 Instantiate: Xn0:=Xn:fofType
% 185.07/185.43 Found (x3 x22) as proof of (cNUMBER Xn)
% 185.07/185.43 Found (x3 x22) as proof of (cNUMBER Xn)
% 185.07/185.43 Found x30:=(x3 x20):(cNUMBER Xn0)
% 185.07/185.43 Found (x3 x20) as proof of (cNUMBER Xn)
% 185.07/185.43 Found (x3 x20) as proof of (cNUMBER Xn)
% 185.07/185.43 Found (x3 x20) as proof of (cNUMBER Xn)
% 185.07/185.43 Found x70:=(x7 x60):(cNUMBER Xn00)
% 185.07/185.43 Instantiate: Xn00:=Xn:fofType
% 185.07/185.43 Found (x7 x60) as proof of (cNUMBER Xn)
% 185.07/185.43 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x7 x60)) as proof of (cNUMBER Xn)
% 185.07/185.43 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x7 x60)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 185.07/185.43 Found x50:=(x5 x40):(cNUMBER Xn0)
% 185.07/185.43 Instantiate: Xn0:=Xn:fofType
% 185.07/185.43 Found (x5 x40) as proof of (cNUMBER Xn)
% 185.07/185.43 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 185.07/185.43 Found (fun (x9:(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))
% 185.07/185.43 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 185.07/185.43 Instantiate: Xn00:=Xn0:fofType
% 185.07/185.43 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 185.07/185.43 Found (x5 x20) as proof of (cNUMBER Xn00)
% 185.07/185.43 Found (x5 x20) as proof of (cNUMBER Xn00)
% 185.07/185.43 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 185.07/185.43 Instantiate: Xn0:=Xn00:fofType
% 185.07/185.43 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 185.07/185.43 Found (x3 x40) as proof of (cNUMBER Xn0)
% 185.07/185.43 Found (x3 x40) as proof of (cNUMBER Xn0)
% 185.07/185.43 Found x30:=(x3 x20):(cNUMBER Xn0)
% 185.07/185.43 Found (x3 x20) as proof of (cNUMBER Xn)
% 185.07/185.43 Found (x3 x20) as proof of (cNUMBER Xn)
% 185.07/185.43 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 185.07/185.43 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))
% 185.07/185.43 Found x30:=(x3 x20):(cNUMBER Xn0)
% 185.07/185.43 Found (x3 x20) as proof of (cNUMBER Xn0)
% 185.07/185.43 Found (x3 x20) as proof of (cNUMBER Xn0)
% 185.07/185.43 Found x30:=(x3 x21):(cNUMBER Xn0)
% 185.07/185.43 Instantiate: Xn0:=Xn:fofType
% 185.07/185.43 Found (x3 x21) as proof of (cNUMBER Xn)
% 185.07/185.43 Found (x3 x21) as proof of (cNUMBER Xn)
% 185.07/185.43 Found x30:=(x3 x21):(cNUMBER Xn0)
% 185.07/185.43 Found (x3 x21) as proof of (cNUMBER Xn)
% 185.07/185.43 Found (x3 x21) as proof of (cNUMBER Xn)
% 185.07/185.43 Found (x3 x21) as proof of (cNUMBER Xn)
% 185.07/185.43 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 185.07/185.43 Instantiate: Xn00:=Xn:fofType
% 185.07/185.43 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 185.07/185.43 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 185.07/185.43 Instantiate: Xn00:=Xn:fofType
% 185.07/185.43 Found (fun (x9:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x40) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 185.07/185.43 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x9:(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)))
% 185.07/185.43 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x9:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x40) as proof of (((and ((and (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))))
% 185.07/185.43 Found x50:=(x5 x40):(cNUMBER Xn0)
% 185.07/185.43 Found (x5 x40) as proof of (cNUMBER Xn0)
% 185.07/185.43 Found (x5 x40) as proof of (cNUMBER Xn0)
% 185.07/185.43 Found x50:=(x5 x41):(cNUMBER Xn0)
% 185.07/185.43 Instantiate: Xn0:=Xn:fofType
% 185.07/185.43 Found (x5 x41) as proof of (cNUMBER Xn)
% 185.07/185.43 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x41)) as proof of (cNUMBER Xn)
% 188.30/188.63 Found (fun (x12:(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))
% 188.30/188.63 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 188.30/188.63 Instantiate: Xn00:=Xn:fofType
% 188.30/188.63 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 188.30/188.63 Found x80:((or (cEVEN Xn00)) (cODD Xn00))
% 188.30/188.63 Instantiate: Xn00:=Xn:fofType
% 188.30/188.63 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x80) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 188.30/188.63 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)))
% 188.30/188.63 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 188.30/188.63 Instantiate: Xn00:=Xn:fofType
% 188.30/188.63 Found (fun (x9:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x60) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 188.30/188.63 Found (fun (x9:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x60) as proof of ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 188.30/188.63 Found x50:=(x5 x40):(cNUMBER Xn0)
% 188.30/188.63 Instantiate: Xn0:=Xn:fofType
% 188.30/188.63 Found (x5 x40) as proof of (cNUMBER Xn)
% 188.30/188.63 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 188.30/188.63 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))
% 188.30/188.63 Found (fun (x8:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x9:(((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)))
% 188.30/188.63 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 188.30/188.63 Instantiate: Xn0:=Xn:fofType
% 188.30/188.63 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x20) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 188.30/188.63 Found (fun (x9:(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)))
% 188.30/188.63 Found x90:=(x9 x80):(cNUMBER Xn00)
% 188.30/188.63 Found (x9 x80) as proof of (cNUMBER Xn)
% 188.30/188.63 Found (x9 x80) as proof of (cNUMBER Xn)
% 188.30/188.63 Found (x9 x80) as proof of (cNUMBER Xn)
% 188.30/188.63 Found x50:=(x5 x41):(cNUMBER Xn0)
% 188.30/188.63 Found (x5 x41) as proof of (cNUMBER Xn0)
% 188.30/188.63 Found (x5 x41) as proof of (cNUMBER Xn0)
% 188.30/188.63 Found x50:=(x5 x42):(cNUMBER Xn0)
% 188.30/188.63 Instantiate: Xn0:=Xn:fofType
% 188.30/188.63 Found (x5 x42) as proof of (cNUMBER Xn)
% 188.30/188.63 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x42)) as proof of (cNUMBER Xn)
% 188.30/188.63 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x42)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 188.30/188.63 Found x70:=(x7 x60):(cNUMBER Xn0)
% 188.30/188.63 Found (x7 x60) as proof of (cNUMBER Xn)
% 188.30/188.63 Found (x7 x60) as proof of (cNUMBER Xn)
% 188.30/188.63 Found (x7 x60) as proof of (cNUMBER Xn)
% 188.30/188.63 Found x40:=(x4 x50):((or (cEVEN Xn0)) (cODD Xn0))
% 188.30/188.63 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 188.30/188.63 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 188.30/188.63 Found x50:(cNUMBER Xn00)
% 188.30/188.63 Instantiate: Xn0:=Xn00:fofType
% 188.30/188.63 Found x50 as proof of (cNUMBER Xn0)
% 188.30/188.63 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 188.30/188.63 Instantiate: Xn00:=Xn:fofType
% 188.30/188.63 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 188.30/188.63 Found x80:((or (cEVEN Xn00)) (cODD Xn00))
% 188.30/188.63 Instantiate: Xn00:=Xn:fofType
% 188.30/188.63 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x80) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 188.30/188.63 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)))
% 188.30/188.63 Found x30:=(x3 x20):(cNUMBER Xn0)
% 188.30/188.63 Found (x3 x20) as proof of (cNUMBER Xn00)
% 188.30/188.63 Found (x3 x20) as proof of (cNUMBER Xn00)
% 188.30/188.63 Found (x3 x20) as proof of (cNUMBER Xn00)
% 188.30/188.63 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 188.30/188.63 Instantiate: Xn0:=Xn:fofType
% 188.30/188.63 Found x40 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 188.30/188.63 Found x40:=(x4 x51):((or (cEVEN Xn0)) (cODD Xn0))
% 188.30/188.63 Found (x4 x51) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 188.85/189.24 Found (x4 x51) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 188.85/189.24 Found x50:=(x5 x40):(cNUMBER Xn00)
% 188.85/189.24 Found (x5 x40) as proof of (cNUMBER Xn0)
% 188.85/189.24 Found (x5 x40) as proof of (cNUMBER Xn0)
% 188.85/189.24 Found (x5 x40) as proof of (cNUMBER Xn0)
% 188.85/189.24 Found x80:((or (cEVEN Xn0)) (cODD Xn0))
% 188.85/189.24 Found x80 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 188.85/189.24 Found (x9 x80) as proof of (cNUMBER Xn)
% 188.85/189.24 Found (x9 x80) as proof of (cNUMBER Xn)
% 188.85/189.24 Found (fun (x9:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x9 x80)) as proof of (cNUMBER Xn)
% 188.85/189.24 Found (fun (x9:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x9 x80)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 188.85/189.24 Found x70:(cNUMBER Xn0)
% 188.85/189.24 Instantiate: Xn0:=Xn:fofType
% 188.85/189.24 Found (fun (x11:(cODD (cS c0)))=> x70) as proof of (cNUMBER Xn)
% 188.85/189.24 Found (fun (x9:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x11:(cODD (cS c0)))=> x70) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 188.85/189.24 Found (fun (x8:(cEVEN Xn0)) (x9:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x11:(cODD (cS c0)))=> x70) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 188.85/189.24 Found (fun (x8:(cEVEN Xn0)) (x9:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x11:(cODD (cS c0)))=> x70) as proof of ((cEVEN Xn0)->(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn))))
% 188.85/189.24 Found x70:(cNUMBER Xn0)
% 188.85/189.24 Instantiate: Xn0:=Xn:fofType
% 188.85/189.24 Found (fun (x11:(cODD (cS c0)))=> x70) as proof of (cNUMBER Xn)
% 188.85/189.24 Found (fun (x9:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x11:(cODD (cS c0)))=> x70) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 188.85/189.24 Found (fun (x8:(cODD Xn0)) (x9:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x11:(cODD (cS c0)))=> x70) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 188.85/189.24 Found (fun (x8:(cODD Xn0)) (x9:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x11:(cODD (cS c0)))=> x70) as proof of ((cODD Xn0)->(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn))))
% 188.85/189.24 Found ((or_ind00 (fun (x8:(cEVEN Xn0)) (x9:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x11:(cODD (cS c0)))=> x70)) (fun (x8:(cODD Xn0)) (x9:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x11:(cODD (cS c0)))=> x70)) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 188.85/189.24 Found (((or_ind0 (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))) (fun (x8:(cEVEN Xn0)) (x9:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x11:(cODD (cS c0)))=> x70)) (fun (x8:(cODD Xn0)) (x9:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x11:(cODD (cS c0)))=> x70)) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 188.85/189.24 Found ((((fun (P:Prop) (x8:((cEVEN Xn0)->P)) (x9:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x8) x9) x60)) (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->(cNUMBER Xn)))) (fun (x8:(cEVEN Xn0)) (x9:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x11:(cODD (cS c0)))=> x70)) (fun (x8:(cODD Xn0)) (x9:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x11:(cODD (cS c0)))=> x70)) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 188.85/189.24 Found ((((fun (P:Prop) (x8:((cEVEN Xn0)->P)) (x9:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x8) x9) (x6 x70))) (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->(cNUMBER Xn)))) (fun (x8:(cEVEN Xn0)) (x9:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x11:(cODD (cS c0)))=> x70)) (fun (x8:(cODD Xn0)) (x9:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x11:(cODD (cS c0)))=> x70)) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 190.38/190.73 Found ((((fun (P:Prop) (x8:((cEVEN Xn0)->P)) (x9:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x8) x9) (x6 x70))) (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->(cNUMBER Xn)))) (fun (x8:(cEVEN Xn0)) (x9:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x11:(cODD (cS c0)))=> x70)) (fun (x8:(cODD Xn0)) (x9:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x11:(cODD (cS c0)))=> x70)) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 190.38/190.73 Found x71:(cNUMBER Xn0)
% 190.38/190.73 Instantiate: Xn0:=Xn:fofType
% 190.38/190.73 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x71) as proof of (cNUMBER Xn)
% 190.38/190.73 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x71) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 190.38/190.73 Found x30:=(x3 x20):(cNUMBER Xn0)
% 190.38/190.73 Found (x3 x20) as proof of (cNUMBER Xn)
% 190.38/190.73 Found (x3 x20) as proof of (cNUMBER Xn)
% 190.38/190.73 Found (x3 x20) as proof of (cNUMBER Xn)
% 190.38/190.73 Found x50:=(x5 x40):(cNUMBER Xn00)
% 190.38/190.73 Found (x5 x40) as proof of (cNUMBER Xn)
% 190.38/190.73 Found (x5 x40) as proof of (cNUMBER Xn)
% 190.38/190.73 Found (x5 x40) as proof of (cNUMBER Xn)
% 190.38/190.73 Found x80:((or (cEVEN Xn00)) (cODD Xn00))
% 190.38/190.73 Instantiate: Xn00:=Xn:fofType
% 190.38/190.73 Found x80 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 190.38/190.73 Found x30:=(x3 x21):(cNUMBER Xn0)
% 190.38/190.73 Found (x3 x21) as proof of (cNUMBER Xn)
% 190.38/190.73 Found (x3 x21) as proof of (cNUMBER Xn)
% 190.38/190.73 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x21)) as proof of (cNUMBER Xn)
% 190.38/190.73 Found (fun (x11:(cEVEN c0)) (x12:(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))
% 190.38/190.73 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x21)) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 190.38/190.73 Found x50:=(x5 x40):(cNUMBER Xn00)
% 190.38/190.73 Found (x5 x40) as proof of (cNUMBER Xn)
% 190.38/190.73 Found (x5 x40) as proof of (cNUMBER Xn)
% 190.38/190.73 Found (x5 x40) as proof of (cNUMBER Xn)
% 190.38/190.73 Found x30:=(x3 x20):(cNUMBER Xn0)
% 190.38/190.73 Found (x3 x20) as proof of (cNUMBER Xn)
% 190.38/190.73 Found (x3 x20) as proof of (cNUMBER Xn)
% 190.38/190.73 Found (x3 x20) as proof of (cNUMBER Xn)
% 190.38/190.73 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 190.38/190.73 Instantiate: Xn0:=Xn00:fofType
% 190.38/190.73 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 190.38/190.73 Found x50:=(x5 x42):(cNUMBER Xn0)
% 190.38/190.73 Instantiate: Xn0:=Xn:fofType
% 190.38/190.73 Found (x5 x42) as proof of (cNUMBER Xn)
% 190.38/190.73 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x42)) as proof of (cNUMBER Xn)
% 190.38/190.73 Found (fun (x6:((and ((and (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 x42)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 190.38/190.73 Found (fun (x6:((and ((and (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 x42)) as proof of (((and ((and (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)))
% 190.38/190.73 Found x30:=(x3 x21):(cNUMBER Xn0)
% 190.38/190.73 Found (x3 x21) as proof of (cNUMBER Xn)
% 190.38/190.73 Found (x3 x21) as proof of (cNUMBER Xn)
% 190.38/190.73 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x21)) as proof of (cNUMBER Xn)
% 190.38/190.73 Found (fun (x12:(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))
% 192.35/192.67 Found x30:=(x3 x20):(cNUMBER Xn0)
% 192.35/192.67 Found (x3 x20) as proof of (cNUMBER Xn)
% 192.35/192.67 Found (x3 x20) as proof of (cNUMBER Xn)
% 192.35/192.67 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 192.35/192.67 Found (fun (x9:(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))
% 192.35/192.67 Found x70:=(x7 x60):(cNUMBER Xn00)
% 192.35/192.67 Found (x7 x60) as proof of (cNUMBER Xn)
% 192.35/192.67 Found (x7 x60) as proof of (cNUMBER Xn)
% 192.35/192.67 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x7 x60)) as proof of (cNUMBER Xn)
% 192.35/192.67 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x7 x60)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 192.35/192.67 Found x40:=(x4 x50):((or (cEVEN Xn00)) (cODD Xn00))
% 192.35/192.67 Instantiate: Xn00:=Xn:fofType
% 192.35/192.67 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 192.35/192.67 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 192.35/192.67 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 192.35/192.67 Instantiate: Xn0:=Xn:fofType
% 192.35/192.67 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 192.35/192.67 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 192.35/192.67 Found or_comm_i100:=(or_comm_i10 x40):((or (cODD Xn0)) (cEVEN Xn0))
% 192.35/192.67 Found (or_comm_i10 x40) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 192.35/192.67 Found ((or_comm_i1 (cODD Xn0)) x40) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 192.35/192.67 Found (((or_comm_i (cEVEN Xn0)) (cODD Xn0)) x40) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 192.35/192.67 Found (((or_comm_i (cEVEN Xn0)) (cODD Xn0)) x40) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 192.35/192.67 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 192.35/192.67 Instantiate: Xn00:=Xn:fofType
% 192.35/192.67 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 192.35/192.67 Found (x3 x40) as proof of (cNUMBER Xn)
% 192.35/192.67 Found (x3 x40) as proof of (cNUMBER Xn)
% 192.35/192.67 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x40)) as proof of (cNUMBER Xn)
% 192.35/192.67 Found (fun (x9:(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))
% 192.35/192.67 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 192.35/192.67 Found x40 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 192.35/192.67 Found (x5 x40) as proof of (cNUMBER Xn)
% 192.35/192.67 Found (x5 x40) as proof of (cNUMBER Xn)
% 192.35/192.67 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 192.35/192.67 Found (fun (x9:(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))
% 192.35/192.67 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 192.35/192.67 Instantiate: Xn0:=Xn:fofType
% 192.35/192.67 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 192.35/192.67 Found (x5 x20) as proof of (cNUMBER Xn)
% 192.35/192.67 Found (x5 x20) as proof of (cNUMBER Xn)
% 192.35/192.67 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x20)) as proof of (cNUMBER Xn)
% 192.35/192.67 Found (fun (x9:(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))
% 192.35/192.67 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 192.35/192.67 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 192.35/192.67 Found (x3 x20) as proof of (cNUMBER Xn)
% 192.35/192.67 Found (x3 x20) as proof of (cNUMBER Xn)
% 192.35/192.67 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 192.35/192.67 Found (fun (x9:(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))
% 192.35/192.67 Found x40:=(x4 x50):((or (cEVEN Xn00)) (cODD Xn00))
% 192.35/192.67 Found (x4 x50) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 192.35/192.67 Found (x4 x50) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 192.35/192.67 Found x40:=(x4 x51):((or (cEVEN Xn00)) (cODD Xn00))
% 192.35/192.67 Instantiate: Xn00:=Xn:fofType
% 192.35/192.67 Found (x4 x51) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 192.35/192.67 Found (x4 x51) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 192.35/192.67 Found x40:=(x4 x50):((or (cEVEN Xn00)) (cODD Xn00))
% 192.35/192.67 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 193.94/194.26 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 193.94/194.26 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 193.94/194.26 Found x50:(cNUMBER Xn00)
% 193.94/194.26 Found x50 as proof of (cNUMBER Xn00)
% 193.94/194.26 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 193.94/194.26 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 193.94/194.26 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 193.94/194.26 Found x30:(cNUMBER Xn0)
% 193.94/194.26 Found x30 as proof of (cNUMBER Xn0)
% 193.94/194.26 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 193.94/194.26 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 193.94/194.26 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 193.94/194.26 Found x80:((or (cEVEN Xn00)) (cODD Xn00))
% 193.94/194.26 Instantiate: Xn00:=Xn:fofType
% 193.94/194.26 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x80) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 193.94/194.26 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)))
% 193.94/194.26 Found x52:(cNUMBER Xn0)
% 193.94/194.26 Instantiate: Xn0:=Xn:fofType
% 193.94/194.26 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x52) as proof of (cNUMBER Xn)
% 193.94/194.26 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x52) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 193.94/194.26 Found x50:=(x5 x40):(cNUMBER Xn00)
% 193.94/194.26 Instantiate: Xn0:=Xn00:fofType
% 193.94/194.26 Found (x5 x40) as proof of (cNUMBER Xn0)
% 193.94/194.26 Found (x5 x40) as proof of (cNUMBER Xn0)
% 193.94/194.26 Found x30:=(x3 x20):(cNUMBER Xn0)
% 193.94/194.26 Instantiate: Xn00:=Xn0:fofType
% 193.94/194.26 Found (x3 x20) as proof of (cNUMBER Xn00)
% 193.94/194.26 Found (x3 x20) as proof of (cNUMBER Xn00)
% 193.94/194.26 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 193.94/194.26 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 193.94/194.26 Found (x3 x20) as proof of (cNUMBER Xn00)
% 193.94/194.26 Found (x3 x20) as proof of (cNUMBER Xn00)
% 193.94/194.26 Found (x3 x20) as proof of (cNUMBER Xn00)
% 193.94/194.26 Found x52:(cNUMBER Xn0)
% 193.94/194.26 Instantiate: Xn0:=Xn:fofType
% 193.94/194.26 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x52) as proof of (cNUMBER Xn)
% 193.94/194.26 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x52) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 193.94/194.26 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 193.94/194.26 Instantiate: Xn0:=Xn:fofType
% 193.94/194.26 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 193.94/194.26 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 193.94/194.26 Found x40:=(x4 x50):((or (cEVEN Xn00)) (cODD Xn00))
% 193.94/194.26 Instantiate: Xn00:=Xn:fofType
% 193.94/194.26 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 193.94/194.26 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 193.94/194.26 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 193.94/194.26 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 193.94/194.26 Found (x3 x40) as proof of (cNUMBER Xn00)
% 193.94/194.26 Found (x3 x40) as proof of (cNUMBER Xn00)
% 193.94/194.26 Found (x3 x40) as proof of (cNUMBER Xn00)
% 193.94/194.26 Found x50:=(x5 x40):(cNUMBER Xn0)
% 193.94/194.26 Found (x5 x40) as proof of (cNUMBER Xn0)
% 193.94/194.26 Found (x5 x40) as proof of (cNUMBER Xn0)
% 193.94/194.26 Found x50:=(x5 x41):(cNUMBER Xn0)
% 193.94/194.26 Instantiate: Xn0:=Xn:fofType
% 193.94/194.26 Found (x5 x41) as proof of (cNUMBER Xn)
% 193.94/194.26 Found (x5 x41) as proof of (cNUMBER Xn)
% 193.94/194.26 Found x50:=(x5 x41):(cNUMBER Xn0)
% 193.94/194.26 Found (x5 x41) as proof of (cNUMBER Xn)
% 193.94/194.26 Found (x5 x41) as proof of (cNUMBER Xn)
% 193.94/194.26 Found (x5 x41) as proof of (cNUMBER Xn)
% 193.94/194.26 Found x30:=(x3 x20):(cNUMBER Xn0)
% 193.94/194.26 Found (x3 x20) as proof of (cNUMBER Xn)
% 193.94/194.26 Found (x3 x20) as proof of (cNUMBER Xn)
% 193.94/194.26 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 193.94/194.26 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))
% 193.94/194.26 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)))
% 193.94/194.26 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 193.94/194.26 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 193.94/194.26 Found (x3 x20) as proof of (cNUMBER Xn00)
% 193.94/194.26 Found (x3 x20) as proof of (cNUMBER Xn00)
% 193.94/194.26 Found (x3 x20) as proof of (cNUMBER Xn00)
% 193.94/194.26 Found x21:((or (cEVEN Xn0)) (cODD Xn0))
% 195.27/195.64 Found x21 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 195.27/195.64 Found (x3 x21) as proof of (cNUMBER Xn)
% 195.27/195.64 Found (x3 x21) as proof of (cNUMBER Xn)
% 195.27/195.64 Found (x3 x21) as proof of (cNUMBER Xn)
% 195.27/195.64 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 195.27/195.64 Instantiate: Xn00:=Xn0:fofType
% 195.27/195.64 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 195.27/195.64 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 195.27/195.64 Found x40:=(x4 x50):((or (cEVEN Xn00)) (cODD Xn00))
% 195.27/195.64 Instantiate: Xn0:=Xn00:fofType
% 195.27/195.64 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 195.27/195.64 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 195.27/195.64 Found x30:=(x3 x21):(cNUMBER Xn0)
% 195.27/195.64 Found (x3 x21) as proof of (cNUMBER Xn0)
% 195.27/195.64 Found (x3 x21) as proof of (cNUMBER Xn0)
% 195.27/195.64 Found x30:=(x3 x22):(cNUMBER Xn0)
% 195.27/195.64 Instantiate: Xn0:=Xn:fofType
% 195.27/195.64 Found (x3 x22) as proof of (cNUMBER Xn)
% 195.27/195.64 Found (x3 x22) as proof of (cNUMBER Xn)
% 195.27/195.64 Found x30:=(x3 x20):(cNUMBER Xn0)
% 195.27/195.64 Found (x3 x20) as proof of (cNUMBER Xn)
% 195.27/195.64 Found (x3 x20) as proof of (cNUMBER Xn)
% 195.27/195.64 Found (x3 x20) as proof of (cNUMBER Xn)
% 195.27/195.64 Found x90:=(x9 x80):(cNUMBER Xn00)
% 195.27/195.64 Found (x9 x80) as proof of (cNUMBER Xn)
% 195.27/195.64 Found (x9 x80) as proof of (cNUMBER Xn)
% 195.27/195.64 Found (x9 x80) as proof of (cNUMBER Xn)
% 195.27/195.64 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 195.27/195.64 Instantiate: Xn00:=Xn:fofType
% 195.27/195.64 Found (fun (x9:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x60) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 195.27/195.64 Found (fun (x9:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x60) as proof of ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 195.27/195.64 Found x50:=(x5 x40):(cNUMBER Xn0)
% 195.27/195.64 Found (x5 x40) as proof of (cNUMBER Xn)
% 195.27/195.64 Found (x5 x40) as proof of (cNUMBER Xn)
% 195.27/195.64 Found (x5 x40) as proof of (cNUMBER Xn)
% 195.27/195.64 Found x30:=(x3 x21):(cNUMBER Xn0)
% 195.27/195.64 Found (x3 x21) as proof of (cNUMBER Xn0)
% 195.27/195.64 Found (x3 x21) as proof of (cNUMBER Xn0)
% 195.27/195.64 Found x30:=(x3 x22):(cNUMBER Xn0)
% 195.27/195.64 Instantiate: Xn0:=Xn:fofType
% 195.27/195.64 Found (x3 x22) as proof of (cNUMBER Xn)
% 195.27/195.64 Found (x3 x22) as proof of (cNUMBER Xn)
% 195.27/195.64 Found x30:=(x3 x20):(cNUMBER Xn0)
% 195.27/195.64 Found (x3 x20) as proof of (cNUMBER Xn)
% 195.27/195.64 Found (x3 x20) as proof of (cNUMBER Xn)
% 195.27/195.64 Found (x3 x20) as proof of (cNUMBER Xn)
% 195.27/195.64 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 195.27/195.64 Instantiate: Xn00:=Xn0:fofType
% 195.27/195.64 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 195.27/195.64 Found (x5 x20) as proof of (cNUMBER Xn00)
% 195.27/195.64 Found (x5 x20) as proof of (cNUMBER Xn00)
% 195.27/195.64 Found x70:=(x7 x60):(cNUMBER Xn00)
% 195.27/195.64 Instantiate: Xn00:=Xn:fofType
% 195.27/195.64 Found (x7 x60) as proof of (cNUMBER Xn)
% 195.27/195.64 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x7 x60)) as proof of (cNUMBER Xn)
% 195.27/195.64 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x7 x60)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 195.27/195.64 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x7 x60)) as proof of (((and ((and (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)))
% 195.27/195.64 Found x70:=(x7 x60):(cNUMBER Xn0)
% 195.27/195.64 Found (x7 x60) as proof of (cNUMBER Xn0)
% 195.27/195.64 Found (x7 x60) as proof of (cNUMBER Xn0)
% 195.27/195.64 Found x70:=(x7 x61):(cNUMBER Xn0)
% 195.27/195.64 Instantiate: Xn0:=Xn:fofType
% 195.27/195.64 Found (x7 x61) as proof of (cNUMBER Xn)
% 195.27/195.64 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x61)) as proof of (cNUMBER Xn)
% 195.27/195.64 Found (fun (x12:(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))
% 195.27/195.64 Found x50:=(x5 x40):(cNUMBER Xn0)
% 195.27/195.64 Instantiate: Xn0:=Xn:fofType
% 195.27/195.64 Found (x5 x40) as proof of (cNUMBER Xn)
% 195.27/195.64 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 195.27/195.64 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(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))
% 196.64/196.98 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (((and ((and (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)))
% 196.64/196.98 Found x30:=(x3 x20):(cNUMBER Xn0)
% 196.64/196.98 Found (x3 x20) as proof of (cNUMBER Xn)
% 196.64/196.98 Found (x3 x20) as proof of (cNUMBER Xn)
% 196.64/196.98 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 196.64/196.98 Found (fun (x6:((and ((and (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))
% 196.64/196.98 Found (fun (x6:((and ((and (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 (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)))
% 196.64/196.98 Found x30:=(x3 x20):(cNUMBER Xn0)
% 196.64/196.98 Found (x3 x20) as proof of (cNUMBER Xn)
% 196.64/196.98 Found (x3 x20) as proof of (cNUMBER Xn)
% 196.64/196.98 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 196.64/196.98 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))
% 196.64/196.98 Found x30:=(x3 x20):(cNUMBER Xn0)
% 196.64/196.98 Found (x3 x20) as proof of (cNUMBER Xn)
% 196.64/196.98 Found (x3 x20) as proof of (cNUMBER Xn)
% 196.64/196.98 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 196.64/196.98 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))
% 196.64/196.98 Found x30:=(x3 x20):(cNUMBER Xn0)
% 196.64/196.98 Found (x3 x20) as proof of (cNUMBER Xn0)
% 196.64/196.98 Found (x3 x20) as proof of (cNUMBER Xn0)
% 196.64/196.98 Found x30:=(x3 x21):(cNUMBER Xn0)
% 196.64/196.98 Instantiate: Xn0:=Xn:fofType
% 196.64/196.98 Found (x3 x21) as proof of (cNUMBER Xn)
% 196.64/196.98 Found (x3 x21) as proof of (cNUMBER Xn)
% 196.64/196.98 Found x30:=(x3 x21):(cNUMBER Xn0)
% 196.64/196.98 Found (x3 x21) as proof of (cNUMBER Xn)
% 196.64/196.98 Found (x3 x21) as proof of (cNUMBER Xn)
% 196.64/196.98 Found (x3 x21) as proof of (cNUMBER Xn)
% 196.64/196.98 Found x80:((or (cEVEN Xn00)) (cODD Xn00))
% 196.64/196.98 Instantiate: Xn00:=Xn:fofType
% 196.64/196.98 Found x80 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 196.64/196.98 Found (x3 x80) as proof of (cNUMBER Xn)
% 196.64/196.98 Found (x3 x80) as proof of (cNUMBER Xn)
% 196.64/196.98 Found (x3 x80) as proof of (cNUMBER Xn)
% 196.64/196.98 Found x80:((or (cEVEN Xn00)) (cODD Xn00))
% 196.64/196.98 Found x80 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 196.64/196.98 Found (x9 x80) as proof of (cNUMBER Xn)
% 196.64/196.98 Found (x9 x80) as proof of (cNUMBER Xn)
% 196.64/196.98 Found (x9 x80) as proof of (cNUMBER Xn)
% 196.64/196.98 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 196.64/196.98 Instantiate: Xn0:=Xn:fofType
% 196.64/196.98 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 196.64/196.98 Found (x9 x20) as proof of (cNUMBER Xn)
% 196.64/196.98 Found (x9 x20) as proof of (cNUMBER Xn)
% 196.64/196.98 Found (x9 x20) as proof of (cNUMBER Xn)
% 196.64/196.98 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 196.64/196.98 Instantiate: Xn00:=Xn:fofType
% 196.64/196.98 Found (fun (x9:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x60) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 196.64/196.98 Found (fun (x9:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x60) as proof of ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 196.64/196.98 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 196.64/196.98 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 196.64/196.98 Found (x3 x20) as proof of (cNUMBER Xn)
% 196.64/196.98 Found (x3 x20) as proof of (cNUMBER Xn)
% 196.64/196.98 Found (x3 x20) as proof of (cNUMBER Xn)
% 196.64/196.98 Found x11:(cEVEN c0)
% 196.64/196.98 Instantiate: Xn0:=c0:fofType
% 196.64/196.98 Found x11 as proof of (cEVEN Xn0)
% 196.64/196.98 Found (or_intror00 x11) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 196.64/196.98 Found ((or_intror0 (cEVEN Xn0)) x11) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 198.05/198.38 Found (((or_intror (cODD Xn0)) (cEVEN Xn0)) x11) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 198.05/198.38 Found (((or_intror (cODD Xn0)) (cEVEN Xn0)) x11) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 198.05/198.38 Found (or_comm_i00 (((or_intror (cODD Xn0)) (cEVEN Xn0)) x11)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 198.05/198.38 Found ((or_comm_i0 (cEVEN Xn0)) (((or_intror (cODD Xn0)) (cEVEN Xn0)) x11)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 198.05/198.38 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((or_intror (cODD Xn0)) (cEVEN Xn0)) x11)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 198.05/198.38 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((or_intror (cODD Xn0)) (cEVEN Xn0)) x11)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 198.05/198.38 Found x60:=(x6 x70):((or (cEVEN Xn0)) (cODD Xn0))
% 198.05/198.38 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 198.05/198.38 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 198.05/198.38 Found x11:(cEVEN c0)
% 198.05/198.38 Instantiate: Xn0:=c0:fofType
% 198.05/198.38 Found x11 as proof of (cEVEN Xn0)
% 198.05/198.38 Found (or_intror00 x11) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 198.05/198.38 Found ((or_intror0 (cEVEN Xn0)) x11) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 198.05/198.38 Found (((or_intror (cODD Xn0)) (cEVEN Xn0)) x11) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 198.05/198.38 Found (((or_intror (cODD Xn0)) (cEVEN Xn0)) x11) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 198.05/198.38 Found (or_comm_i00 (((or_intror (cODD Xn0)) (cEVEN Xn0)) x11)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 198.05/198.38 Found ((or_comm_i0 (cEVEN Xn0)) (((or_intror (cODD Xn0)) (cEVEN Xn0)) x11)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 198.05/198.38 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((or_intror (cODD Xn0)) (cEVEN Xn0)) x11)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 198.05/198.38 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((or_intror (cODD Xn0)) (cEVEN Xn0)) x11)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 198.05/198.38 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 198.05/198.38 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 198.05/198.38 Found (x3 x20) as proof of (cNUMBER Xn)
% 198.05/198.38 Found (x3 x20) as proof of (cNUMBER Xn)
% 198.05/198.38 Found (x3 x20) as proof of (cNUMBER Xn)
% 198.05/198.38 Found x80:=(x8 x90):((or (cEVEN Xn00)) (cODD Xn00))
% 198.05/198.38 Instantiate: Xn00:=Xn:fofType
% 198.05/198.38 Found (x8 x90) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 198.05/198.38 Found (x8 x90) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 198.05/198.38 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 198.05/198.38 Instantiate: Xn0:=Xn:fofType
% 198.05/198.38 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 198.05/198.38 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 198.05/198.38 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 198.05/198.38 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 198.05/198.38 Found (x5 x40) as proof of (cNUMBER Xn)
% 198.05/198.38 Found (x5 x40) as proof of (cNUMBER Xn)
% 198.05/198.38 Found (x5 x40) as proof of (cNUMBER Xn)
% 198.05/198.38 Found x70:=(x7 x60):(cNUMBER Xn0)
% 198.05/198.38 Found (x7 x60) as proof of (cNUMBER Xn)
% 198.05/198.38 Found (x7 x60) as proof of (cNUMBER Xn)
% 198.05/198.38 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x7 x60)) as proof of (cNUMBER Xn)
% 198.05/198.38 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x7 x60)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 198.05/198.38 Found x90:=(x9 x80):(cNUMBER Xn00)
% 198.05/198.38 Found (x9 x80) as proof of (cNUMBER Xn)
% 198.05/198.38 Found (x9 x80) as proof of (cNUMBER Xn)
% 198.05/198.38 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x9 x80)) as proof of (cNUMBER Xn)
% 198.05/198.38 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x9 x80)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 198.05/198.38 Found x90:=(x9 x80):(cNUMBER Xn0)
% 198.05/198.38 Found (x9 x80) as proof of (cNUMBER Xn0)
% 198.05/198.38 Found (x9 x80) as proof of (cNUMBER Xn0)
% 198.05/198.38 Found x7:(cODD (cS c0))
% 198.05/198.38 Instantiate: Xn0:=(cS c0):fofType
% 198.05/198.38 Found x7 as proof of (cODD Xn0)
% 198.05/198.38 Found (or_introl00 x7) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 198.05/198.38 Found ((or_introl0 (cEVEN Xn0)) x7) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 198.05/198.38 Found (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 198.05/198.38 Found (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 198.05/198.38 Found (or_comm_i00 (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 198.05/198.38 Found ((or_comm_i0 (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 200.09/200.43 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 200.09/200.43 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 200.09/200.43 Found x70:=(x7 x61):(cNUMBER Xn0)
% 200.09/200.43 Found (x7 x61) as proof of (cNUMBER Xn0)
% 200.09/200.43 Found (x7 x61) as proof of (cNUMBER Xn0)
% 200.09/200.43 Found x70:=(x7 x62):(cNUMBER Xn0)
% 200.09/200.43 Instantiate: Xn0:=Xn:fofType
% 200.09/200.43 Found (x7 x62) as proof of (cNUMBER Xn)
% 200.09/200.43 Found (x7 x62) as proof of (cNUMBER Xn)
% 200.09/200.43 Found x70:=(x7 x62):(cNUMBER Xn0)
% 200.09/200.43 Found (x7 x62) as proof of (cNUMBER Xn)
% 200.09/200.43 Found (x7 x62) as proof of (cNUMBER Xn)
% 200.09/200.43 Found (x7 x62) as proof of (cNUMBER Xn)
% 200.09/200.43 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 200.09/200.43 Instantiate: Xn00:=Xn:fofType
% 200.09/200.43 Found (fun (x9:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x60) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 200.09/200.43 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x9:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x60) as proof of ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 200.09/200.43 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x9:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x60) as proof of (((and ((and (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))))
% 200.09/200.43 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 200.09/200.43 Instantiate: Xn0:=Xn:fofType
% 200.09/200.43 Found x40 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 200.09/200.43 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 200.09/200.43 Instantiate: Xn0:=Xn:fofType
% 200.09/200.43 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x20) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 200.09/200.43 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(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)))
% 200.09/200.43 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x20) as proof of (((and ((and (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))))
% 200.09/200.43 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 200.09/200.43 Instantiate: Xn00:=Xn:fofType
% 200.09/200.43 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 200.09/200.43 Found x11:(cEVEN c0)
% 200.09/200.43 Instantiate: Xn0:=c0:fofType
% 200.09/200.43 Found x11 as proof of (cEVEN Xn0)
% 200.09/200.43 Found (or_introl00 x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 200.09/200.43 Found ((or_introl0 (cODD Xn0)) x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 200.09/200.43 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 200.09/200.43 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 200.09/200.43 Found (x7 (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11)) as proof of (cNUMBER Xn0)
% 200.09/200.43 Found (fun (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (x7 (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11))) as proof of (cNUMBER Xn0)
% 200.09/200.43 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (x7 (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11))) as proof of ((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->(cNUMBER Xn0))
% 200.09/200.43 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (x7 (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11))) as proof of ((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->(cNUMBER Xn0)))
% 200.09/200.43 Found (and_rect50 (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (x7 (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11)))) as proof of (cNUMBER Xn0)
% 200.09/200.43 Found ((and_rect5 (cNUMBER Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (x7 (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11)))) as proof of (cNUMBER Xn0)
% 201.01/201.33 Found (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (x7 (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11)))) as proof of (cNUMBER Xn0)
% 201.01/201.33 Found (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (x7 (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11)))) as proof of (cNUMBER Xn0)
% 201.01/201.33 Found x50:=(x5 x41):(cNUMBER Xn0)
% 201.01/201.33 Found (x5 x41) as proof of (cNUMBER Xn0)
% 201.01/201.33 Found (x5 x41) as proof of (cNUMBER Xn0)
% 201.01/201.33 Found x50:=(x5 x42):(cNUMBER Xn0)
% 201.01/201.33 Instantiate: Xn0:=Xn:fofType
% 201.01/201.33 Found (x5 x42) as proof of (cNUMBER Xn)
% 201.01/201.33 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x42)) as proof of (cNUMBER Xn)
% 201.01/201.33 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x42)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 201.01/201.33 Found x80:((or (cEVEN Xn00)) (cODD Xn00))
% 201.01/201.33 Instantiate: Xn00:=Xn:fofType
% 201.01/201.33 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x80) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 201.01/201.33 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)))
% 201.01/201.33 Found x30:(cNUMBER Xn0)
% 201.01/201.33 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30) as proof of (cNUMBER Xn0)
% 201.01/201.33 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn0))
% 201.01/201.33 Found x50:=(x5 x41):(cNUMBER Xn0)
% 201.01/201.33 Found (x5 x41) as proof of (cNUMBER Xn0)
% 201.01/201.33 Found (x5 x41) as proof of (cNUMBER Xn0)
% 201.01/201.33 Found x50:=(x5 x42):(cNUMBER Xn0)
% 201.01/201.33 Instantiate: Xn0:=Xn:fofType
% 201.01/201.33 Found (x5 x42) as proof of (cNUMBER Xn)
% 201.01/201.33 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x42)) as proof of (cNUMBER Xn)
% 201.01/201.33 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x42)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 201.01/201.33 Found x50:=(x5 x41):(cNUMBER Xn0)
% 201.01/201.33 Found (x5 x41) as proof of (cNUMBER Xn)
% 201.01/201.33 Found (x5 x41) as proof of (cNUMBER Xn)
% 201.01/201.33 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x41)) as proof of (cNUMBER Xn)
% 201.01/201.33 Found (fun (x12:(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))
% 201.01/201.33 Found x30:=(x3 x20):(cNUMBER Xn0)
% 201.01/201.33 Found (x3 x20) as proof of (cNUMBER Xn00)
% 201.01/201.33 Found (x3 x20) as proof of (cNUMBER Xn00)
% 201.01/201.33 Found (x3 x20) as proof of (cNUMBER Xn00)
% 201.01/201.33 Found x80:=(x8 x90):((or (cEVEN Xn0)) (cODD Xn0))
% 201.01/201.33 Found (x8 x90) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 201.01/201.33 Found (x8 x90) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 201.01/201.33 Found x91:(cNUMBER Xn0)
% 201.01/201.33 Instantiate: Xn0:=Xn:fofType
% 201.01/201.33 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x91) as proof of (cNUMBER Xn)
% 201.01/201.33 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x91) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 201.01/201.33 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x91) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 201.01/201.33 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 201.01/201.33 Instantiate: Xn0:=Xn00:fofType
% 201.01/201.33 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x40) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 201.01/201.33 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)))
% 202.19/202.54 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 202.19/202.54 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x20) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 202.19/202.54 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x20) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->((or (cEVEN Xn0)) (cODD Xn0)))
% 202.19/202.54 Found x40:=(x4 x51):((or (cEVEN Xn0)) (cODD Xn0))
% 202.19/202.54 Found (x4 x51) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 202.19/202.54 Found (x4 x51) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 202.19/202.54 Found x80:((or (cEVEN Xn00)) (cODD Xn00))
% 202.19/202.54 Instantiate: Xn00:=Xn:fofType
% 202.19/202.54 Found x80 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 202.19/202.54 Found x50:=(x5 x40):(cNUMBER Xn00)
% 202.19/202.54 Found (x5 x40) as proof of (cNUMBER Xn)
% 202.19/202.54 Found (x5 x40) as proof of (cNUMBER Xn)
% 202.19/202.54 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 202.19/202.54 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 202.19/202.54 Found x30:=(x3 x20):(cNUMBER Xn0)
% 202.19/202.54 Found (x3 x20) as proof of (cNUMBER Xn)
% 202.19/202.54 Found (x3 x20) as proof of (cNUMBER Xn)
% 202.19/202.54 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 202.19/202.54 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 202.19/202.54 Found x30:=(x3 x20):(cNUMBER Xn0)
% 202.19/202.54 Found (x3 x20) as proof of (cNUMBER Xn)
% 202.19/202.54 Found (x3 x20) as proof of (cNUMBER Xn)
% 202.19/202.54 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 202.19/202.54 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 202.19/202.54 Found x50:=(x5 x40):(cNUMBER Xn00)
% 202.19/202.54 Found (x5 x40) as proof of (cNUMBER Xn)
% 202.19/202.54 Found (x5 x40) as proof of (cNUMBER Xn)
% 202.19/202.54 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 202.19/202.54 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 202.19/202.54 Found x30:=(x3 x20):(cNUMBER Xn0)
% 202.19/202.54 Found (x3 x20) as proof of (cNUMBER Xn)
% 202.19/202.54 Found (x3 x20) as proof of (cNUMBER Xn)
% 202.19/202.54 Found (x3 x20) as proof of (cNUMBER Xn)
% 202.19/202.54 Found x11:(cEVEN c0)
% 202.19/202.54 Instantiate: Xn0:=c0:fofType
% 202.19/202.54 Found (fun (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11) as proof of (cEVEN Xn0)
% 202.19/202.54 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11) as proof of ((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->(cEVEN Xn0))
% 202.19/202.54 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11) as proof of ((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->(cEVEN Xn0)))
% 202.19/202.54 Found (and_rect50 (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11)) as proof of (cEVEN Xn0)
% 202.19/202.54 Found ((and_rect5 (cEVEN Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11)) as proof of (cEVEN Xn0)
% 202.19/202.54 Found (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x11) x8)) (cEVEN Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11)) as proof of (cEVEN Xn0)
% 202.19/202.54 Found (fun (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x11) x8)) (cEVEN Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11))) as proof of (cEVEN Xn0)
% 202.19/202.54 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x11) x8)) (cEVEN Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11))) as proof of ((cODD (cS c0))->(cEVEN Xn0))
% 202.19/202.55 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x11) x8)) (cEVEN Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->(cEVEN Xn0)))
% 202.19/202.55 Found (and_rect40 (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x11) x8)) (cEVEN Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11)))) as proof of (cEVEN Xn0)
% 202.19/202.55 Found ((and_rect4 (cEVEN Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x11) x8)) (cEVEN Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11)))) as proof of (cEVEN Xn0)
% 202.19/202.55 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cEVEN Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x11) x8)) (cEVEN Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11)))) as proof of (cEVEN Xn0)
% 202.19/202.55 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cEVEN Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x11) x8)) (cEVEN Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11)))) as proof of (cEVEN Xn0)
% 202.19/202.55 Found (or_introl00 (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) (cEVEN Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x11) x8)) (cEVEN Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 202.74/203.12 Found ((or_introl0 (cODD Xn0)) (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) (cEVEN Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x11) x8)) (cEVEN Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 202.74/203.12 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) (cEVEN Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x11) x8)) (cEVEN Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 202.74/203.12 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) (cEVEN Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x11) x8)) (cEVEN Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 202.74/203.12 Found x50:=(x5 x40):(cNUMBER Xn00)
% 202.74/203.12 Found (x5 x40) as proof of (cNUMBER Xn)
% 202.74/203.12 Found (x5 x40) as proof of (cNUMBER Xn)
% 202.74/203.12 Found (x5 x40) as proof of (cNUMBER Xn)
% 202.74/203.12 Found x40:=(x4 x51):((or (cEVEN Xn0)) (cODD Xn0))
% 202.74/203.12 Found (x4 x51) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 202.74/203.12 Found (x4 x51) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 202.74/203.12 Found x40:=(x4 x50):((or (cEVEN Xn00)) (cODD Xn00))
% 202.74/203.12 Instantiate: Xn00:=Xn:fofType
% 202.74/203.12 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 202.74/203.12 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 202.74/203.12 Found x50:=(x5 x41):(cNUMBER Xn00)
% 202.74/203.12 Found (x5 x41) as proof of (cNUMBER Xn)
% 202.74/203.12 Found (x5 x41) as proof of (cNUMBER Xn)
% 202.74/203.12 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x41)) as proof of (cNUMBER Xn)
% 202.74/203.12 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x41)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 202.74/203.12 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 202.74/203.12 Instantiate: Xn0:=Xn:fofType
% 202.74/203.12 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 202.74/203.12 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x2 x30)) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 202.74/203.12 Found (fun (x9:(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)))
% 202.74/203.12 Found x40:=(x4 x50):((or (cEVEN Xn00)) (cODD Xn00))
% 202.74/203.12 Instantiate: Xn00:=Xn:fofType
% 202.74/203.12 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 202.74/203.12 Found (fun (x9:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x4 x50)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 202.74/203.12 Found (fun (x9:(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)))
% 204.72/205.06 Found x71:(cNUMBER Xn0)
% 204.72/205.06 Instantiate: Xn0:=Xn:fofType
% 204.72/205.06 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x71) as proof of (cNUMBER Xn)
% 204.72/205.06 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x71) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 204.72/205.06 Found x70:=(x7 x60):(cNUMBER Xn00)
% 204.72/205.06 Found (x7 x60) as proof of (cNUMBER Xn)
% 204.72/205.06 Found (x7 x60) as proof of (cNUMBER Xn)
% 204.72/205.06 Found (x7 x60) as proof of (cNUMBER Xn)
% 204.72/205.06 Found x50:=(x5 x40):(cNUMBER Xn0)
% 204.72/205.06 Found (x5 x40) as proof of (cNUMBER Xn)
% 204.72/205.06 Found (x5 x40) as proof of (cNUMBER Xn)
% 204.72/205.06 Found (x5 x40) as proof of (cNUMBER Xn)
% 204.72/205.06 Found x50:(cNUMBER Xn00)
% 204.72/205.06 Found x50 as proof of (cNUMBER Xn00)
% 204.72/205.06 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 204.72/205.06 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 204.72/205.06 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 204.72/205.06 Found x70:=(x7 x61):(cNUMBER Xn0)
% 204.72/205.06 Instantiate: Xn0:=Xn:fofType
% 204.72/205.06 Found (x7 x61) as proof of (cNUMBER Xn)
% 204.72/205.06 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x61)) as proof of (cNUMBER Xn)
% 204.72/205.06 Found (fun (x11:(cEVEN c0)) (x12:(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))
% 204.72/205.06 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x61)) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 204.72/205.06 Found x70:=(x7 x60):(cNUMBER Xn00)
% 204.72/205.06 Found (x7 x60) as proof of (cNUMBER Xn)
% 204.72/205.06 Found (x7 x60) as proof of (cNUMBER Xn)
% 204.72/205.06 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x7 x60)) as proof of (cNUMBER Xn)
% 204.72/205.06 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x7 x60)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 204.72/205.06 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x7 x60)) as proof of (((and ((and (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)))
% 204.72/205.06 Found x30:=(x3 x20):(cNUMBER Xn0)
% 204.72/205.06 Found (x3 x20) as proof of (cNUMBER Xn)
% 204.72/205.06 Found (x3 x20) as proof of (cNUMBER Xn)
% 204.72/205.06 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 204.72/205.06 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(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))
% 204.72/205.06 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (((and ((and (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)))
% 204.72/205.06 Found x40:=(x4 x50):((or (cEVEN Xn00)) (cODD Xn00))
% 204.72/205.06 Instantiate: Xn00:=Xn:fofType
% 204.72/205.06 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 204.72/205.06 Found (fun (x9:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x4 x50)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 204.72/205.06 Found (fun (x9:(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)))
% 204.72/205.06 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 204.72/205.06 Instantiate: Xn0:=Xn:fofType
% 204.72/205.06 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 204.72/205.06 Found (x7 x20) as proof of (cNUMBER Xn)
% 205.62/205.97 Found (x7 x20) as proof of (cNUMBER Xn)
% 205.62/205.97 Found (x7 x20) as proof of (cNUMBER Xn)
% 205.62/205.97 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 205.62/205.97 Instantiate: Xn00:=Xn:fofType
% 205.62/205.97 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 205.62/205.97 Found (x3 x60) as proof of (cNUMBER Xn)
% 205.62/205.97 Found (x3 x60) as proof of (cNUMBER Xn)
% 205.62/205.97 Found (x3 x60) as proof of (cNUMBER Xn)
% 205.62/205.97 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 205.62/205.97 Found x60 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 205.62/205.97 Found (x7 x60) as proof of (cNUMBER Xn)
% 205.62/205.97 Found (x7 x60) as proof of (cNUMBER Xn)
% 205.62/205.97 Found (x7 x60) as proof of (cNUMBER Xn)
% 205.62/205.97 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 205.62/205.97 Instantiate: Xn0:=Xn:fofType
% 205.62/205.97 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 205.62/205.97 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x2 x30)) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 205.62/205.97 Found (fun (x9:(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)))
% 205.62/205.97 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 205.62/205.97 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 205.62/205.97 Found (x3 x20) as proof of (cNUMBER Xn)
% 205.62/205.97 Found (x3 x20) as proof of (cNUMBER Xn)
% 205.62/205.97 Found (x3 x20) as proof of (cNUMBER Xn)
% 205.62/205.97 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 205.62/205.97 Instantiate: Xn0:=Xn:fofType
% 205.62/205.97 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 205.62/205.97 Found (x5 x20) as proof of (cNUMBER Xn)
% 205.62/205.97 Found (x5 x20) as proof of (cNUMBER Xn)
% 205.62/205.97 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x20)) as proof of (cNUMBER Xn)
% 205.62/205.97 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(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))
% 205.62/205.97 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x20)) as proof of (((and ((and (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)))
% 205.62/205.97 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 205.62/205.97 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 205.62/205.97 Found (x3 x20) as proof of (cNUMBER Xn)
% 205.62/205.97 Found (x3 x20) as proof of (cNUMBER Xn)
% 205.62/205.97 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 205.62/205.97 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(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))
% 205.62/205.97 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (((and ((and (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)))
% 205.62/205.97 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 205.62/205.97 Instantiate: Xn00:=Xn:fofType
% 205.62/205.97 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 205.62/205.97 Found (x3 x40) as proof of (cNUMBER Xn)
% 205.62/205.97 Found (x3 x40) as proof of (cNUMBER Xn)
% 205.62/205.97 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x40)) as proof of (cNUMBER Xn)
% 205.62/205.97 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(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))
% 205.62/205.97 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x40)) as proof of (((and ((and (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)))
% 206.41/206.79 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 206.41/206.79 Found x40 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 206.41/206.79 Found (x5 x40) as proof of (cNUMBER Xn)
% 206.41/206.79 Found (x5 x40) as proof of (cNUMBER Xn)
% 206.41/206.79 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 206.41/206.79 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(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))
% 206.41/206.79 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (((and ((and (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)))
% 206.41/206.79 Found x30:=(x3 x20):(cNUMBER Xn0)
% 206.41/206.79 Instantiate: Xn0:=Xn:fofType
% 206.41/206.79 Found (x3 x20) as proof of (cNUMBER Xn)
% 206.41/206.79 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 206.41/206.79 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))
% 206.41/206.79 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)))
% 206.41/206.79 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)
% 206.41/206.79 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)
% 206.41/206.79 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)
% 206.41/206.79 Found x50:=(x5 x40):(cNUMBER Xn0)
% 206.41/206.79 Found (x5 x40) as proof of (cNUMBER Xn)
% 206.41/206.79 Found (x5 x40) as proof of (cNUMBER Xn)
% 206.41/206.79 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 206.41/206.79 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 206.41/206.79 Found x21:((or (cEVEN Xn0)) (cODD Xn0))
% 206.41/206.79 Found x21 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 206.41/206.79 Found (x3 x21) as proof of (cNUMBER Xn)
% 206.41/206.79 Found (x3 x21) as proof of (cNUMBER Xn)
% 206.41/206.79 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x21)) as proof of (cNUMBER Xn)
% 206.41/206.79 Found (fun (x12:(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))
% 206.41/206.79 Found x90:=(x9 x80):(cNUMBER Xn00)
% 206.41/206.79 Found (x9 x80) as proof of (cNUMBER Xn)
% 206.41/206.79 Found (x9 x80) as proof of (cNUMBER Xn)
% 206.41/206.79 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x9 x80)) as proof of (cNUMBER Xn)
% 206.41/206.79 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x9 x80)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 206.41/206.79 Found x60:=(x6 x70):((or (cEVEN Xn00)) (cODD Xn00))
% 206.41/206.79 Instantiate: Xn00:=Xn:fofType
% 206.41/206.79 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 206.41/206.79 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 206.41/206.79 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 206.41/206.79 Instantiate: Xn0:=Xn:fofType
% 206.41/206.79 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 206.41/206.79 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 206.41/206.79 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 207.95/208.29 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 207.95/208.29 Found (x3 x20) as proof of (cNUMBER Xn00)
% 207.95/208.29 Found (x3 x20) as proof of (cNUMBER Xn00)
% 207.95/208.29 Found (x3 x20) as proof of (cNUMBER Xn00)
% 207.95/208.29 Found x50:=(x5 x41):(cNUMBER Xn0)
% 207.95/208.29 Found (x5 x41) as proof of (cNUMBER Xn0)
% 207.95/208.29 Found (x5 x41) as proof of (cNUMBER Xn0)
% 207.95/208.29 Found x50:=(x5 x42):(cNUMBER Xn0)
% 207.95/208.29 Instantiate: Xn0:=Xn:fofType
% 207.95/208.29 Found (x5 x42) as proof of (cNUMBER Xn)
% 207.95/208.29 Found (x5 x42) as proof of (cNUMBER Xn)
% 207.95/208.29 Found x50:=(x5 x41):(cNUMBER Xn0)
% 207.95/208.29 Found (x5 x41) as proof of (cNUMBER Xn)
% 207.95/208.29 Found (x5 x41) as proof of (cNUMBER Xn)
% 207.95/208.29 Found (x5 x41) as proof of (cNUMBER Xn)
% 207.95/208.29 Found x30:=(x3 x22):(cNUMBER Xn0)
% 207.95/208.29 Found (x3 x22) as proof of (cNUMBER Xn0)
% 207.95/208.29 Found (x3 x22) as proof of (cNUMBER Xn0)
% 207.95/208.29 Found x30:=(x3 x23):(cNUMBER Xn0)
% 207.95/208.29 Instantiate: Xn0:=Xn:fofType
% 207.95/208.29 Found (x3 x23) as proof of (cNUMBER Xn)
% 207.95/208.29 Found (x3 x23) as proof of (cNUMBER Xn)
% 207.95/208.29 Found x30:=(x3 x22):(cNUMBER Xn0)
% 207.95/208.29 Found (x3 x22) as proof of (cNUMBER Xn)
% 207.95/208.29 Found (x3 x22) as proof of (cNUMBER Xn)
% 207.95/208.29 Found (x3 x22) as proof of (cNUMBER Xn)
% 207.95/208.29 Found x21:((or (cEVEN Xn0)) (cODD Xn0))
% 207.95/208.29 Found x21 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 207.95/208.29 Found (x3 x21) as proof of (cNUMBER Xn)
% 207.95/208.29 Found (x3 x21) as proof of (cNUMBER Xn)
% 207.95/208.29 Found (x3 x21) as proof of (cNUMBER Xn)
% 207.95/208.29 Found x50:=(x5 x41):(cNUMBER Xn0)
% 207.95/208.29 Found (x5 x41) as proof of (cNUMBER Xn)
% 207.95/208.29 Found (x5 x41) as proof of (cNUMBER Xn)
% 207.95/208.29 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x41)) as proof of (cNUMBER Xn)
% 207.95/208.29 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x41)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 207.95/208.29 Found x50:=(x5 x40):(cNUMBER Xn0)
% 207.95/208.29 Found (x5 x40) as proof of (cNUMBER Xn0)
% 207.95/208.29 Found (x5 x40) as proof of (cNUMBER Xn0)
% 207.95/208.29 Found x50:=(x5 x41):(cNUMBER Xn0)
% 207.95/208.29 Instantiate: Xn0:=Xn:fofType
% 207.95/208.29 Found (x5 x41) as proof of (cNUMBER Xn)
% 207.95/208.29 Found (x5 x41) as proof of (cNUMBER Xn)
% 207.95/208.29 Found x50:=(x5 x41):(cNUMBER Xn0)
% 207.95/208.29 Found (x5 x41) as proof of (cNUMBER Xn)
% 207.95/208.29 Found (x5 x41) as proof of (cNUMBER Xn)
% 207.95/208.29 Found (x5 x41) as proof of (cNUMBER Xn)
% 207.95/208.29 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 207.95/208.29 Instantiate: Xn0:=Xn:fofType
% 207.95/208.29 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 207.95/208.29 Found (x9 x20) as proof of (cNUMBER Xn)
% 207.95/208.29 Found (x9 x20) as proof of (cNUMBER Xn)
% 207.95/208.29 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x9 x20)) as proof of (cNUMBER Xn)
% 207.95/208.29 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x9 x20)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 207.95/208.29 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 207.95/208.29 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 207.95/208.29 Found (x3 x20) as proof of (cNUMBER Xn)
% 207.95/208.29 Found (x3 x20) as proof of (cNUMBER Xn)
% 207.95/208.29 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 207.95/208.29 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 207.95/208.29 Found x30:=(x3 x21):(cNUMBER Xn0)
% 207.95/208.29 Found (x3 x21) as proof of (cNUMBER Xn0)
% 207.95/208.29 Found (x3 x21) as proof of (cNUMBER Xn0)
% 207.95/208.29 Found x30:=(x3 x22):(cNUMBER Xn0)
% 207.95/208.29 Instantiate: Xn0:=Xn:fofType
% 207.95/208.29 Found (x3 x22) as proof of (cNUMBER Xn)
% 207.95/208.29 Found (x3 x22) as proof of (cNUMBER Xn)
% 207.95/208.29 Found x30:=(x3 x20):(cNUMBER Xn0)
% 207.95/208.29 Found (x3 x20) as proof of (cNUMBER Xn)
% 207.95/208.29 Found (x3 x20) as proof of (cNUMBER Xn)
% 207.95/208.29 Found (x3 x20) as proof of (cNUMBER Xn)
% 207.95/208.29 Found x80:((or (cEVEN Xn00)) (cODD Xn00))
% 207.95/208.29 Instantiate: Xn00:=Xn:fofType
% 207.95/208.29 Found x80 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 207.95/208.29 Found (x3 x80) as proof of (cNUMBER Xn)
% 207.95/208.29 Found (x3 x80) as proof of (cNUMBER Xn)
% 207.95/208.29 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x80)) as proof of (cNUMBER Xn)
% 207.95/208.29 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x80)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 207.95/208.29 Found x80:=(x8 x90):((or (cEVEN Xn00)) (cODD Xn00))
% 207.95/208.29 Instantiate: Xn00:=Xn:fofType
% 207.95/208.29 Found (x8 x90) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 207.95/208.29 Found (x8 x90) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 207.95/208.29 Found x80:((or (cEVEN Xn00)) (cODD Xn00))
% 207.95/208.29 Found x80 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 210.02/210.38 Found (x9 x80) as proof of (cNUMBER Xn)
% 210.02/210.38 Found (x9 x80) as proof of (cNUMBER Xn)
% 210.02/210.38 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x9 x80)) as proof of (cNUMBER Xn)
% 210.02/210.38 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x9 x80)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 210.02/210.38 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 210.02/210.38 Instantiate: Xn00:=Xn:fofType
% 210.02/210.38 Found (fun (x9:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x60) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 210.02/210.38 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x9:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x60) as proof of ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 210.02/210.38 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x9:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x60) as proof of (((and ((and (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))))
% 210.02/210.38 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 210.02/210.38 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 210.02/210.38 Found (x3 x20) as proof of (cNUMBER Xn)
% 210.02/210.38 Found (x3 x20) as proof of (cNUMBER Xn)
% 210.02/210.38 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 210.02/210.38 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))
% 210.02/210.38 Found x30:=(x3 x21):(cNUMBER Xn0)
% 210.02/210.38 Found (x3 x21) as proof of (cNUMBER Xn0)
% 210.02/210.38 Found (x3 x21) as proof of (cNUMBER Xn0)
% 210.02/210.38 Found x30:=(x3 x22):(cNUMBER Xn0)
% 210.02/210.38 Instantiate: Xn0:=Xn:fofType
% 210.02/210.38 Found (x3 x22) as proof of (cNUMBER Xn)
% 210.02/210.38 Found (x3 x22) as proof of (cNUMBER Xn)
% 210.02/210.38 Found x30:=(x3 x20):(cNUMBER Xn0)
% 210.02/210.38 Found (x3 x20) as proof of (cNUMBER Xn)
% 210.02/210.38 Found (x3 x20) as proof of (cNUMBER Xn)
% 210.02/210.38 Found (x3 x20) as proof of (cNUMBER Xn)
% 210.02/210.38 Found x30:=(x3 x21):(cNUMBER Xn0)
% 210.02/210.38 Found (x3 x21) as proof of (cNUMBER Xn0)
% 210.02/210.38 Found (x3 x21) as proof of (cNUMBER Xn0)
% 210.02/210.38 Found x30:=(x3 x22):(cNUMBER Xn0)
% 210.02/210.38 Instantiate: Xn0:=Xn:fofType
% 210.02/210.38 Found (x3 x22) as proof of (cNUMBER Xn)
% 210.02/210.38 Found (x3 x22) as proof of (cNUMBER Xn)
% 210.02/210.38 Found x30:=(x3 x20):(cNUMBER Xn0)
% 210.02/210.38 Found (x3 x20) as proof of (cNUMBER Xn)
% 210.02/210.38 Found (x3 x20) as proof of (cNUMBER Xn)
% 210.02/210.38 Found (x3 x20) as proof of (cNUMBER Xn)
% 210.02/210.38 Found x70:=(x7 x60):(cNUMBER Xn0)
% 210.02/210.38 Found (x7 x60) as proof of (cNUMBER Xn0)
% 210.02/210.38 Found (x7 x60) as proof of (cNUMBER Xn0)
% 210.02/210.38 Found x70:=(x7 x61):(cNUMBER Xn0)
% 210.02/210.38 Instantiate: Xn0:=Xn:fofType
% 210.02/210.38 Found (x7 x61) as proof of (cNUMBER Xn)
% 210.02/210.38 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x61)) as proof of (cNUMBER Xn)
% 210.02/210.38 Found (fun (x12:(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))
% 210.02/210.38 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 210.02/210.38 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 210.02/210.38 Found (x3 x20) as proof of (cNUMBER Xn)
% 210.02/210.38 Found (x3 x20) as proof of (cNUMBER Xn)
% 210.02/210.38 Found (x3 x20) as proof of (cNUMBER Xn)
% 210.02/210.38 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 210.02/210.38 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 210.02/210.38 Found (x3 x20) as proof of (cNUMBER Xn)
% 210.02/210.38 Found (x3 x20) as proof of (cNUMBER Xn)
% 210.02/210.38 Found (x3 x20) as proof of (cNUMBER Xn)
% 210.02/210.38 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 210.02/210.38 Instantiate: Xn00:=Xn:fofType
% 210.02/210.38 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 210.02/210.38 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 210.02/210.38 Instantiate: Xn00:=Xn:fofType
% 210.02/210.38 Found (fun (x9:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x60) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 210.02/210.38 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x9:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x60) as proof of ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 213.67/214.04 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x9:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x60) as proof of (((and ((and (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))))
% 213.67/214.04 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 213.67/214.04 Instantiate: Xn0:=Xn:fofType
% 213.67/214.04 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x40) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 213.67/214.04 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x40) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->((or (cEVEN Xn00)) (cODD Xn00)))
% 213.67/214.04 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 213.67/214.04 Instantiate: Xn00:=Xn:fofType
% 213.67/214.04 Found (fun (x9:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x60) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 213.67/214.04 Found (fun (x9:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x60) as proof of ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 213.67/214.04 Found x70:=(x7 x60):(cNUMBER Xn0)
% 213.67/214.04 Found (x7 x60) as proof of (cNUMBER Xn)
% 213.67/214.04 Found (x7 x60) as proof of (cNUMBER Xn)
% 213.67/214.04 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x7 x60)) as proof of (cNUMBER Xn)
% 213.67/214.04 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))
% 213.67/214.04 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)))
% 213.67/214.04 Found x60:=(x6 x70):((or (cEVEN Xn0)) (cODD Xn0))
% 213.67/214.04 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 213.67/214.04 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 213.67/214.04 Found x70:=(x7 x61):(cNUMBER Xn0)
% 213.67/214.04 Found (x7 x61) as proof of (cNUMBER Xn0)
% 213.67/214.04 Found (x7 x61) as proof of (cNUMBER Xn0)
% 213.67/214.04 Found x70:=(x7 x62):(cNUMBER Xn0)
% 213.67/214.04 Instantiate: Xn0:=Xn:fofType
% 213.67/214.04 Found (x7 x62) as proof of (cNUMBER Xn)
% 213.67/214.04 Found (x7 x62) as proof of (cNUMBER Xn)
% 213.67/214.04 Found x70:=(x7 x62):(cNUMBER Xn0)
% 213.67/214.04 Found (x7 x62) as proof of (cNUMBER Xn)
% 213.67/214.04 Found (x7 x62) as proof of (cNUMBER Xn)
% 213.67/214.04 Found (x7 x62) as proof of (cNUMBER Xn)
% 213.67/214.04 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 213.67/214.04 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 213.67/214.04 Found (x3 x20) as proof of (cNUMBER Xn00)
% 213.67/214.04 Found (x3 x20) as proof of (cNUMBER Xn00)
% 213.67/214.04 Found (x3 x20) as proof of (cNUMBER Xn00)
% 213.67/214.04 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 213.67/214.04 Found x40 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 213.67/214.04 Found (x5 x40) as proof of (cNUMBER Xn0)
% 213.67/214.04 Found (x5 x40) as proof of (cNUMBER Xn0)
% 213.67/214.04 Found (x5 x40) as proof of (cNUMBER Xn0)
% 213.67/214.04 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 213.67/214.04 Found x40 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 213.67/214.04 Found (x5 x40) as proof of (cNUMBER Xn0)
% 213.67/214.04 Found (x5 x40) as proof of (cNUMBER Xn0)
% 213.67/214.04 Found (x5 x40) as proof of (cNUMBER Xn0)
% 213.67/214.04 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 213.67/214.04 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 213.67/214.04 Found (x3 x20) as proof of (cNUMBER Xn00)
% 213.67/214.04 Found (x3 x20) as proof of (cNUMBER Xn00)
% 213.67/214.04 Found (x3 x20) as proof of (cNUMBER Xn00)
% 213.67/214.04 Found x80:((or (cEVEN Xn00)) (cODD Xn00))
% 213.67/214.04 Instantiate: Xn00:=Xn:fofType
% 213.67/214.04 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x80) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 213.67/214.04 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)))
% 213.67/214.04 Found x30:=(x3 x40):(cNUMBER Xn0)
% 213.67/214.04 Found (x3 x40) as proof of (cNUMBER Xn00)
% 213.67/214.04 Found (x3 x40) as proof of (cNUMBER Xn00)
% 213.67/214.04 Found (x3 x40) as proof of (cNUMBER Xn00)
% 213.67/214.04 Found x22:((or (cEVEN Xn0)) (cODD Xn0))
% 213.67/214.04 Found x22 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 213.67/214.04 Found (x3 x22) as proof of (cNUMBER Xn)
% 213.67/214.04 Found (x3 x22) as proof of (cNUMBER Xn)
% 213.67/214.04 Found (x3 x22) as proof of (cNUMBER Xn)
% 213.67/214.04 Found x60:((or (cEVEN Xn0)) (cODD Xn0))
% 213.82/214.17 Instantiate: Xn0:=Xn:fofType
% 213.82/214.17 Found x60 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 213.82/214.17 Found (x9 x60) as proof of (cNUMBER Xn)
% 213.82/214.17 Found (x9 x60) as proof of (cNUMBER Xn)
% 213.82/214.17 Found (x9 x60) as proof of (cNUMBER Xn)
% 213.82/214.17 Found x60:((or (cEVEN Xn0)) (cODD Xn0))
% 213.82/214.17 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 213.82/214.17 Found (x7 x60) as proof of (cNUMBER Xn)
% 213.82/214.17 Found (x7 x60) as proof of (cNUMBER Xn)
% 213.82/214.17 Found (x7 x60) as proof of (cNUMBER Xn)
% 213.82/214.17 Found x30:=(x3 x20):(cNUMBER Xn0)
% 213.82/214.17 Instantiate: Xn0:=Xn:fofType
% 213.82/214.17 Found (x3 x20) as proof of (cNUMBER Xn)
% 213.82/214.17 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 213.82/214.17 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(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))
% 213.82/214.17 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (((and ((and (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)))
% 213.82/214.17 Found (and_rect40 (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 213.82/214.17 Found ((and_rect4 (cNUMBER Xn)) (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 213.82/214.17 Found (((fun (P:Type) (x8:(((and ((and (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 (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 213.82/214.17 Found (((fun (P:Type) (x8:(((and ((and (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 (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 213.82/214.17 Found x50:=(x5 x40):(cNUMBER Xn00)
% 213.82/214.17 Instantiate: Xn00:=Xn:fofType
% 213.82/214.17 Found (x5 x40) as proof of (cNUMBER Xn)
% 213.82/214.17 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 213.82/214.17 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(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))
% 213.82/214.17 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (((and ((and (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)))
% 213.82/214.17 Found (and_rect40 (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 214.20/214.55 Found ((and_rect4 (cNUMBER Xn)) (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 214.20/214.55 Found (((fun (P:Type) (x8:(((and ((and (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 (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 214.20/214.55 Found (((fun (P:Type) (x8:(((and ((and (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 (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 214.20/214.55 Found x40:=(x4 x50):((or (cEVEN Xn00)) (cODD Xn00))
% 214.20/214.55 Instantiate: Xn00:=Xn:fofType
% 214.20/214.55 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 214.20/214.55 Found (fun (x9:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x4 x50)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 214.20/214.55 Found (fun (x9:(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)))
% 214.20/214.55 Found x80:((or (cEVEN Xn00)) (cODD Xn00))
% 214.20/214.55 Instantiate: Xn00:=Xn:fofType
% 214.20/214.55 Found x80 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 214.20/214.55 Found (x7 x80) as proof of (cNUMBER Xn)
% 214.20/214.55 Found (x7 x80) as proof of (cNUMBER Xn)
% 214.20/214.55 Found (x7 x80) as proof of (cNUMBER Xn)
% 214.20/214.55 Found x80:((or (cEVEN Xn00)) (cODD Xn00))
% 214.20/214.55 Found x80 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 214.20/214.55 Found (x9 x80) as proof of (cNUMBER Xn)
% 214.20/214.55 Found (x9 x80) as proof of (cNUMBER Xn)
% 214.20/214.55 Found (x9 x80) as proof of (cNUMBER Xn)
% 214.20/214.55 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 214.20/214.55 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 214.20/214.55 Found (x3 x20) as proof of (cNUMBER Xn)
% 214.20/214.55 Found (x3 x20) as proof of (cNUMBER Xn)
% 214.20/214.55 Found (x3 x20) as proof of (cNUMBER Xn)
% 214.20/214.55 Found x91:(cNUMBER Xn0)
% 214.20/214.55 Instantiate: Xn0:=Xn:fofType
% 214.20/214.55 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x91) as proof of (cNUMBER Xn)
% 214.20/214.55 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x91) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 214.20/214.55 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 214.20/214.55 Instantiate: Xn0:=Xn:fofType
% 214.20/214.55 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 214.20/214.55 Found (x5 x20) as proof of (cNUMBER Xn)
% 214.20/214.55 Found (x5 x20) as proof of (cNUMBER Xn)
% 214.20/214.55 Found (x5 x20) as proof of (cNUMBER Xn)
% 214.20/214.55 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 214.20/214.55 Instantiate: Xn0:=Xn:fofType
% 214.20/214.55 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 214.20/214.55 Found (x5 x20) as proof of (cNUMBER Xn)
% 214.20/214.55 Found (x5 x20) as proof of (cNUMBER Xn)
% 214.20/214.55 Found (x5 x20) as proof of (cNUMBER Xn)
% 214.20/214.55 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 214.20/214.55 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 214.20/214.55 Found (x3 x20) as proof of (cNUMBER Xn)
% 214.20/214.55 Found (x3 x20) as proof of (cNUMBER Xn)
% 214.20/214.55 Found (x3 x20) as proof of (cNUMBER Xn)
% 214.20/214.55 Found x50:=(x5 x40):(cNUMBER Xn0)
% 214.20/214.55 Found (x5 x40) as proof of (cNUMBER Xn)
% 214.20/214.55 Found (x5 x40) as proof of (cNUMBER Xn)
% 214.20/214.55 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 214.20/214.55 Found (fun (x9:(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))
% 215.19/215.54 Found x50:=(x5 x41):(cNUMBER Xn0)
% 215.19/215.54 Found (x5 x41) as proof of (cNUMBER Xn)
% 215.19/215.54 Found (x5 x41) as proof of (cNUMBER Xn)
% 215.19/215.54 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x41)) as proof of (cNUMBER Xn)
% 215.19/215.54 Found (fun (x12:(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))
% 215.19/215.54 Found x70:=(x7 x60):(cNUMBER Xn00)
% 215.19/215.54 Found (x7 x60) as proof of (cNUMBER Xn)
% 215.19/215.54 Found (x7 x60) as proof of (cNUMBER Xn)
% 215.19/215.54 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x7 x60)) as proof of (cNUMBER Xn)
% 215.19/215.54 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x7 x60)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 215.19/215.54 Found x62:((or (cEVEN Xn0)) (cODD Xn0))
% 215.19/215.54 Found x62 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 215.19/215.54 Found (x7 x62) as proof of (cNUMBER Xn)
% 215.19/215.54 Found (x7 x62) as proof of (cNUMBER Xn)
% 215.19/215.54 Found (x7 x62) as proof of (cNUMBER Xn)
% 215.19/215.55 Found x50:=(x5 x41):(cNUMBER Xn0)
% 215.19/215.55 Found (x5 x41) as proof of (cNUMBER Xn)
% 215.19/215.55 Found (x5 x41) as proof of (cNUMBER Xn)
% 215.19/215.55 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x41)) as proof of (cNUMBER Xn)
% 215.19/215.55 Found (fun (x11:(cEVEN c0)) (x12:(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))
% 215.19/215.55 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x41)) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 215.19/215.55 Found x30:(cNUMBER Xn0)
% 215.19/215.55 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30) as proof of (cNUMBER Xn0)
% 215.19/215.55 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 Xn0))
% 215.19/215.55 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 Xn0)))
% 215.19/215.55 Found x30:(cNUMBER Xn0)
% 215.19/215.55 Found x30 as proof of (cNUMBER Xn0)
% 215.19/215.55 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 215.19/215.55 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 215.19/215.55 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 215.19/215.55 Found x50:=(x5 x40):(cNUMBER Xn00)
% 215.19/215.55 Found (x5 x40) as proof of (cNUMBER Xn)
% 215.19/215.55 Found (x5 x40) as proof of (cNUMBER Xn)
% 215.19/215.55 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 215.19/215.55 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 215.19/215.55 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 215.19/215.55 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x20) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 215.19/215.55 Found (fun (x4:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x20) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->((or (cEVEN Xn0)) (cODD Xn0)))
% 215.19/215.55 Found (fun (x4:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x20) as proof of (((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))->((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->((or (cEVEN Xn0)) (cODD Xn0))))
% 215.19/215.55 Found x60:=(x6 x70):((or (cEVEN Xn0)) (cODD Xn0))
% 215.19/215.55 Instantiate: Xn0:=Xn:fofType
% 215.19/215.55 Found (x6 x70) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 215.19/215.55 Found (x6 x70) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 215.19/215.55 Found x80:=(x8 x90):((or (cEVEN Xn00)) (cODD Xn00))
% 215.19/215.55 Instantiate: Xn00:=Xn:fofType
% 215.19/215.55 Found (x8 x90) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 215.19/215.55 Found (x8 x90) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 215.19/215.55 Found x30:=(x3 x20):(cNUMBER Xn0)
% 215.19/215.55 Found (x3 x20) as proof of (cNUMBER Xn)
% 215.19/215.55 Found (x3 x20) as proof of (cNUMBER Xn)
% 215.19/215.55 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 216.81/217.18 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 216.81/217.18 Found x50:(cNUMBER Xn00)
% 216.81/217.18 Found x50 as proof of (cNUMBER Xn00)
% 216.81/217.18 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 216.81/217.18 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 216.81/217.18 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 216.81/217.18 Found x50:(cNUMBER Xn00)
% 216.81/217.18 Instantiate: Xn00:=Xn:fofType
% 216.81/217.18 Found x50 as proof of (cNUMBER Xn)
% 216.81/217.18 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 216.81/217.18 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 216.81/217.18 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 216.81/217.18 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 216.81/217.18 Found x40:=(x4 x50):((or (cEVEN Xn00)) (cODD Xn00))
% 216.81/217.18 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 216.81/217.18 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 216.81/217.18 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 216.81/217.18 Found x30:(cNUMBER Xn0)
% 216.81/217.18 Instantiate: Xn0:=Xn:fofType
% 216.81/217.18 Found x30 as proof of (cNUMBER Xn)
% 216.81/217.18 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 216.81/217.18 Instantiate: Xn0:=Xn:fofType
% 216.81/217.18 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 216.81/217.18 Found (x7 x20) as proof of (cNUMBER Xn)
% 216.81/217.18 Found (x7 x20) as proof of (cNUMBER Xn)
% 216.81/217.18 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x7 x20)) as proof of (cNUMBER Xn)
% 216.81/217.18 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x7 x20)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 216.81/217.18 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 216.81/217.18 Instantiate: Xn00:=Xn:fofType
% 216.81/217.18 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 216.81/217.18 Found (x3 x60) as proof of (cNUMBER Xn)
% 216.81/217.18 Found (x3 x60) as proof of (cNUMBER Xn)
% 216.81/217.18 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x60)) as proof of (cNUMBER Xn)
% 216.81/217.18 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x60)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 216.81/217.18 Found x40:=(x4 x30):(cNUMBER Xn00)
% 216.81/217.18 Instantiate: Xn0:=Xn00:fofType
% 216.81/217.18 Found (x4 x30) as proof of (cNUMBER Xn0)
% 216.81/217.18 Found (x4 x30) as proof of (cNUMBER Xn0)
% 216.81/217.18 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 216.81/217.18 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 216.81/217.18 Found (x3 x20) as proof of (cNUMBER Xn)
% 216.81/217.18 Found (x3 x20) as proof of (cNUMBER Xn)
% 216.81/217.18 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 216.81/217.18 Found (fun (x9:(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))
% 216.81/217.18 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 216.81/217.18 Found x60 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 216.81/217.18 Found (x7 x60) as proof of (cNUMBER Xn)
% 216.81/217.18 Found (x7 x60) as proof of (cNUMBER Xn)
% 216.81/217.18 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x7 x60)) as proof of (cNUMBER Xn)
% 216.81/217.18 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x7 x60)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 216.81/217.18 Found x40:=(x4 x50):((or (cEVEN Xn00)) (cODD Xn00))
% 216.81/217.18 Instantiate: Xn00:=Xn:fofType
% 216.81/217.18 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 216.81/217.18 Found (fun (x9:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x4 x50)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 216.81/217.18 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x9:(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)))
% 216.81/217.18 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x9:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x4 x50)) as proof of (((and ((and (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))))
% 219.92/220.28 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 219.92/220.28 Instantiate: Xn0:=Xn:fofType
% 219.92/220.28 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 219.92/220.28 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x2 x30)) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 219.92/220.28 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(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)))
% 219.92/220.28 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x2 x30)) as proof of (((and ((and (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))))
% 219.92/220.28 Found x60:=(x6 x70):((or (cEVEN Xn00)) (cODD Xn00))
% 219.92/220.28 Instantiate: Xn00:=Xn:fofType
% 219.92/220.28 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 219.92/220.28 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 219.92/220.28 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 219.92/220.28 Instantiate: Xn0:=Xn:fofType
% 219.92/220.28 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 219.92/220.28 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 219.92/220.28 Found x80:=(x8 x90):((or (cEVEN Xn00)) (cODD Xn00))
% 219.92/220.28 Instantiate: Xn00:=Xn:fofType
% 219.92/220.28 Found (x8 x90) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 219.92/220.28 Found (x8 x90) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 219.92/220.28 Found x30:=(x3 x20):(cNUMBER Xn0)
% 219.92/220.28 Instantiate: Xn0:=Xn:fofType
% 219.92/220.28 Found (x3 x20) as proof of (cNUMBER Xn)
% 219.92/220.28 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 219.92/220.28 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))
% 219.92/220.28 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)))
% 219.92/220.28 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)
% 219.92/220.28 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)
% 219.92/220.28 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)
% 219.92/220.28 Found x41:((or (cEVEN Xn0)) (cODD Xn0))
% 219.92/220.28 Found x41 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 219.92/220.28 Found (x5 x41) as proof of (cNUMBER Xn)
% 219.92/220.28 Found (x5 x41) as proof of (cNUMBER Xn)
% 219.92/220.28 Found (x5 x41) as proof of (cNUMBER Xn)
% 219.92/220.28 Found x50:=(x5 x40):(cNUMBER Xn0)
% 219.92/220.28 Found (x5 x40) as proof of (cNUMBER Xn)
% 219.92/220.28 Found (x5 x40) as proof of (cNUMBER Xn)
% 219.92/220.28 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 219.92/220.28 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))
% 219.92/220.28 Found (fun (x8:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x9:(((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)))
% 219.92/220.28 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 219.92/220.28 Instantiate: Xn0:=Xn:fofType
% 219.92/220.28 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 221.50/221.86 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x2 x30)) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 221.50/221.86 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(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)))
% 221.50/221.86 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x2 x30)) as proof of (((and ((and (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))))
% 221.50/221.86 Found x40:=(x4 x50):((or (cEVEN Xn00)) (cODD Xn00))
% 221.50/221.86 Instantiate: Xn00:=Xn:fofType
% 221.50/221.86 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 221.50/221.86 Found (fun (x9:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x4 x50)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 221.50/221.86 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x9:(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)))
% 221.50/221.86 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x9:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x4 x50)) as proof of (((and ((and (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))))
% 221.50/221.86 Found x70:=(x7 x60):(cNUMBER Xn0)
% 221.50/221.86 Found (x7 x60) as proof of (cNUMBER Xn0)
% 221.50/221.86 Found (x7 x60) as proof of (cNUMBER Xn0)
% 221.50/221.86 Found x70:=(x7 x61):(cNUMBER Xn0)
% 221.50/221.86 Instantiate: Xn0:=Xn:fofType
% 221.50/221.86 Found (x7 x61) as proof of (cNUMBER Xn)
% 221.50/221.86 Found (x7 x61) as proof of (cNUMBER Xn)
% 221.50/221.86 Found x70:=(x7 x61):(cNUMBER Xn0)
% 221.50/221.86 Found (x7 x61) as proof of (cNUMBER Xn)
% 221.50/221.86 Found (x7 x61) as proof of (cNUMBER Xn)
% 221.50/221.86 Found (x7 x61) as proof of (cNUMBER Xn)
% 221.50/221.86 Found x50:=(x5 x41):(cNUMBER Xn0)
% 221.50/221.86 Found (x5 x41) as proof of (cNUMBER Xn0)
% 221.50/221.86 Found (x5 x41) as proof of (cNUMBER Xn0)
% 221.50/221.86 Found x50:=(x5 x42):(cNUMBER Xn0)
% 221.50/221.86 Instantiate: Xn0:=Xn:fofType
% 221.50/221.86 Found (x5 x42) as proof of (cNUMBER Xn)
% 221.50/221.86 Found (x5 x42) as proof of (cNUMBER Xn)
% 221.50/221.86 Found x50:=(x5 x41):(cNUMBER Xn0)
% 221.50/221.86 Found (x5 x41) as proof of (cNUMBER Xn)
% 221.50/221.86 Found (x5 x41) as proof of (cNUMBER Xn)
% 221.50/221.86 Found (x5 x41) as proof of (cNUMBER Xn)
% 221.50/221.86 Found x21:((or (cEVEN Xn0)) (cODD Xn0))
% 221.50/221.86 Found x21 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 221.50/221.86 Found (x3 x21) as proof of (cNUMBER Xn)
% 221.50/221.86 Found (x3 x21) as proof of (cNUMBER Xn)
% 221.50/221.86 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x21)) as proof of (cNUMBER Xn)
% 221.50/221.86 Found (fun (x12:(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))
% 221.50/221.86 Found x21:((or (cEVEN Xn0)) (cODD Xn0))
% 221.50/221.86 Found x21 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 221.50/221.86 Found (x3 x21) as proof of (cNUMBER Xn)
% 221.50/221.86 Found (x3 x21) as proof of (cNUMBER Xn)
% 221.50/221.86 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x21)) as proof of (cNUMBER Xn)
% 221.50/221.86 Found (fun (x11:(cEVEN c0)) (x12:(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))
% 221.50/221.86 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x21)) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 221.50/221.86 Found x50:=(x5 x41):(cNUMBER Xn0)
% 221.50/221.86 Found (x5 x41) as proof of (cNUMBER Xn0)
% 221.50/221.86 Found (x5 x41) as proof of (cNUMBER Xn0)
% 221.50/221.86 Found x50:=(x5 x42):(cNUMBER Xn0)
% 221.50/221.86 Instantiate: Xn0:=Xn:fofType
% 221.50/221.86 Found (x5 x42) as proof of (cNUMBER Xn)
% 221.50/221.86 Found (x5 x42) as proof of (cNUMBER Xn)
% 221.50/221.86 Found x50:=(x5 x41):(cNUMBER Xn0)
% 222.44/222.85 Found (x5 x41) as proof of (cNUMBER Xn)
% 222.44/222.85 Found (x5 x41) as proof of (cNUMBER Xn)
% 222.44/222.85 Found (x5 x41) as proof of (cNUMBER Xn)
% 222.44/222.85 Found x30:=(x3 x22):(cNUMBER Xn0)
% 222.44/222.85 Found (x3 x22) as proof of (cNUMBER Xn0)
% 222.44/222.85 Found (x3 x22) as proof of (cNUMBER Xn0)
% 222.44/222.85 Found x30:=(x3 x23):(cNUMBER Xn0)
% 222.44/222.85 Instantiate: Xn0:=Xn:fofType
% 222.44/222.85 Found (x3 x23) as proof of (cNUMBER Xn)
% 222.44/222.85 Found (x3 x23) as proof of (cNUMBER Xn)
% 222.44/222.85 Found x30:=(x3 x22):(cNUMBER Xn0)
% 222.44/222.85 Found (x3 x22) as proof of (cNUMBER Xn)
% 222.44/222.85 Found (x3 x22) as proof of (cNUMBER Xn)
% 222.44/222.85 Found (x3 x22) as proof of (cNUMBER Xn)
% 222.44/222.85 Found x80:=(x8 x90):((or (cEVEN Xn00)) (cODD Xn00))
% 222.44/222.85 Instantiate: Xn00:=Xn:fofType
% 222.44/222.85 Found (x8 x90) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 222.44/222.85 Found (x8 x90) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 222.44/222.85 Found x90:=(x9 x80):(cNUMBER Xn0)
% 222.44/222.85 Found (x9 x80) as proof of (cNUMBER Xn0)
% 222.44/222.85 Found (x9 x80) as proof of (cNUMBER Xn0)
% 222.44/222.85 Found x90:=(x9 x81):(cNUMBER Xn0)
% 222.44/222.85 Instantiate: Xn0:=Xn:fofType
% 222.44/222.85 Found (x9 x81) as proof of (cNUMBER Xn)
% 222.44/222.85 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x9 x81)) as proof of (cNUMBER Xn)
% 222.44/222.85 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x9 x81)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 222.44/222.85 Found x50:=(x5 x41):(cNUMBER Xn0)
% 222.44/222.85 Found (x5 x41) as proof of (cNUMBER Xn)
% 222.44/222.85 Found (x5 x41) as proof of (cNUMBER Xn)
% 222.44/222.85 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x41)) as proof of (cNUMBER Xn)
% 222.44/222.85 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x41)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 222.44/222.85 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 222.44/222.85 Instantiate: Xn0:=Xn:fofType
% 222.44/222.85 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 222.44/222.85 Found (x9 x20) as proof of (cNUMBER Xn)
% 222.44/222.85 Found (x9 x20) as proof of (cNUMBER Xn)
% 222.44/222.85 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x9 x20)) as proof of (cNUMBER Xn)
% 222.44/222.85 Found (fun (x8:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x9 x20)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 222.44/222.85 Found (fun (x8:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x9 x20)) as proof of (((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))->((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn)))
% 222.44/222.85 Found x50:=(x5 x41):(cNUMBER Xn0)
% 222.44/222.85 Found (x5 x41) as proof of (cNUMBER Xn)
% 222.44/222.85 Found (x5 x41) as proof of (cNUMBER Xn)
% 222.44/222.85 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x41)) as proof of (cNUMBER Xn)
% 222.44/222.85 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x41)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 222.44/222.85 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 222.44/222.85 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 222.44/222.85 Found (x3 x20) as proof of (cNUMBER Xn)
% 222.44/222.85 Found (x3 x20) as proof of (cNUMBER Xn)
% 222.44/222.85 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 222.44/222.85 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))
% 222.44/222.85 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)))
% 222.44/222.85 Found x21:((or (cEVEN Xn0)) (cODD Xn0))
% 222.44/222.85 Found x21 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 222.44/222.85 Found (x3 x21) as proof of (cNUMBER Xn)
% 222.44/222.85 Found (x3 x21) as proof of (cNUMBER Xn)
% 222.44/222.85 Found (x3 x21) as proof of (cNUMBER Xn)
% 222.44/222.85 Found x50:=(x5 x41):(cNUMBER Xn0)
% 222.44/222.85 Found (x5 x41) as proof of (cNUMBER Xn)
% 222.44/222.85 Found (x5 x41) as proof of (cNUMBER Xn)
% 222.44/222.85 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x41)) as proof of (cNUMBER Xn)
% 222.44/222.85 Found (fun (x6:((and ((and (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 x41)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 223.70/224.10 Found (fun (x6:((and ((and (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 x41)) as proof of (((and ((and (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)))
% 223.70/224.10 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 223.70/224.10 Instantiate: Xn00:=Xn0:fofType
% 223.70/224.10 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 223.70/224.10 Found x80:((or (cEVEN Xn00)) (cODD Xn00))
% 223.70/224.10 Instantiate: Xn00:=Xn:fofType
% 223.70/224.10 Found x80 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 223.70/224.10 Found (x5 x80) as proof of (cNUMBER Xn)
% 223.70/224.10 Found (x5 x80) as proof of (cNUMBER Xn)
% 223.70/224.10 Found (x5 x80) as proof of (cNUMBER Xn)
% 223.70/224.10 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 223.70/224.10 Instantiate: Xn0:=Xn:fofType
% 223.70/224.10 Found x40 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 223.70/224.10 Found (x9 x40) as proof of (cNUMBER Xn)
% 223.70/224.10 Found (x9 x40) as proof of (cNUMBER Xn)
% 223.70/224.10 Found (x9 x40) as proof of (cNUMBER Xn)
% 223.70/224.10 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 223.70/224.10 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 223.70/224.10 Found (x5 x40) as proof of (cNUMBER Xn)
% 223.70/224.10 Found (x5 x40) as proof of (cNUMBER Xn)
% 223.70/224.10 Found (x5 x40) as proof of (cNUMBER Xn)
% 223.70/224.10 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 223.70/224.10 Instantiate: Xn0:=Xn00:fofType
% 223.70/224.10 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 223.70/224.10 Found x80:((or (cEVEN Xn00)) (cODD Xn00))
% 223.70/224.10 Found x80 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 223.70/224.10 Found (x9 x80) as proof of (cNUMBER Xn)
% 223.70/224.10 Found (x9 x80) as proof of (cNUMBER Xn)
% 223.70/224.10 Found (x9 x80) as proof of (cNUMBER Xn)
% 223.70/224.10 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 223.70/224.10 Instantiate: Xn00:=Xn:fofType
% 223.70/224.10 Found (fun (x9:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x60) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 223.70/224.10 Found (fun (x9:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x60) as proof of ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 223.70/224.10 Found x50:=(x5 x40):(cNUMBER Xn0)
% 223.70/224.10 Found (x5 x40) as proof of (cNUMBER Xn0)
% 223.70/224.10 Found (x5 x40) as proof of (cNUMBER Xn0)
% 223.70/224.10 Found x50:=(x5 x41):(cNUMBER Xn0)
% 223.70/224.10 Instantiate: Xn0:=Xn:fofType
% 223.70/224.10 Found (x5 x41) as proof of (cNUMBER Xn)
% 223.70/224.10 Found (x5 x41) as proof of (cNUMBER Xn)
% 223.70/224.10 Found x50:=(x5 x41):(cNUMBER Xn0)
% 223.70/224.10 Found (x5 x41) as proof of (cNUMBER Xn)
% 223.70/224.10 Found (x5 x41) as proof of (cNUMBER Xn)
% 223.70/224.10 Found (x5 x41) as proof of (cNUMBER Xn)
% 223.70/224.10 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 223.70/224.10 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 223.70/224.10 Found (x3 x20) as proof of (cNUMBER Xn)
% 223.70/224.10 Found (x3 x20) as proof of (cNUMBER Xn)
% 223.70/224.10 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 223.70/224.10 Found (fun (x6:((and ((and (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))
% 223.70/224.10 Found (fun (x6:((and ((and (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 (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)))
% 223.70/224.10 Found x50:(cNUMBER Xn00)
% 223.70/224.10 Instantiate: Xn0:=Xn00:fofType
% 223.70/224.10 Found x50 as proof of (cNUMBER Xn0)
% 223.70/224.10 Found x50:(cNUMBER Xn00)
% 223.70/224.10 Instantiate: Xn0:=Xn00:fofType
% 223.70/224.10 Found x50 as proof of (cNUMBER Xn0)
% 223.70/224.10 Found x30:(cNUMBER Xn0)
% 223.70/224.10 Instantiate: Xn00:=Xn0:fofType
% 223.70/224.10 Found x30 as proof of (cNUMBER Xn00)
% 223.70/224.10 Found x30:(cNUMBER Xn0)
% 223.70/224.10 Instantiate: Xn00:=Xn0:fofType
% 223.70/224.10 Found x30 as proof of (cNUMBER Xn00)
% 223.70/224.10 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 223.70/224.10 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 223.70/224.10 Found (x3 x20) as proof of (cNUMBER Xn)
% 223.70/224.10 Found (x3 x20) as proof of (cNUMBER Xn)
% 223.70/224.10 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 225.53/225.87 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))
% 225.53/225.87 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 225.53/225.87 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 225.53/225.87 Found (x3 x20) as proof of (cNUMBER Xn)
% 225.53/225.87 Found (x3 x20) as proof of (cNUMBER Xn)
% 225.53/225.87 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 225.53/225.87 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))
% 225.53/225.87 Found x11:(cEVEN c0)
% 225.53/225.87 Instantiate: Xn0:=c0:fofType
% 225.53/225.87 Found x11 as proof of (cEVEN Xn0)
% 225.53/225.87 Found (or_intror00 x11) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 225.53/225.87 Found ((or_intror0 (cEVEN Xn0)) x11) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 225.53/225.87 Found (((or_intror (cODD Xn0)) (cEVEN Xn0)) x11) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 225.53/225.87 Found (((or_intror (cODD Xn0)) (cEVEN Xn0)) x11) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 225.53/225.87 Found (or_comm_i00 (((or_intror (cODD Xn0)) (cEVEN Xn0)) x11)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 225.53/225.87 Found ((or_comm_i0 (cEVEN Xn0)) (((or_intror (cODD Xn0)) (cEVEN Xn0)) x11)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 225.53/225.87 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((or_intror (cODD Xn0)) (cEVEN Xn0)) x11)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 225.53/225.87 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((or_intror (cODD Xn0)) (cEVEN Xn0)) x11)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 225.53/225.87 Found x50:(cNUMBER Xn0)
% 225.53/225.87 Instantiate: Xn00:=Xn0:fofType
% 225.53/225.87 Found x50 as proof of (cNUMBER Xn00)
% 225.53/225.87 Found x7:(cODD (cS c0))
% 225.53/225.87 Instantiate: Xn0:=(cS c0):fofType
% 225.53/225.87 Found x7 as proof of (cODD Xn0)
% 225.53/225.87 Found (or_introl00 x7) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 225.53/225.87 Found ((or_introl0 (cEVEN Xn0)) x7) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 225.53/225.87 Found (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 225.53/225.87 Found (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 225.53/225.87 Found (or_comm_i00 (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 225.53/225.87 Found ((or_comm_i0 (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 225.53/225.87 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 225.53/225.87 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 225.53/225.87 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 225.53/225.87 Instantiate: Xn0:=Xn00:fofType
% 225.53/225.87 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 225.53/225.87 Found x80:=(x8 x90):((or (cEVEN Xn0)) (cODD Xn0))
% 225.53/225.87 Found (x8 x90) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 225.53/225.87 Found (x8 x90) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 225.53/225.87 Found x41:((or (cEVEN Xn0)) (cODD Xn0))
% 225.53/225.87 Found x41 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 225.53/225.87 Found (x5 x41) as proof of (cNUMBER Xn)
% 225.53/225.87 Found (x5 x41) as proof of (cNUMBER Xn)
% 225.53/225.87 Found (x5 x41) as proof of (cNUMBER Xn)
% 225.53/225.87 Found x80:=(x8 x90):((or (cEVEN Xn00)) (cODD Xn00))
% 225.53/225.87 Instantiate: Xn00:=Xn:fofType
% 225.53/225.87 Found (x8 x90) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 225.53/225.87 Found (x8 x90) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 225.53/225.87 Found x40:=(x4 x50):((or (cEVEN Xn0)) (cODD Xn0))
% 225.53/225.87 Instantiate: Xn0:=Xn:fofType
% 225.53/225.87 Found (x4 x50) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 225.53/225.87 Found (x4 x50) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 225.53/225.87 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 225.53/225.87 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 225.53/225.87 Found (x3 x20) as proof of (cNUMBER Xn)
% 225.53/225.87 Found (x3 x20) as proof of (cNUMBER Xn)
% 225.53/225.87 Found (x3 x20) as proof of (cNUMBER Xn)
% 225.53/225.87 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 225.53/225.87 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 225.53/225.87 Found (x3 x20) as proof of (cNUMBER Xn)
% 225.53/225.87 Found (x3 x20) as proof of (cNUMBER Xn)
% 225.53/225.87 Found (x3 x20) as proof of (cNUMBER Xn)
% 225.53/225.87 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 225.53/225.87 Instantiate: Xn0:=Xn00:fofType
% 225.53/225.87 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 225.53/225.87 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 225.53/225.87 Instantiate: Xn00:=Xn0:fofType
% 226.95/227.31 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 226.95/227.31 Found x50:(cNUMBER Xn0)
% 226.95/227.31 Instantiate: Xn00:=Xn0:fofType
% 226.95/227.31 Found x50 as proof of (cNUMBER Xn00)
% 226.95/227.31 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 226.95/227.31 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 226.95/227.31 Found (x3 x20) as proof of (cNUMBER Xn)
% 226.95/227.31 Found (x3 x20) as proof of (cNUMBER Xn)
% 226.95/227.31 Found (x3 x20) as proof of (cNUMBER Xn)
% 226.95/227.31 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 226.95/227.31 Instantiate: Xn0:=Xn:fofType
% 226.95/227.31 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x40) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 226.95/227.31 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x40) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->((or (cEVEN Xn00)) (cODD Xn00)))
% 226.95/227.31 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x40) as proof of (((and ((and (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))))
% 226.95/227.31 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 226.95/227.31 Instantiate: Xn00:=Xn:fofType
% 226.95/227.31 Found (fun (x9:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x60) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 226.95/227.31 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x9:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x60) as proof of ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 226.95/227.31 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x9:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x60) as proof of (((and ((and (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))))
% 226.95/227.31 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 226.95/227.31 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 226.95/227.31 Found (x3 x20) as proof of (cNUMBER Xn00)
% 226.95/227.31 Found (x3 x20) as proof of (cNUMBER Xn00)
% 226.95/227.31 Found (x3 x20) as proof of (cNUMBER Xn00)
% 226.95/227.31 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 226.95/227.31 Found x40 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 226.95/227.31 Found (x5 x40) as proof of (cNUMBER Xn0)
% 226.95/227.31 Found (x5 x40) as proof of (cNUMBER Xn0)
% 226.95/227.31 Found (x5 x40) as proof of (cNUMBER Xn0)
% 226.95/227.31 Found x60:((or (cEVEN Xn0)) (cODD Xn0))
% 226.95/227.31 Instantiate: Xn0:=Xn:fofType
% 226.95/227.31 Found x60 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 226.95/227.31 Found (x9 x60) as proof of (cNUMBER Xn)
% 226.95/227.31 Found (x9 x60) as proof of (cNUMBER Xn)
% 226.95/227.31 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x9 x60)) as proof of (cNUMBER Xn)
% 226.95/227.31 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x9 x60)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 226.95/227.31 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 226.95/227.31 Instantiate: Xn0:=Xn00:fofType
% 226.95/227.31 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 226.95/227.31 Found x60:((or (cEVEN Xn0)) (cODD Xn0))
% 226.95/227.31 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 226.95/227.31 Found (x7 x60) as proof of (cNUMBER Xn)
% 226.95/227.31 Found (x7 x60) as proof of (cNUMBER Xn)
% 226.95/227.31 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x7 x60)) as proof of (cNUMBER Xn)
% 226.95/227.31 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x7 x60)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 226.95/227.31 Found x50:=(x5 x40):(cNUMBER Xn00)
% 226.95/227.31 Instantiate: Xn00:=Xn:fofType
% 226.95/227.31 Found (x5 x40) as proof of (cNUMBER Xn)
% 226.95/227.31 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 226.95/227.31 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(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))
% 227.29/227.65 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (((and ((and (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)))
% 227.29/227.65 Found (and_rect40 (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 227.29/227.65 Found ((and_rect4 (cNUMBER Xn)) (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 227.29/227.65 Found (((fun (P:Type) (x8:(((and ((and (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 (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 227.29/227.65 Found (fun (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (((fun (P:Type) (x8:(((and ((and (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 (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)))) as proof of (cNUMBER Xn)
% 227.29/227.65 Found (fun (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (((fun (P:Type) (x8:(((and ((and (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 (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)))) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 227.29/227.65 Found x80:=(x8 x90):((or (cEVEN Xn00)) (cODD Xn00))
% 227.29/227.65 Instantiate: Xn00:=Xn:fofType
% 227.29/227.65 Found (x8 x90) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 227.29/227.65 Found (x8 x90) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 227.29/227.65 Found x30:=(x3 x20):(cNUMBER Xn0)
% 227.29/227.65 Instantiate: Xn0:=Xn:fofType
% 227.29/227.65 Found (x3 x20) as proof of (cNUMBER Xn)
% 227.29/227.65 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 227.29/227.65 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(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))
% 227.29/227.65 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (((and ((and (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)))
% 227.29/227.65 Found (and_rect40 (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 227.29/227.65 Found ((and_rect4 (cNUMBER Xn)) (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 227.29/227.65 Found (((fun (P:Type) (x8:(((and ((and (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 (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 227.29/227.65 Found (fun (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (((fun (P:Type) (x8:(((and ((and (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 (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)))) as proof of (cNUMBER Xn)
% 227.29/227.65 Found (fun (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (((fun (P:Type) (x8:(((and ((and (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 (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)))) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 227.29/227.65 Found x7:(cODD (cS c0))
% 227.29/227.65 Instantiate: Xn0:=(cS c0):fofType
% 227.29/227.65 Found x7 as proof of (cODD Xn0)
% 227.29/227.65 Found (or_intror00 x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 227.29/227.65 Found ((or_intror0 (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 227.29/227.65 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 227.29/227.65 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 227.29/227.65 Found (x9 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7)) as proof of (cNUMBER Xn0)
% 227.29/227.65 Found (fun (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (x9 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7))) as proof of (cNUMBER Xn0)
% 227.29/227.65 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (x9 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7))) as proof of ((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->(cNUMBER Xn0))
% 227.82/228.22 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (x9 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7))) as proof of ((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->(cNUMBER Xn0)))
% 227.82/228.22 Found (and_rect50 (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (x9 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7)))) as proof of (cNUMBER Xn0)
% 227.82/228.22 Found ((and_rect5 (cNUMBER Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (x9 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7)))) as proof of (cNUMBER Xn0)
% 227.82/228.22 Found (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x6)) (cNUMBER Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (x9 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7)))) as proof of (cNUMBER Xn0)
% 227.82/228.22 Found (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x6)) (cNUMBER Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (x9 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7)))) as proof of (cNUMBER Xn0)
% 227.82/228.22 Found x80:((or (cEVEN Xn00)) (cODD Xn00))
% 227.82/228.22 Instantiate: Xn00:=Xn:fofType
% 227.82/228.22 Found x80 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 227.82/228.22 Found (x7 x80) as proof of (cNUMBER Xn)
% 227.82/228.22 Found (x7 x80) as proof of (cNUMBER Xn)
% 227.82/228.22 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x7 x80)) as proof of (cNUMBER Xn)
% 227.82/228.22 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x7 x80)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 227.82/228.22 Found x80:((or (cEVEN Xn00)) (cODD Xn00))
% 227.82/228.22 Found x80 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 227.82/228.22 Found (x9 x80) as proof of (cNUMBER Xn)
% 227.82/228.22 Found (x9 x80) as proof of (cNUMBER Xn)
% 227.82/228.22 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x9 x80)) as proof of (cNUMBER Xn)
% 227.82/228.22 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x9 x80)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 227.82/228.22 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 227.82/228.22 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 227.82/228.22 Found (x3 x20) as proof of (cNUMBER Xn)
% 227.82/228.22 Found (x3 x20) as proof of (cNUMBER Xn)
% 227.82/228.22 Found (x3 x20) as proof of (cNUMBER Xn)
% 227.82/228.22 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 227.82/228.22 Instantiate: Xn0:=Xn:fofType
% 227.82/228.22 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 227.82/228.22 Found (x5 x20) as proof of (cNUMBER Xn)
% 227.82/228.22 Found (x5 x20) as proof of (cNUMBER Xn)
% 227.82/228.22 Found (x5 x20) as proof of (cNUMBER Xn)
% 227.82/228.22 Found x70:=(x7 x61):(cNUMBER Xn0)
% 227.82/228.22 Found (x7 x61) as proof of (cNUMBER Xn)
% 227.82/228.22 Found (x7 x61) as proof of (cNUMBER Xn)
% 227.82/228.22 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x61)) as proof of (cNUMBER Xn)
% 227.82/228.22 Found (fun (x12:(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))
% 227.82/228.22 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 227.82/228.22 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 227.82/228.22 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 227.82/228.22 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 227.82/228.22 Found x40:=(x4 x50):((or (cEVEN Xn00)) (cODD Xn00))
% 227.82/228.22 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 227.82/228.22 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 227.82/228.22 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 227.82/228.22 Found x22:((or (cEVEN Xn0)) (cODD Xn0))
% 227.82/228.22 Found x22 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 227.82/228.22 Found (x3 x22) as proof of (cNUMBER Xn)
% 227.82/228.22 Found (x3 x22) as proof of (cNUMBER Xn)
% 227.82/228.22 Found (x3 x22) as proof of (cNUMBER Xn)
% 227.82/228.22 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 227.82/228.22 Instantiate: Xn0:=Xn:fofType
% 228.73/229.14 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 228.73/229.14 Found (x5 x20) as proof of (cNUMBER Xn)
% 228.73/229.14 Found (x5 x20) as proof of (cNUMBER Xn)
% 228.73/229.14 Found (x5 x20) as proof of (cNUMBER Xn)
% 228.73/229.14 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 228.73/229.14 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 228.73/229.14 Found (x3 x20) as proof of (cNUMBER Xn)
% 228.73/229.14 Found (x3 x20) as proof of (cNUMBER Xn)
% 228.73/229.14 Found (x3 x20) as proof of (cNUMBER Xn)
% 228.73/229.14 Found x62:((or (cEVEN Xn0)) (cODD Xn0))
% 228.73/229.14 Found x62 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 228.73/229.14 Found (x7 x62) as proof of (cNUMBER Xn)
% 228.73/229.14 Found (x7 x62) as proof of (cNUMBER Xn)
% 228.73/229.14 Found (x7 x62) as proof of (cNUMBER Xn)
% 228.73/229.14 Found x11:(cEVEN c0)
% 228.73/229.14 Instantiate: Xn0:=c0:fofType
% 228.73/229.14 Found (fun (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11) as proof of (cEVEN Xn0)
% 228.73/229.14 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11) as proof of ((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->(cEVEN Xn0))
% 228.73/229.14 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11) as proof of ((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->(cEVEN Xn0)))
% 228.73/229.14 Found (and_rect50 (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11)) as proof of (cEVEN Xn0)
% 228.73/229.14 Found ((and_rect5 (cEVEN Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11)) as proof of (cEVEN Xn0)
% 228.73/229.14 Found (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x11) x8)) (cEVEN Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11)) as proof of (cEVEN Xn0)
% 228.73/229.14 Found (fun (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x11) x8)) (cEVEN Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11))) as proof of (cEVEN Xn0)
% 228.73/229.14 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x11) x8)) (cEVEN Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11))) as proof of ((cODD (cS c0))->(cEVEN Xn0))
% 228.73/229.14 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x11) x8)) (cEVEN Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->(cEVEN Xn0)))
% 228.73/229.14 Found (and_rect40 (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x11) x8)) (cEVEN Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11)))) as proof of (cEVEN Xn0)
% 228.73/229.14 Found ((and_rect4 (cEVEN Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x11) x8)) (cEVEN Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11)))) as proof of (cEVEN Xn0)
% 228.73/229.15 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x4)) (cEVEN Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x11) x8)) (cEVEN Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11)))) as proof of (cEVEN Xn0)
% 228.73/229.15 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x4)) (cEVEN Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x11) x8)) (cEVEN Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11)))) as proof of (cEVEN Xn0)
% 228.73/229.15 Found (or_introl00 (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x4)) (cEVEN Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x11) x8)) (cEVEN Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 228.73/229.15 Found ((or_introl0 (cODD Xn0)) (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x4)) (cEVEN Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x11) x8)) (cEVEN Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 228.73/229.15 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x4)) (cEVEN Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x11) x8)) (cEVEN Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 228.73/229.15 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x4)) (cEVEN Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x11) x8)) (cEVEN Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 229.45/229.82 Found x60:=(x6 x70):((or (cEVEN Xn00)) (cODD Xn00))
% 229.45/229.82 Instantiate: Xn00:=Xn:fofType
% 229.45/229.82 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 229.45/229.82 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 229.45/229.82 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 229.45/229.82 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 229.45/229.82 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 229.45/229.82 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 229.45/229.82 Found x40:=(x4 x50):((or (cEVEN Xn00)) (cODD Xn00))
% 229.45/229.82 Instantiate: Xn00:=Xn:fofType
% 229.45/229.82 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 229.45/229.82 Found (fun (x9:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x4 x50)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 229.45/229.82 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x9:(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)))
% 229.45/229.82 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x9:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x4 x50)) as proof of (((and ((and (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))))
% 229.45/229.82 Found x40:=(x4 x50):((or (cEVEN Xn00)) (cODD Xn00))
% 229.45/229.82 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 229.45/229.82 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 229.45/229.82 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 229.45/229.82 Found x50:(cNUMBER Xn00)
% 229.45/229.82 Instantiate: Xn00:=Xn:fofType
% 229.45/229.82 Found (fun (x13:(cODD (cS c0)))=> x50) as proof of (cNUMBER Xn)
% 229.45/229.82 Found (fun (x13:(cODD (cS c0)))=> x50) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 229.45/229.82 Found x30:(cNUMBER Xn0)
% 229.45/229.82 Instantiate: Xn0:=Xn:fofType
% 229.45/229.82 Found (fun (x13:(cODD (cS c0)))=> x30) as proof of (cNUMBER Xn)
% 229.45/229.82 Found (fun (x13:(cODD (cS c0)))=> x30) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 229.45/229.82 Found x50:=(x5 x40):(cNUMBER Xn0)
% 229.45/229.82 Found (x5 x40) as proof of (cNUMBER Xn)
% 229.45/229.82 Found (x5 x40) as proof of (cNUMBER Xn)
% 229.45/229.82 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 229.45/229.82 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(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))
% 229.45/229.82 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (((and ((and (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)))
% 229.45/229.82 Found x70:=(x7 x60):(cNUMBER Xn00)
% 229.45/229.82 Found (x7 x60) as proof of (cNUMBER Xn)
% 229.45/229.82 Found (x7 x60) as proof of (cNUMBER Xn)
% 229.45/229.82 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x7 x60)) as proof of (cNUMBER Xn)
% 229.45/229.82 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x7 x60)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 230.41/230.85 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x7 x60)) as proof of (((and ((and (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)))
% 230.41/230.85 Found x90:=(x9 x81):(cNUMBER Xn0)
% 230.41/230.85 Instantiate: Xn0:=Xn:fofType
% 230.41/230.85 Found (x9 x81) as proof of (cNUMBER Xn)
% 230.41/230.85 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x9 x81)) as proof of (cNUMBER Xn)
% 230.41/230.85 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x9 x81)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 230.41/230.85 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x9 x81)) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 230.41/230.85 Found x91:(cNUMBER Xn0)
% 230.41/230.85 Instantiate: Xn0:=Xn:fofType
% 230.41/230.85 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x91) as proof of (cNUMBER Xn)
% 230.41/230.85 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x91) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 230.41/230.85 Found x60:=(x6 x70):((or (cEVEN Xn00)) (cODD Xn00))
% 230.41/230.85 Instantiate: Xn00:=Xn:fofType
% 230.41/230.85 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 230.41/230.85 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 230.41/230.85 Found x40:=(x4 x30):(cNUMBER Xn00)
% 230.41/230.85 Instantiate: Xn0:=Xn00:fofType
% 230.41/230.85 Found (x4 x30) as proof of (cNUMBER Xn0)
% 230.41/230.85 Found (fun (x4:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x4 x30)) as proof of (cNUMBER Xn0)
% 230.41/230.85 Found (fun (x4:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x4 x30)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn0))
% 230.41/230.85 Found x50:=(x5 x40):(cNUMBER Xn00)
% 230.41/230.85 Instantiate: Xn00:=Xn:fofType
% 230.41/230.85 Found (x5 x40) as proof of (cNUMBER Xn)
% 230.41/230.85 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 230.41/230.85 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(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))
% 230.41/230.85 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (((and ((and (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)))
% 230.41/230.85 Found (and_rect40 (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 230.41/230.85 Found ((and_rect4 (cNUMBER Xn)) (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 230.41/230.85 Found (((fun (P:Type) (x8:(((and ((and (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 (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 230.41/230.85 Found (fun (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (((fun (P:Type) (x8:(((and ((and (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 (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)))) as proof of (cNUMBER Xn)
% 230.66/231.01 Found (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (((fun (P:Type) (x8:(((and ((and (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 (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)))) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 230.66/231.01 Found (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (((fun (P:Type) (x8:(((and ((and (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 (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)))) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn)))
% 230.66/231.01 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 230.66/231.01 Instantiate: Xn0:=Xn:fofType
% 230.66/231.01 Found x40 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 230.66/231.01 Found (x7 x40) as proof of (cNUMBER Xn)
% 230.66/231.01 Found (x7 x40) as proof of (cNUMBER Xn)
% 230.66/231.01 Found (x7 x40) as proof of (cNUMBER Xn)
% 230.66/231.01 Found x60:=(x6 x70):((or (cEVEN Xn00)) (cODD Xn00))
% 230.66/231.01 Instantiate: Xn00:=Xn:fofType
% 230.66/231.01 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 230.66/231.01 Found (fun (x9:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x6 x70)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 230.66/231.01 Found (fun (x9:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x6 x70)) as proof of ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 230.66/231.01 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 230.66/231.01 Instantiate: Xn00:=Xn:fofType
% 230.66/231.01 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 230.91/231.31 Found (x5 x60) as proof of (cNUMBER Xn)
% 230.91/231.31 Found (x5 x60) as proof of (cNUMBER Xn)
% 230.91/231.31 Found (x5 x60) as proof of (cNUMBER Xn)
% 230.91/231.31 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 230.91/231.31 Found x60 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 230.91/231.31 Found (x7 x60) as proof of (cNUMBER Xn)
% 230.91/231.31 Found (x7 x60) as proof of (cNUMBER Xn)
% 230.91/231.31 Found (x7 x60) as proof of (cNUMBER Xn)
% 230.91/231.31 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 230.91/231.31 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 230.91/231.31 Found (x5 x40) as proof of (cNUMBER Xn)
% 230.91/231.31 Found (x5 x40) as proof of (cNUMBER Xn)
% 230.91/231.31 Found (x5 x40) as proof of (cNUMBER Xn)
% 230.91/231.31 Found x30:=(x3 x20):(cNUMBER Xn0)
% 230.91/231.31 Instantiate: Xn0:=Xn:fofType
% 230.91/231.31 Found (x3 x20) as proof of (cNUMBER Xn)
% 230.91/231.31 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 230.91/231.31 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(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))
% 230.91/231.31 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (((and ((and (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)))
% 230.91/231.31 Found (and_rect40 (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 230.91/231.31 Found ((and_rect4 (cNUMBER Xn)) (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 230.91/231.31 Found (((fun (P:Type) (x8:(((and ((and (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 (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 230.91/231.31 Found (fun (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (((fun (P:Type) (x8:(((and ((and (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 (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)))) as proof of (cNUMBER Xn)
% 230.91/231.31 Found (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (((fun (P:Type) (x8:(((and ((and (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 (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)))) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 231.79/232.16 Found (fun (x6:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x7:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (((fun (P:Type) (x8:(((and ((and (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 (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)))) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn)))
% 231.79/232.16 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 231.79/232.16 Instantiate: Xn0:=Xn:fofType
% 231.79/232.16 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 231.79/232.16 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x2 x30)) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 231.79/232.16 Found (fun (x9:(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)))
% 231.79/232.16 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 231.79/232.16 Instantiate: Xn00:=Xn:fofType
% 231.79/232.16 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 231.79/232.16 Found (x3 x60) as proof of (cNUMBER Xn)
% 231.79/232.16 Found (x3 x60) as proof of (cNUMBER Xn)
% 231.79/232.16 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x60)) as proof of (cNUMBER Xn)
% 231.79/232.16 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x60)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 231.79/232.16 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x60)) as proof of (((and ((and (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)))
% 231.79/232.16 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 231.79/232.16 Instantiate: Xn0:=Xn:fofType
% 231.79/232.16 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 231.79/232.16 Found (x7 x20) as proof of (cNUMBER Xn)
% 231.79/232.16 Found (x7 x20) as proof of (cNUMBER Xn)
% 231.79/232.16 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x7 x20)) as proof of (cNUMBER Xn)
% 231.79/232.16 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x7 x20)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 231.79/232.16 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x7 x20)) as proof of (((and ((and (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)))
% 233.39/233.75 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 233.39/233.75 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 233.39/233.75 Found (x3 x20) as proof of (cNUMBER Xn)
% 233.39/233.75 Found (x3 x20) as proof of (cNUMBER Xn)
% 233.39/233.75 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 233.39/233.75 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(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))
% 233.39/233.75 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (((and ((and (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)))
% 233.39/233.75 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 233.39/233.75 Found x60 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 233.39/233.75 Found (x7 x60) as proof of (cNUMBER Xn)
% 233.39/233.75 Found (x7 x60) as proof of (cNUMBER Xn)
% 233.39/233.75 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x7 x60)) as proof of (cNUMBER Xn)
% 233.39/233.75 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x7 x60)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 233.39/233.75 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x7 x60)) as proof of (((and ((and (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)))
% 233.39/233.75 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 233.39/233.75 Instantiate: Xn0:=Xn00:fofType
% 233.39/233.75 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 233.39/233.75 Found x30:(cNUMBER Xn0)
% 233.39/233.75 Instantiate: Xn00:=Xn0:fofType
% 233.39/233.75 Found x30 as proof of (cNUMBER Xn00)
% 233.39/233.75 Found x50:=(x5 x40):(cNUMBER Xn0)
% 233.39/233.75 Found (x5 x40) as proof of (cNUMBER Xn)
% 233.39/233.75 Found (x5 x40) as proof of (cNUMBER Xn)
% 233.39/233.75 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 233.39/233.75 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x5 x40)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 233.39/233.75 Found x40:=(x4 x50):((or (cEVEN Xn0)) (cODD Xn0))
% 233.39/233.75 Instantiate: Xn0:=Xn:fofType
% 233.39/233.75 Found (x4 x50) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 233.39/233.75 Found (x4 x50) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 233.39/233.75 Found x60:=(x6 x70):((or (cEVEN Xn00)) (cODD Xn00))
% 233.39/233.75 Instantiate: Xn00:=Xn:fofType
% 233.39/233.75 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 233.39/233.75 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 233.39/233.75 Found x30:=(x3 x21):(cNUMBER Xn0)
% 233.39/233.75 Instantiate: Xn0:=Xn:fofType
% 233.39/233.75 Found (x3 x21) as proof of (cNUMBER Xn)
% 233.39/233.75 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x21)) as proof of (cNUMBER Xn)
% 233.39/233.75 Found (fun (x11:(cEVEN c0)) (x12:(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))
% 233.39/233.75 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x21)) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 233.39/233.75 Found (and_rect50 (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x21))) as proof of (cNUMBER Xn)
% 233.39/233.75 Found ((and_rect5 (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x21))) as proof of (cNUMBER Xn)
% 233.39/233.75 Found (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x21))) as proof of (cNUMBER Xn)
% 233.59/233.99 Found (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x21))) as proof of (cNUMBER Xn)
% 233.59/233.99 Found x9:(cEVEN c0)
% 233.59/233.99 Instantiate: Xn0:=c0:fofType
% 233.59/233.99 Found (fun (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x9) as proof of (cEVEN Xn0)
% 233.59/233.99 Found (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x9) as proof of ((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->(cEVEN Xn0))
% 233.59/233.99 Found (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x9) as proof of ((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->(cEVEN Xn0)))
% 233.59/233.99 Found (and_rect50 (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x9)) as proof of (cEVEN Xn0)
% 233.59/233.99 Found ((and_rect5 (cEVEN Xn0)) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x9)) as proof of (cEVEN Xn0)
% 233.59/233.99 Found (((fun (P:Type) (x9:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x9) x7)) (cEVEN Xn0)) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x9)) as proof of (cEVEN Xn0)
% 233.59/233.99 Found (fun (x8:(cODD (cS c0)))=> (((fun (P:Type) (x9:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x9) x7)) (cEVEN Xn0)) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x9))) as proof of (cEVEN Xn0)
% 233.59/233.99 Found (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> (((fun (P:Type) (x9:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x9) x7)) (cEVEN Xn0)) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x9))) as proof of ((cODD (cS c0))->(cEVEN Xn0))
% 233.59/233.99 Found (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> (((fun (P:Type) (x9:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x9) x7)) (cEVEN Xn0)) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x9))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->(cEVEN Xn0)))
% 233.59/233.99 Found (and_rect40 (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> (((fun (P:Type) (x9:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x9) x7)) (cEVEN Xn0)) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x9)))) as proof of (cEVEN Xn0)
% 233.59/233.99 Found ((and_rect4 (cEVEN Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> (((fun (P:Type) (x9:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x9) x7)) (cEVEN Xn0)) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x9)))) as proof of (cEVEN Xn0)
% 233.59/233.99 Found (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) (cEVEN Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> (((fun (P:Type) (x9:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x9) x7)) (cEVEN Xn0)) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x9)))) as proof of (cEVEN Xn0)
% 233.59/233.99 Found (fun (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) (cEVEN Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> (((fun (P:Type) (x9:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x9) x7)) (cEVEN Xn0)) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x9))))) as proof of (cEVEN Xn0)
% 233.59/233.99 Found (fun (x5:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) (cEVEN Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> (((fun (P:Type) (x9:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x9) x7)) (cEVEN Xn0)) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x9))))) as proof of ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->(cEVEN Xn0))
% 233.59/233.99 Found (fun (x5:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) (cEVEN Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> (((fun (P:Type) (x9:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x9) x7)) (cEVEN Xn0)) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x9))))) as proof of (((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))->((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->(cEVEN Xn0)))
% 233.59/233.99 Found (and_rect30 (fun (x5:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) (cEVEN Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> (((fun (P:Type) (x9:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x9) x7)) (cEVEN Xn0)) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x9)))))) as proof of (cEVEN Xn0)
% 233.59/233.99 Found ((and_rect3 (cEVEN Xn0)) (fun (x5:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) (cEVEN Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> (((fun (P:Type) (x9:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x9) x7)) (cEVEN Xn0)) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x9)))))) as proof of (cEVEN Xn0)
% 233.59/233.99 Found (((fun (P:Type) (x5:(((and ((and (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 (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x5) x4)) (cEVEN Xn0)) (fun (x5:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) (cEVEN Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> (((fun (P:Type) (x9:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x9) x7)) (cEVEN Xn0)) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x9)))))) as proof of (cEVEN Xn0)
% 233.59/233.99 Found (((fun (P:Type) (x5:(((and ((and (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 (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x5) x4)) (cEVEN Xn0)) (fun (x5:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) (cEVEN Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> (((fun (P:Type) (x9:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x9) x7)) (cEVEN Xn0)) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x9)))))) as proof of (cEVEN Xn0)
% 233.64/234.00 Found (or_introl00 (((fun (P:Type) (x5:(((and ((and (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 (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x5) x4)) (cEVEN Xn0)) (fun (x5:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) (cEVEN Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> (((fun (P:Type) (x9:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x9) x7)) (cEVEN Xn0)) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x9))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 233.64/234.00 Found ((or_introl0 (cODD Xn0)) (((fun (P:Type) (x5:(((and ((and (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 (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x5) x4)) (cEVEN Xn0)) (fun (x5:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) (cEVEN Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> (((fun (P:Type) (x9:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x9) x7)) (cEVEN Xn0)) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x9))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 233.64/234.00 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) (((fun (P:Type) (x5:(((and ((and (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 (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x5) x4)) (cEVEN Xn0)) (fun (x5:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) (cEVEN Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> (((fun (P:Type) (x9:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x9) x7)) (cEVEN Xn0)) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x9))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 235.32/235.71 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) (((fun (P:Type) (x5:(((and ((and (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 (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x5) x4)) (cEVEN Xn0)) (fun (x5:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x7:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x7) x5)) (cEVEN Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> (((fun (P:Type) (x9:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x9) x7)) (cEVEN Xn0)) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x9))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 235.32/235.71 Found x30:(cNUMBER Xn0)
% 235.32/235.71 Instantiate: Xn00:=Xn0:fofType
% 235.32/235.71 Found x30 as proof of (cNUMBER Xn00)
% 235.32/235.71 Found x41:((or (cEVEN Xn0)) (cODD Xn0))
% 235.32/235.71 Found x41 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 235.32/235.71 Found (x5 x41) as proof of (cNUMBER Xn)
% 235.32/235.71 Found (x5 x41) as proof of (cNUMBER Xn)
% 235.32/235.71 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x41)) as proof of (cNUMBER Xn)
% 235.32/235.71 Found (fun (x12:(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))
% 235.32/235.71 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 235.32/235.71 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 235.32/235.71 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 235.32/235.71 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 235.32/235.71 Found x41:((or (cEVEN Xn0)) (cODD Xn0))
% 235.32/235.71 Found x41 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 235.32/235.71 Found (x5 x41) as proof of (cNUMBER Xn)
% 235.32/235.71 Found (x5 x41) as proof of (cNUMBER Xn)
% 235.32/235.71 Found (x5 x41) as proof of (cNUMBER Xn)
% 235.32/235.71 Found x80:=(x8 x90):((or (cEVEN Xn00)) (cODD Xn00))
% 235.32/235.71 Found (x8 x90) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 235.32/235.71 Found (x8 x90) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 235.32/235.71 Found (x8 x90) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 235.32/235.71 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 235.32/235.71 Instantiate: Xn0:=Xn:fofType
% 235.32/235.71 Found x40 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 235.32/235.71 Found (x9 x40) as proof of (cNUMBER Xn)
% 235.32/235.71 Found (x9 x40) as proof of (cNUMBER Xn)
% 235.32/235.71 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x9 x40)) as proof of (cNUMBER Xn)
% 235.32/235.71 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x9 x40)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 235.32/235.71 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 235.32/235.71 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 235.32/235.71 Found (x5 x40) as proof of (cNUMBER Xn)
% 235.32/235.71 Found (x5 x40) as proof of (cNUMBER Xn)
% 235.32/235.71 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 235.32/235.71 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 235.32/235.71 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 235.32/235.71 Instantiate: Xn0:=Xn00:fofType
% 235.32/235.71 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 235.32/235.71 Found x70:=(x7 x60):(cNUMBER Xn0)
% 235.32/235.71 Found (x7 x60) as proof of (cNUMBER Xn0)
% 235.32/235.71 Found (x7 x60) as proof of (cNUMBER Xn0)
% 235.32/235.71 Found x70:=(x7 x61):(cNUMBER Xn0)
% 235.32/235.71 Instantiate: Xn0:=Xn:fofType
% 235.32/235.71 Found (x7 x61) as proof of (cNUMBER Xn)
% 235.32/235.71 Found (x7 x61) as proof of (cNUMBER Xn)
% 235.32/235.71 Found x70:=(x7 x61):(cNUMBER Xn0)
% 235.32/235.71 Found (x7 x61) as proof of (cNUMBER Xn)
% 237.49/237.85 Found (x7 x61) as proof of (cNUMBER Xn)
% 237.49/237.85 Found (x7 x61) as proof of (cNUMBER Xn)
% 237.49/237.85 Found x41:((or (cEVEN Xn0)) (cODD Xn0))
% 237.49/237.85 Found x41 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 237.49/237.85 Found (x5 x41) as proof of (cNUMBER Xn)
% 237.49/237.85 Found (x5 x41) as proof of (cNUMBER Xn)
% 237.49/237.85 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x41)) as proof of (cNUMBER Xn)
% 237.49/237.85 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x41)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 237.49/237.85 Found x80:((or (cEVEN Xn00)) (cODD Xn00))
% 237.49/237.85 Instantiate: Xn00:=Xn:fofType
% 237.49/237.85 Found x80 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 237.49/237.85 Found (x5 x80) as proof of (cNUMBER Xn)
% 237.49/237.85 Found (x5 x80) as proof of (cNUMBER Xn)
% 237.49/237.85 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x80)) as proof of (cNUMBER Xn)
% 237.49/237.85 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x80)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 237.49/237.85 Found x80:((or (cEVEN Xn00)) (cODD Xn00))
% 237.49/237.85 Found x80 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 237.49/237.85 Found (x9 x80) as proof of (cNUMBER Xn)
% 237.49/237.85 Found (x9 x80) as proof of (cNUMBER Xn)
% 237.49/237.85 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x9 x80)) as proof of (cNUMBER Xn)
% 237.49/237.85 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x9 x80)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 237.49/237.85 Found x50:=(x5 x41):(cNUMBER Xn0)
% 237.49/237.85 Found (x5 x41) as proof of (cNUMBER Xn0)
% 237.49/237.85 Found (x5 x41) as proof of (cNUMBER Xn0)
% 237.49/237.85 Found x50:=(x5 x42):(cNUMBER Xn0)
% 237.49/237.85 Instantiate: Xn0:=Xn:fofType
% 237.49/237.85 Found (x5 x42) as proof of (cNUMBER Xn)
% 237.49/237.85 Found (x5 x42) as proof of (cNUMBER Xn)
% 237.49/237.85 Found x50:=(x5 x41):(cNUMBER Xn0)
% 237.49/237.85 Found (x5 x41) as proof of (cNUMBER Xn)
% 237.49/237.85 Found (x5 x41) as proof of (cNUMBER Xn)
% 237.49/237.85 Found (x5 x41) as proof of (cNUMBER Xn)
% 237.49/237.85 Found x50:=(x5 x41):(cNUMBER Xn0)
% 237.49/237.85 Found (x5 x41) as proof of (cNUMBER Xn0)
% 237.49/237.85 Found (x5 x41) as proof of (cNUMBER Xn0)
% 237.49/237.85 Found x50:=(x5 x42):(cNUMBER Xn0)
% 237.49/237.85 Instantiate: Xn0:=Xn:fofType
% 237.49/237.85 Found (x5 x42) as proof of (cNUMBER Xn)
% 237.49/237.85 Found (x5 x42) as proof of (cNUMBER Xn)
% 237.49/237.85 Found x50:=(x5 x41):(cNUMBER Xn0)
% 237.49/237.85 Found (x5 x41) as proof of (cNUMBER Xn)
% 237.49/237.85 Found (x5 x41) as proof of (cNUMBER Xn)
% 237.49/237.85 Found (x5 x41) as proof of (cNUMBER Xn)
% 237.49/237.85 Found x80:=(x8 x90):((or (cEVEN Xn00)) (cODD Xn00))
% 237.49/237.85 Instantiate: Xn00:=Xn:fofType
% 237.49/237.85 Found (x8 x90) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 237.49/237.85 Found (x8 x90) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 237.49/237.85 Found x50:=(x5 x41):(cNUMBER Xn0)
% 237.49/237.85 Found (x5 x41) as proof of (cNUMBER Xn0)
% 237.49/237.85 Found (x5 x41) as proof of (cNUMBER Xn0)
% 237.49/237.85 Found x50:=(x5 x42):(cNUMBER Xn0)
% 237.49/237.85 Instantiate: Xn0:=Xn:fofType
% 237.49/237.85 Found (x5 x42) as proof of (cNUMBER Xn)
% 237.49/237.85 Found (x5 x42) as proof of (cNUMBER Xn)
% 237.49/237.85 Found x50:=(x5 x41):(cNUMBER Xn0)
% 237.49/237.85 Found (x5 x41) as proof of (cNUMBER Xn)
% 237.49/237.85 Found (x5 x41) as proof of (cNUMBER Xn)
% 237.49/237.85 Found (x5 x41) as proof of (cNUMBER Xn)
% 237.49/237.85 Found x41:((or (cEVEN Xn0)) (cODD Xn0))
% 237.49/237.85 Found x41 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 237.49/237.85 Found (x5 x41) as proof of (cNUMBER Xn)
% 237.49/237.85 Found (x5 x41) as proof of (cNUMBER Xn)
% 237.49/237.85 Found (x5 x41) as proof of (cNUMBER Xn)
% 237.49/237.85 Found x90:=(x9 x80):(cNUMBER Xn0)
% 237.49/237.85 Found (x9 x80) as proof of (cNUMBER Xn0)
% 237.49/237.85 Found (x9 x80) as proof of (cNUMBER Xn0)
% 237.49/237.85 Found x90:=(x9 x81):(cNUMBER Xn0)
% 237.49/237.85 Instantiate: Xn0:=Xn:fofType
% 237.49/237.85 Found (x9 x81) as proof of (cNUMBER Xn)
% 237.49/237.85 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x9 x81)) as proof of (cNUMBER Xn)
% 237.49/237.85 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x9 x81)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 237.49/237.85 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 237.49/237.85 Instantiate: Xn00:=Xn:fofType
% 237.49/237.85 Found (fun (x9:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x60) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 237.49/237.85 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x9:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x60) as proof of ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 240.00/240.38 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x9:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x60) as proof of (((and ((and (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))))
% 240.00/240.38 Found x41:((or (cEVEN Xn0)) (cODD Xn0))
% 240.00/240.38 Found x41 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 240.00/240.38 Found (x5 x41) as proof of (cNUMBER Xn)
% 240.00/240.38 Found (x5 x41) as proof of (cNUMBER Xn)
% 240.00/240.38 Found (x5 x41) as proof of (cNUMBER Xn)
% 240.00/240.38 Found x120:=(x12 x110):(cNUMBER Xn0)
% 240.00/240.38 Found (x12 x110) as proof of (cNUMBER Xn0)
% 240.00/240.38 Found (x12 x110) as proof of (cNUMBER Xn0)
% 240.00/240.38 Found x120:=(x12 x111):(cNUMBER Xn0)
% 240.00/240.38 Instantiate: Xn0:=Xn:fofType
% 240.00/240.38 Found (x12 x111) as proof of (cNUMBER Xn)
% 240.00/240.38 Found (x12 x111) as proof of (cNUMBER Xn)
% 240.00/240.38 Found x120:=(x12 x111):(cNUMBER Xn0)
% 240.00/240.38 Found (x12 x111) as proof of (cNUMBER Xn)
% 240.00/240.38 Found (x12 x111) as proof of (cNUMBER Xn)
% 240.00/240.38 Found (x12 x111) as proof of (cNUMBER Xn)
% 240.00/240.38 Found x50:(cNUMBER Xn0)
% 240.00/240.38 Instantiate: Xn00:=Xn0:fofType
% 240.00/240.38 Found x50 as proof of (cNUMBER Xn00)
% 240.00/240.38 Found x50:=(x5 x40):(cNUMBER Xn00)
% 240.00/240.38 Found (x5 x40) as proof of (cNUMBER Xn0)
% 240.00/240.38 Found (x5 x40) as proof of (cNUMBER Xn0)
% 240.00/240.38 Found (x5 x40) as proof of (cNUMBER Xn0)
% 240.00/240.38 Found x80:=(x8 x90):((or (cEVEN Xn0)) (cODD Xn0))
% 240.00/240.38 Found (x8 x90) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 240.00/240.38 Found (x8 x90) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 240.00/240.38 Found x40:=(x4 x50):((or (cEVEN Xn00)) (cODD Xn00))
% 240.00/240.38 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 240.00/240.38 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 240.00/240.38 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 240.00/240.38 Found x30:=(x3 x20):(cNUMBER Xn0)
% 240.00/240.38 Found (x3 x20) as proof of (cNUMBER Xn00)
% 240.00/240.38 Found (x3 x20) as proof of (cNUMBER Xn00)
% 240.00/240.38 Found (x3 x20) as proof of (cNUMBER Xn00)
% 240.00/240.38 Found x40:=(x4 x50):((or (cEVEN Xn00)) (cODD Xn00))
% 240.00/240.38 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 240.00/240.38 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 240.00/240.38 Found (fun (x9:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x4 x50)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 240.00/240.38 Found (fun (x9:(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)))
% 240.00/240.38 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 240.00/240.38 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 240.00/240.38 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 240.00/240.38 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x2 x30)) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 240.00/240.38 Found (fun (x9:(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)))
% 240.00/240.38 Found x50:=(x5 x40):(cNUMBER Xn00)
% 240.00/240.38 Instantiate: Xn0:=Xn00:fofType
% 240.00/240.38 Found (x5 x40) as proof of (cNUMBER Xn0)
% 240.00/240.38 Found (x5 x40) as proof of (cNUMBER Xn0)
% 240.00/240.38 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 240.00/240.38 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 240.00/240.38 Found (x3 x20) as proof of (cNUMBER Xn00)
% 240.00/240.38 Found (x3 x20) as proof of (cNUMBER Xn00)
% 240.00/240.38 Found (x3 x20) as proof of (cNUMBER Xn00)
% 240.00/240.38 Found x40:=(x4 x50):((or (cEVEN Xn00)) (cODD Xn00))
% 240.00/240.38 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 240.00/240.38 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 240.00/240.38 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 240.00/240.38 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 240.00/240.38 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 240.00/240.38 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 240.00/240.38 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 240.00/240.38 Found x60:((or (cEVEN Xn0)) (cODD Xn0))
% 240.00/240.38 Instantiate: Xn0:=Xn:fofType
% 240.00/240.38 Found x60 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 240.00/240.38 Found (x9 x60) as proof of (cNUMBER Xn)
% 240.00/240.38 Found (x9 x60) as proof of (cNUMBER Xn)
% 240.00/240.38 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x9 x60)) as proof of (cNUMBER Xn)
% 240.00/240.38 Found (fun (x8:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x9 x60)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 240.00/240.42 Found (fun (x8:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x9 x60)) as proof of (((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))->((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn)))
% 240.00/240.42 Found x60:((or (cEVEN Xn0)) (cODD Xn0))
% 240.00/240.42 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 240.00/240.42 Found (x7 x60) as proof of (cNUMBER Xn)
% 240.00/240.42 Found (x7 x60) as proof of (cNUMBER Xn)
% 240.00/240.42 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x7 x60)) as proof of (cNUMBER Xn)
% 240.00/240.42 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))
% 240.00/240.42 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)))
% 240.00/240.42 Found x70:=(x7 x60):(cNUMBER Xn00)
% 240.00/240.42 Instantiate: Xn00:=Xn:fofType
% 240.00/240.42 Found (x7 x60) as proof of (cNUMBER Xn)
% 240.00/240.42 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x7 x60)) as proof of (cNUMBER Xn)
% 240.00/240.42 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x7 x60)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 240.00/240.42 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x7 x60)) as proof of (((and ((and (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)))
% 240.00/240.42 Found (and_rect40 (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x7 x60))) as proof of (cNUMBER Xn)
% 240.00/240.42 Found ((and_rect4 (cNUMBER Xn)) (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x7 x60))) as proof of (cNUMBER Xn)
% 240.00/240.42 Found (((fun (P:Type) (x8:(((and ((and (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 (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x8) x4)) (cNUMBER Xn)) (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x7 x60))) as proof of (cNUMBER Xn)
% 240.00/240.42 Found (((fun (P:Type) (x8:(((and ((and (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 (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x8) x4)) (cNUMBER Xn)) (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x7 x60))) as proof of (cNUMBER Xn)
% 240.00/240.42 Found x30:=(x3 x20):(cNUMBER Xn0)
% 240.00/240.42 Instantiate: Xn0:=Xn:fofType
% 240.00/240.42 Found (x3 x20) as proof of (cNUMBER Xn)
% 240.00/240.42 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 240.00/240.42 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(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))
% 240.10/240.49 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (((and ((and (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)))
% 240.10/240.49 Found (and_rect40 (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 240.10/240.49 Found ((and_rect4 (cNUMBER Xn)) (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 240.10/240.49 Found (((fun (P:Type) (x8:(((and ((and (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 (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x8) x4)) (cNUMBER Xn)) (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 240.10/240.49 Found (((fun (P:Type) (x8:(((and ((and (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 (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x8) x4)) (cNUMBER Xn)) (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 240.10/240.49 Found x30:=(x3 x21):(cNUMBER Xn0)
% 240.10/240.49 Instantiate: Xn0:=Xn:fofType
% 240.10/240.49 Found (x3 x21) as proof of (cNUMBER Xn)
% 240.10/240.49 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x21)) as proof of (cNUMBER Xn)
% 240.10/240.49 Found (fun (x11:(cEVEN c0)) (x12:(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))
% 240.10/240.49 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x21)) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 240.10/240.49 Found (and_rect50 (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x21))) as proof of (cNUMBER Xn)
% 240.10/240.49 Found ((and_rect5 (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x21))) as proof of (cNUMBER Xn)
% 240.10/240.49 Found (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x21))) as proof of (cNUMBER Xn)
% 240.10/240.49 Found (fun (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x21)))) as proof of (cNUMBER Xn)
% 240.10/240.49 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x21)))) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 241.21/241.58 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x21)))) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 241.21/241.58 Found x60:=(x6 x70):((or (cEVEN Xn00)) (cODD Xn00))
% 241.21/241.58 Instantiate: Xn00:=Xn:fofType
% 241.21/241.58 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 241.21/241.58 Found (fun (x9:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x6 x70)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 241.21/241.58 Found (fun (x9:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x6 x70)) as proof of ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 241.21/241.58 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 241.21/241.58 Instantiate: Xn0:=Xn:fofType
% 241.21/241.58 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 241.21/241.58 Found (x5 x20) as proof of (cNUMBER Xn)
% 241.21/241.58 Found (x5 x20) as proof of (cNUMBER Xn)
% 241.21/241.58 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x20)) as proof of (cNUMBER Xn)
% 241.21/241.58 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x20)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 241.21/241.58 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 241.21/241.58 Instantiate: Xn0:=Xn00:fofType
% 241.21/241.58 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 241.21/241.58 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 241.21/241.58 Instantiate: Xn00:=Xn0:fofType
% 241.21/241.58 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 241.21/241.58 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 241.21/241.58 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 241.21/241.58 Found (x3 x20) as proof of (cNUMBER Xn)
% 241.21/241.58 Found (x3 x20) as proof of (cNUMBER Xn)
% 241.21/241.58 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 241.21/241.58 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 241.21/241.58 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 241.21/241.58 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 241.21/241.58 Found (x3 x20) as proof of (cNUMBER Xn)
% 241.21/241.58 Found (x3 x20) as proof of (cNUMBER Xn)
% 241.21/241.58 Found (x3 x20) as proof of (cNUMBER Xn)
% 241.21/241.58 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 241.21/241.58 Instantiate: Xn0:=Xn:fofType
% 241.21/241.58 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 241.21/241.58 Found (x5 x20) as proof of (cNUMBER Xn)
% 241.21/241.58 Found (x5 x20) as proof of (cNUMBER Xn)
% 241.21/241.58 Found (x5 x20) as proof of (cNUMBER Xn)
% 241.21/241.58 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 241.21/241.58 Instantiate: Xn0:=Xn:fofType
% 241.21/241.58 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 241.21/241.58 Found (x5 x20) as proof of (cNUMBER Xn)
% 241.21/241.58 Found (x5 x20) as proof of (cNUMBER Xn)
% 241.21/241.58 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x20)) as proof of (cNUMBER Xn)
% 241.21/241.58 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x20)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 241.21/241.58 Found x8:(cEVEN c0)
% 241.21/241.58 Instantiate: Xn0:=c0:fofType
% 241.21/241.58 Found x8 as proof of (cEVEN Xn0)
% 241.21/241.58 Found (or_intror00 x8) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 241.21/241.58 Found ((or_intror0 (cEVEN Xn0)) x8) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 241.21/241.58 Found (((or_intror (cODD Xn0)) (cEVEN Xn0)) x8) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 241.21/241.58 Found (((or_intror (cODD Xn0)) (cEVEN Xn0)) x8) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 241.21/241.58 Found (or_comm_i00 (((or_intror (cODD Xn0)) (cEVEN Xn0)) x8)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 241.21/241.58 Found ((or_comm_i0 (cEVEN Xn0)) (((or_intror (cODD Xn0)) (cEVEN Xn0)) x8)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 241.21/241.58 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((or_intror (cODD Xn0)) (cEVEN Xn0)) x8)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 243.13/243.50 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((or_intror (cODD Xn0)) (cEVEN Xn0)) x8)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 243.13/243.50 Found x40:=(x4 x50):((or (cEVEN Xn00)) (cODD Xn00))
% 243.13/243.50 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 243.13/243.50 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 243.13/243.50 Found (fun (x9:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x4 x50)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 243.13/243.50 Found (fun (x9:(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)))
% 243.13/243.50 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 243.13/243.50 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 243.13/243.50 Found (x3 x20) as proof of (cNUMBER Xn)
% 243.13/243.50 Found (x3 x20) as proof of (cNUMBER Xn)
% 243.13/243.50 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 243.13/243.50 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 243.13/243.50 Found x30:(cNUMBER Xn0)
% 243.13/243.50 Instantiate: Xn00:=Xn0:fofType
% 243.13/243.50 Found x30 as proof of (cNUMBER Xn00)
% 243.13/243.50 Found x50:(cNUMBER Xn00)
% 243.13/243.50 Instantiate: Xn0:=Xn00:fofType
% 243.13/243.50 Found x50 as proof of (cNUMBER Xn0)
% 243.13/243.50 Found x41:((or (cEVEN Xn00)) (cODD Xn00))
% 243.13/243.50 Instantiate: Xn00:=Xn:fofType
% 243.13/243.50 Found x41 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 243.13/243.50 Found (x3 x41) as proof of (cNUMBER Xn)
% 243.13/243.50 Found (x3 x41) as proof of (cNUMBER Xn)
% 243.13/243.50 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x41)) as proof of (cNUMBER Xn)
% 243.13/243.50 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x41)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 243.13/243.50 Found x41:((or (cEVEN Xn00)) (cODD Xn00))
% 243.13/243.50 Found x41 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 243.13/243.50 Found (x5 x41) as proof of (cNUMBER Xn)
% 243.13/243.50 Found (x5 x41) as proof of (cNUMBER Xn)
% 243.13/243.50 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x41)) as proof of (cNUMBER Xn)
% 243.13/243.50 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x41)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 243.13/243.50 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 243.13/243.50 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 243.13/243.50 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 243.13/243.50 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x2 x30)) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 243.13/243.50 Found (fun (x9:(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)))
% 243.13/243.50 Found x70:=(x7 x61):(cNUMBER Xn0)
% 243.13/243.50 Found (x7 x61) as proof of (cNUMBER Xn)
% 243.13/243.50 Found (x7 x61) as proof of (cNUMBER Xn)
% 243.13/243.50 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x61)) as proof of (cNUMBER Xn)
% 243.13/243.50 Found (fun (x12:(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))
% 243.13/243.50 Found x70:=(x7 x61):(cNUMBER Xn0)
% 243.13/243.50 Found (x7 x61) as proof of (cNUMBER Xn)
% 243.13/243.50 Found (x7 x61) as proof of (cNUMBER Xn)
% 243.13/243.50 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x61)) as proof of (cNUMBER Xn)
% 243.13/243.50 Found (fun (x11:(cEVEN c0)) (x12:(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))
% 243.13/243.50 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x61)) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 243.13/243.50 Found x30:(cNUMBER Xn0)
% 243.13/243.50 Instantiate: Xn00:=Xn0:fofType
% 243.13/243.50 Found x30 as proof of (cNUMBER Xn00)
% 243.13/243.50 Found x50:(cNUMBER Xn00)
% 243.13/243.50 Instantiate: Xn0:=Xn00:fofType
% 243.13/243.50 Found x50 as proof of (cNUMBER Xn0)
% 243.13/243.50 Found x60:=(x6 x70):((or (cEVEN Xn00)) (cODD Xn00))
% 243.13/243.50 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 243.13/243.50 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 243.13/243.50 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 243.97/244.34 Found x30:(cNUMBER Xn0)
% 243.97/244.34 Instantiate: Xn0:=Xn:fofType
% 243.97/244.34 Found x30 as proof of (cNUMBER Xn)
% 243.97/244.34 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 243.97/244.34 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 243.97/244.34 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 243.97/244.34 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 243.97/244.34 Found x60:=(x6 x70):((or (cEVEN Xn00)) (cODD Xn00))
% 243.97/244.34 Instantiate: Xn00:=Xn:fofType
% 243.97/244.34 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 243.97/244.34 Found (fun (x9:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x6 x70)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 243.97/244.34 Found (fun (x9:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x6 x70)) as proof of ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 243.97/244.34 Found x70:(cNUMBER Xn00)
% 243.97/244.34 Instantiate: Xn00:=Xn:fofType
% 243.97/244.34 Found x70 as proof of (cNUMBER Xn)
% 243.97/244.34 Found x31:(cNUMBER Xn0)
% 243.97/244.34 Instantiate: Xn0:=Xn:fofType
% 243.97/244.34 Found (fun (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x31) as proof of (cNUMBER Xn)
% 243.97/244.34 Found (fun (x7:(cEVEN Xn0)) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x31) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 243.97/244.34 Found (fun (x7:(cEVEN Xn0)) (x8:(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)))
% 243.97/244.34 Found x31:(cNUMBER Xn0)
% 243.97/244.34 Instantiate: Xn0:=Xn:fofType
% 243.97/244.34 Found (fun (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x31) as proof of (cNUMBER Xn)
% 243.97/244.34 Found (fun (x7:(cODD Xn0)) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x31) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 243.97/244.34 Found (fun (x7:(cODD Xn0)) (x8:(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)))
% 243.97/244.34 Found ((or_ind00 (fun (x7:(cEVEN Xn0)) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x31)) (fun (x7:(cODD Xn0)) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x31)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 243.97/244.34 Found (((or_ind0 ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))) (fun (x7:(cEVEN Xn0)) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x31)) (fun (x7:(cODD Xn0)) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x31)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 243.97/244.34 Found ((((fun (P:Prop) (x7:((cEVEN Xn0)->P)) (x8:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x7) x8) x20)) ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->(cNUMBER Xn))) (fun (x7:(cEVEN Xn0)) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x31)) (fun (x7:(cODD Xn0)) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x31)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 243.97/244.34 Found ((((fun (P:Prop) (x7:((cEVEN Xn0)->P)) (x8:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x7) x8) (x2 x31))) ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->(cNUMBER Xn))) (fun (x7:(cEVEN Xn0)) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x31)) (fun (x7:(cODD Xn0)) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x31)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 243.97/244.34 Found ((((fun (P:Prop) (x7:((cEVEN Xn0)->P)) (x8:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x7) x8) (x2 x31))) ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->(cNUMBER Xn))) (fun (x7:(cEVEN Xn0)) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x31)) (fun (x7:(cODD Xn0)) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x31)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 243.97/244.34 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 248.90/249.29 Instantiate: Xn00:=Xn0:fofType
% 248.90/249.29 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 248.90/249.29 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 248.90/249.29 Instantiate: Xn0:=Xn00:fofType
% 248.90/249.29 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 248.90/249.29 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 248.90/249.29 Instantiate: Xn0:=Xn:fofType
% 248.90/249.29 Found x40 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 248.90/249.29 Found (x7 x40) as proof of (cNUMBER Xn)
% 248.90/249.29 Found (x7 x40) as proof of (cNUMBER Xn)
% 248.90/249.29 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x7 x40)) as proof of (cNUMBER Xn)
% 248.90/249.29 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x7 x40)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 248.90/249.29 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 248.90/249.29 Instantiate: Xn00:=Xn:fofType
% 248.90/249.29 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 248.90/249.29 Found (x5 x60) as proof of (cNUMBER Xn)
% 248.90/249.29 Found (x5 x60) as proof of (cNUMBER Xn)
% 248.90/249.29 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x60)) as proof of (cNUMBER Xn)
% 248.90/249.29 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x60)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 248.90/249.29 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 248.90/249.29 Found x60 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 248.90/249.29 Found (x7 x60) as proof of (cNUMBER Xn)
% 248.90/249.29 Found (x7 x60) as proof of (cNUMBER Xn)
% 248.90/249.29 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x7 x60)) as proof of (cNUMBER Xn)
% 248.90/249.29 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x7 x60)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 248.90/249.29 Found x40:=(x4 x50):((or (cEVEN Xn00)) (cODD Xn00))
% 248.90/249.29 Instantiate: Xn0:=Xn00:fofType
% 248.90/249.29 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 248.90/249.29 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 248.90/249.29 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 248.90/249.29 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 248.90/249.29 Found (x5 x40) as proof of (cNUMBER Xn)
% 248.90/249.29 Found (x5 x40) as proof of (cNUMBER Xn)
% 248.90/249.29 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 248.90/249.29 Found (fun (x9:(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))
% 248.90/249.29 Found x50:(cNUMBER Xn00)
% 248.90/249.29 Instantiate: Xn00:=Xn:fofType
% 248.90/249.29 Found (fun (x13:(cODD (cS c0)))=> x50) as proof of (cNUMBER Xn)
% 248.90/249.29 Found (fun (x12:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x13:(cODD (cS c0)))=> x50) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 248.90/249.29 Found (fun (x12:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x13:(cODD (cS c0)))=> x50) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 248.90/249.29 Found x30:(cNUMBER Xn0)
% 248.90/249.29 Instantiate: Xn0:=Xn:fofType
% 248.90/249.29 Found (fun (x13:(cODD (cS c0)))=> x30) as proof of (cNUMBER Xn)
% 248.90/249.29 Found (fun (x12:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x13:(cODD (cS c0)))=> x30) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 248.90/249.29 Found (fun (x12:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x13:(cODD (cS c0)))=> x30) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 248.90/249.29 Found x30:=(x3 x20):(cNUMBER Xn0)
% 248.90/249.29 Instantiate: Xn0:=Xn:fofType
% 248.90/249.29 Found (x3 x20) as proof of (cNUMBER Xn)
% 248.90/249.29 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 248.90/249.29 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))
% 248.90/249.29 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)))
% 248.90/249.29 Found (and_rect40 (fun (x8:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20))) as proof of (cNUMBER Xn)
% 251.69/252.09 Found ((and_rect4 (cNUMBER Xn)) (fun (x8:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20))) as proof of (cNUMBER Xn)
% 251.69/252.09 Found (((fun (P:Type) (x8:(((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) x8) x11)) (cNUMBER Xn)) (fun (x8:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20))) as proof of (cNUMBER Xn)
% 251.69/252.09 Found x80:=(x8 x90):((or (cEVEN Xn00)) (cODD Xn00))
% 251.69/252.09 Found (x8 x90) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 251.69/252.09 Found (x8 x90) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 251.69/252.09 Found (x8 x90) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 251.69/252.09 Found x50:(cNUMBER Xn0)
% 251.69/252.09 Instantiate: Xn00:=Xn0:fofType
% 251.69/252.09 Found x50 as proof of (cNUMBER Xn00)
% 251.69/252.09 Found x70:(cNUMBER Xn00)
% 251.69/252.09 Instantiate: Xn0:=Xn00:fofType
% 251.69/252.09 Found x70 as proof of (cNUMBER Xn0)
% 251.69/252.09 Found x60:=(x6 x70):((or (cEVEN Xn00)) (cODD Xn00))
% 251.69/252.09 Instantiate: Xn00:=Xn:fofType
% 251.69/252.09 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 251.69/252.09 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 251.69/252.09 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 251.69/252.09 Instantiate: Xn0:=Xn00:fofType
% 251.69/252.09 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 251.69/252.09 Found x40:=(x4 x50):((or (cEVEN Xn0)) (cODD Xn0))
% 251.69/252.09 Instantiate: Xn0:=Xn:fofType
% 251.69/252.09 Found (x4 x50) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 251.69/252.09 Found (x4 x50) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 251.69/252.09 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 251.69/252.09 Instantiate: Xn00:=Xn0:fofType
% 251.69/252.09 Found x40 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 251.69/252.09 Found x70:(cNUMBER Xn00)
% 251.69/252.09 Instantiate: Xn00:=Xn:fofType
% 251.69/252.09 Found x70 as proof of (cNUMBER Xn)
% 251.69/252.09 Found x50:(cNUMBER Xn0)
% 251.69/252.09 Instantiate: Xn0:=Xn:fofType
% 251.69/252.09 Found x50 as proof of (cNUMBER Xn)
% 251.69/252.09 Found x61:((or (cEVEN Xn0)) (cODD Xn0))
% 251.69/252.09 Found x61 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 251.69/252.09 Found (x7 x61) as proof of (cNUMBER Xn)
% 251.69/252.09 Found (x7 x61) as proof of (cNUMBER Xn)
% 251.69/252.09 Found (x7 x61) as proof of (cNUMBER Xn)
% 251.69/252.09 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 251.69/252.09 Instantiate: Xn0:=Xn:fofType
% 251.69/252.09 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 251.69/252.09 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x2 x30)) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 251.69/252.09 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(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)))
% 251.69/252.09 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x2 x30)) as proof of (((and ((and (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))))
% 251.69/252.09 Found x60:=(x6 x70):((or (cEVEN Xn00)) (cODD Xn00))
% 251.69/252.09 Instantiate: Xn00:=Xn:fofType
% 251.69/252.09 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 251.69/252.09 Found (fun (x9:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x6 x70)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 251.69/252.09 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x9:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x6 x70)) as proof of ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 251.69/252.09 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x9:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x6 x70)) as proof of (((and ((and (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))))
% 253.41/253.83 Found x30:=(x3 x21):(cNUMBER Xn0)
% 253.41/253.83 Instantiate: Xn0:=Xn:fofType
% 253.41/253.83 Found (x3 x21) as proof of (cNUMBER Xn)
% 253.41/253.83 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x21)) as proof of (cNUMBER Xn)
% 253.41/253.83 Found (fun (x11:(cEVEN c0)) (x12:(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))
% 253.41/253.83 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x21)) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 253.41/253.83 Found (and_rect50 (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x21))) as proof of (cNUMBER Xn)
% 253.41/253.83 Found ((and_rect5 (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x21))) as proof of (cNUMBER Xn)
% 253.41/253.83 Found (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x21))) as proof of (cNUMBER Xn)
% 253.41/253.83 Found (fun (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x21)))) as proof of (cNUMBER Xn)
% 253.41/253.83 Found (fun (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x21)))) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 253.41/253.83 Found x30:(cNUMBER Xn0)
% 253.41/253.83 Found x30 as proof of (cNUMBER Xn0)
% 253.41/253.83 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 253.41/253.83 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 253.41/253.83 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 253.41/253.83 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 253.41/253.83 Instantiate: Xn0:=Xn00:fofType
% 253.41/253.83 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 253.41/253.83 Found x90:=(x9 x80):(cNUMBER Xn0)
% 253.41/253.83 Found (x9 x80) as proof of (cNUMBER Xn0)
% 253.41/253.83 Found (x9 x80) as proof of (cNUMBER Xn0)
% 253.41/253.83 Found x90:=(x9 x81):(cNUMBER Xn0)
% 253.41/253.83 Instantiate: Xn0:=Xn:fofType
% 253.41/253.83 Found (x9 x81) as proof of (cNUMBER Xn)
% 253.41/253.83 Found (x9 x81) as proof of (cNUMBER Xn)
% 253.41/253.83 Found x90:=(x9 x81):(cNUMBER Xn0)
% 253.41/253.83 Found (x9 x81) as proof of (cNUMBER Xn)
% 253.41/253.83 Found (x9 x81) as proof of (cNUMBER Xn)
% 253.41/253.83 Found (x9 x81) as proof of (cNUMBER Xn)
% 253.41/253.83 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 253.41/253.83 Instantiate: Xn00:=Xn0:fofType
% 253.41/253.83 Found x40 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 253.41/253.83 Found x50:(cNUMBER Xn00)
% 253.41/253.83 Found x50 as proof of (cNUMBER Xn00)
% 253.41/253.83 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 253.41/253.83 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 253.41/253.83 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 253.41/253.83 Found x30:(cNUMBER Xn0)
% 253.41/253.83 Instantiate: Xn00:=Xn0:fofType
% 253.41/253.83 Found x30 as proof of (cNUMBER Xn00)
% 253.41/253.83 Found x30:=(x3 x21):(cNUMBER Xn0)
% 253.41/253.83 Instantiate: Xn0:=Xn:fofType
% 253.41/253.83 Found (x3 x21) as proof of (cNUMBER Xn)
% 253.41/253.83 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x21)) as proof of (cNUMBER Xn)
% 253.41/253.83 Found (fun (x11:(cEVEN c0)) (x12:(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))
% 253.41/253.83 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x21)) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 253.41/253.83 Found (and_rect50 (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x21))) as proof of (cNUMBER Xn)
% 256.41/256.80 Found ((and_rect5 (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x21))) as proof of (cNUMBER Xn)
% 256.41/256.80 Found (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x21))) as proof of (cNUMBER Xn)
% 256.41/256.80 Found (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x21))) as proof of (cNUMBER Xn)
% 256.41/256.80 Found x41:((or (cEVEN Xn0)) (cODD Xn0))
% 256.41/256.80 Found x41 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 256.41/256.80 Found (x5 x41) as proof of (cNUMBER Xn)
% 256.41/256.80 Found (x5 x41) as proof of (cNUMBER Xn)
% 256.41/256.80 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x41)) as proof of (cNUMBER Xn)
% 256.41/256.80 Found (fun (x12:(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))
% 256.41/256.80 Found x41:((or (cEVEN Xn0)) (cODD Xn0))
% 256.41/256.80 Found x41 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 256.41/256.80 Found (x5 x41) as proof of (cNUMBER Xn)
% 256.41/256.80 Found (x5 x41) as proof of (cNUMBER Xn)
% 256.41/256.80 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x41)) as proof of (cNUMBER Xn)
% 256.41/256.80 Found (fun (x11:(cEVEN c0)) (x12:(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))
% 256.41/256.80 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x41)) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 256.41/256.80 Found x80:=(x8 x90):((or (cEVEN Xn00)) (cODD Xn00))
% 256.41/256.80 Instantiate: Xn00:=Xn:fofType
% 256.41/256.80 Found (x8 x90) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 256.41/256.80 Found (x8 x90) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 256.41/256.80 Found x41:((or (cEVEN Xn0)) (cODD Xn0))
% 256.41/256.80 Found x41 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 256.41/256.80 Found (x5 x41) as proof of (cNUMBER Xn)
% 256.41/256.80 Found (x5 x41) as proof of (cNUMBER Xn)
% 256.41/256.80 Found (x5 x41) as proof of (cNUMBER Xn)
% 256.41/256.80 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 256.41/256.80 Instantiate: Xn0:=Xn:fofType
% 256.41/256.80 Found x40 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 256.41/256.80 Found (x9 x40) as proof of (cNUMBER Xn)
% 256.41/256.80 Found (x9 x40) as proof of (cNUMBER Xn)
% 256.41/256.80 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x9 x40)) as proof of (cNUMBER Xn)
% 256.41/256.80 Found (fun (x8:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x9 x40)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 256.41/256.80 Found (fun (x8:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x9 x40)) as proof of (((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))->((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn)))
% 256.41/256.80 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 256.41/256.80 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 256.41/256.80 Found (x5 x40) as proof of (cNUMBER Xn)
% 256.41/256.80 Found (x5 x40) as proof of (cNUMBER Xn)
% 256.41/256.80 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 256.41/256.80 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))
% 256.41/256.80 Found (fun (x8:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x9:(((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)))
% 256.41/256.80 Found x70:=(x7 x60):(cNUMBER Xn0)
% 256.41/256.80 Found (x7 x60) as proof of (cNUMBER Xn0)
% 256.41/256.80 Found (x7 x60) as proof of (cNUMBER Xn0)
% 257.37/257.81 Found x70:=(x7 x61):(cNUMBER Xn0)
% 257.37/257.81 Instantiate: Xn0:=Xn:fofType
% 257.37/257.81 Found (x7 x61) as proof of (cNUMBER Xn)
% 257.37/257.81 Found (x7 x61) as proof of (cNUMBER Xn)
% 257.37/257.81 Found x70:=(x7 x61):(cNUMBER Xn0)
% 257.37/257.81 Found (x7 x61) as proof of (cNUMBER Xn)
% 257.37/257.81 Found (x7 x61) as proof of (cNUMBER Xn)
% 257.37/257.81 Found (x7 x61) as proof of (cNUMBER Xn)
% 257.37/257.81 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 257.37/257.81 Instantiate: Xn0:=Xn00:fofType
% 257.37/257.81 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 257.37/257.81 Found x41:((or (cEVEN Xn0)) (cODD Xn0))
% 257.37/257.81 Found x41 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 257.37/257.81 Found (x5 x41) as proof of (cNUMBER Xn)
% 257.37/257.81 Found (x5 x41) as proof of (cNUMBER Xn)
% 257.37/257.81 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x41)) as proof of (cNUMBER Xn)
% 257.37/257.81 Found (fun (x6:((and ((and (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 x41)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 257.37/257.81 Found (fun (x6:((and ((and (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 x41)) as proof of (((and ((and (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)))
% 257.37/257.81 Found x41:((or (cEVEN Xn0)) (cODD Xn0))
% 257.37/257.81 Found x41 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 257.37/257.81 Found (x5 x41) as proof of (cNUMBER Xn)
% 257.37/257.81 Found (x5 x41) as proof of (cNUMBER Xn)
% 257.37/257.81 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x41)) as proof of (cNUMBER Xn)
% 257.37/257.81 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x41)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 257.37/257.81 Found x41:((or (cEVEN Xn0)) (cODD Xn0))
% 257.37/257.81 Found x41 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 257.37/257.81 Found (x5 x41) as proof of (cNUMBER Xn)
% 257.37/257.81 Found (x5 x41) as proof of (cNUMBER Xn)
% 257.37/257.81 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x41)) as proof of (cNUMBER Xn)
% 257.37/257.81 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x41)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 257.37/257.81 Found x50:(cNUMBER Xn00)
% 257.37/257.81 Instantiate: Xn0:=Xn00:fofType
% 257.37/257.81 Found x50 as proof of (cNUMBER Xn0)
% 257.37/257.81 Found x7:(cODD (cS c0))
% 257.37/257.81 Instantiate: Xn0:=(cS c0):fofType
% 257.37/257.81 Found x7 as proof of (cODD Xn0)
% 257.37/257.81 Found (or_introl00 x7) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 257.37/257.81 Found ((or_introl0 (cEVEN Xn0)) x7) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 257.37/257.81 Found (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 257.37/257.81 Found (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 257.37/257.81 Found (or_comm_i00 (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 257.37/257.81 Found ((or_comm_i0 (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 257.37/257.81 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 257.37/257.81 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 257.37/257.81 Found x30:=(x3 x21):(cNUMBER Xn0)
% 257.37/257.81 Instantiate: Xn0:=Xn:fofType
% 257.37/257.81 Found (x3 x21) as proof of (cNUMBER Xn)
% 257.37/257.81 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x21)) as proof of (cNUMBER Xn)
% 257.37/257.81 Found (fun (x11:(cEVEN c0)) (x12:(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))
% 257.37/257.81 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x21)) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 257.37/257.81 Found (and_rect50 (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x21))) as proof of (cNUMBER Xn)
% 257.37/257.81 Found ((and_rect5 (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x21))) as proof of (cNUMBER Xn)
% 258.89/259.32 Found (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x21))) as proof of (cNUMBER Xn)
% 258.89/259.32 Found (fun (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x21)))) as proof of (cNUMBER Xn)
% 258.89/259.32 Found (fun (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x21)))) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 258.89/259.32 Found x40:=(x4 x50):((or (cEVEN Xn00)) (cODD Xn00))
% 258.89/259.32 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 258.89/259.32 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 258.89/259.32 Found (fun (x9:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x4 x50)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 258.89/259.32 Found (fun (x9:(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)))
% 258.89/259.32 Found x41:((or (cEVEN Xn0)) (cODD Xn0))
% 258.89/259.32 Found x41 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 258.89/259.32 Found (x5 x41) as proof of (cNUMBER Xn)
% 258.89/259.32 Found (x5 x41) as proof of (cNUMBER Xn)
% 258.89/259.32 Found (x5 x41) as proof of (cNUMBER Xn)
% 258.89/259.32 Found x41:((or (cEVEN Xn0)) (cODD Xn0))
% 258.89/259.32 Found x41 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 258.89/259.32 Found (x5 x41) as proof of (cNUMBER Xn)
% 258.89/259.32 Found (x5 x41) as proof of (cNUMBER Xn)
% 258.89/259.32 Found (x5 x41) as proof of (cNUMBER Xn)
% 258.89/259.32 Found x30:=(x3 x21):(cNUMBER Xn0)
% 258.89/259.32 Instantiate: Xn0:=Xn:fofType
% 258.89/259.32 Found (x3 x21) as proof of (cNUMBER Xn)
% 258.89/259.32 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x21)) as proof of (cNUMBER Xn)
% 258.89/259.32 Found (fun (x11:(cEVEN c0)) (x12:(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))
% 258.89/259.32 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x21)) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 258.89/259.32 Found (and_rect50 (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x21))) as proof of (cNUMBER Xn)
% 258.89/259.32 Found ((and_rect5 (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x21))) as proof of (cNUMBER Xn)
% 258.89/259.32 Found (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x21))) as proof of (cNUMBER Xn)
% 258.89/259.32 Found (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x21))) as proof of (cNUMBER Xn)
% 258.89/259.32 Found x120:=(x12 x110):(cNUMBER Xn0)
% 258.89/259.32 Found (x12 x110) as proof of (cNUMBER Xn0)
% 258.89/259.32 Found (x12 x110) as proof of (cNUMBER Xn0)
% 258.89/259.32 Found x120:=(x12 x111):(cNUMBER Xn0)
% 258.89/259.32 Instantiate: Xn0:=Xn:fofType
% 258.89/259.32 Found (x12 x111) as proof of (cNUMBER Xn)
% 258.89/259.32 Found (x12 x111) as proof of (cNUMBER Xn)
% 259.86/260.28 Found x120:=(x12 x111):(cNUMBER Xn0)
% 259.86/260.28 Found (x12 x111) as proof of (cNUMBER Xn)
% 259.86/260.28 Found (x12 x111) as proof of (cNUMBER Xn)
% 259.86/260.28 Found (x12 x111) as proof of (cNUMBER Xn)
% 259.86/260.28 Found x41:((or (cEVEN Xn0)) (cODD Xn0))
% 259.86/260.28 Found x41 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 259.86/260.28 Found (x5 x41) as proof of (cNUMBER Xn)
% 259.86/260.28 Found (x5 x41) as proof of (cNUMBER Xn)
% 259.86/260.28 Found (x5 x41) as proof of (cNUMBER Xn)
% 259.86/260.28 Found x80:=(x8 x90):((or (cEVEN Xn00)) (cODD Xn00))
% 259.86/260.28 Found (x8 x90) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 259.86/260.28 Found (x8 x90) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 259.86/260.28 Found (x8 x90) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 259.86/260.28 Found x60:=(x6 x70):((or (cEVEN Xn0)) (cODD Xn0))
% 259.86/260.28 Found (x6 x70) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 259.86/260.28 Found (x6 x70) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 259.86/260.28 Found (x6 x70) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 259.86/260.28 Found x30:=(x3 x20):(cNUMBER Xn0)
% 259.86/260.28 Instantiate: Xn0:=Xn:fofType
% 259.86/260.28 Found (x3 x20) as proof of (cNUMBER Xn)
% 259.86/260.28 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 259.86/260.28 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(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))
% 259.86/260.28 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (((and ((and (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)))
% 259.86/260.28 Found (and_rect40 (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 259.86/260.28 Found ((and_rect4 (cNUMBER Xn)) (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 259.86/260.28 Found (((fun (P:Type) (x8:(((and ((and (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 (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x8) x4)) (cNUMBER Xn)) (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 259.86/260.28 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (((fun (P:Type) (x8:(((and ((and (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 (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x8) x4)) (cNUMBER Xn)) (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)))) as proof of (cNUMBER Xn)
% 259.86/260.28 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (((fun (P:Type) (x8:(((and ((and (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 (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x8) x4)) (cNUMBER Xn)) (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)))) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 260.14/260.54 Found x30:=(x3 x21):(cNUMBER Xn0)
% 260.14/260.54 Instantiate: Xn0:=Xn:fofType
% 260.14/260.54 Found (x3 x21) as proof of (cNUMBER Xn)
% 260.14/260.54 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21)) as proof of (cNUMBER Xn)
% 260.14/260.54 Found (fun (x6:((and ((and (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 x21)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 260.14/260.54 Found (fun (x6:((and ((and (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 x21)) as proof of (((and ((and (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)))
% 260.14/260.54 Found (and_rect30 (fun (x6:((and ((and (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 x21))) as proof of (cNUMBER Xn)
% 260.14/260.54 Found ((and_rect3 (cNUMBER Xn)) (fun (x6:((and ((and (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 x21))) as proof of (cNUMBER Xn)
% 260.14/260.54 Found (((fun (P:Type) (x6:(((and ((and (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 (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) x4)) (cNUMBER Xn)) (fun (x6:((and ((and (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 x21))) as proof of (cNUMBER Xn)
% 260.14/260.54 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (((fun (P:Type) (x6:(((and ((and (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 (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) x4)) (cNUMBER Xn)) (fun (x6:((and ((and (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 x21)))) as proof of (cNUMBER Xn)
% 260.14/260.54 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (((fun (P:Type) (x6:(((and ((and (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 (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) x4)) (cNUMBER Xn)) (fun (x6:((and ((and (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 x21)))) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 260.37/260.81 Found (fun (x4:((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))) (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (((fun (P:Type) (x6:(((and ((and (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 (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) x4)) (cNUMBER Xn)) (fun (x6:((and ((and (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 x21)))) as proof of (((and ((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))->((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn)))
% 260.37/260.81 Found x70:=(x7 x60):(cNUMBER Xn00)
% 260.37/260.81 Instantiate: Xn00:=Xn:fofType
% 260.37/260.81 Found (x7 x60) as proof of (cNUMBER Xn)
% 260.37/260.81 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x7 x60)) as proof of (cNUMBER Xn)
% 260.37/260.81 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x7 x60)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 260.37/260.81 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x7 x60)) as proof of (((and ((and (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)))
% 260.37/260.81 Found (and_rect40 (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x7 x60))) as proof of (cNUMBER Xn)
% 260.37/260.81 Found ((and_rect4 (cNUMBER Xn)) (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x7 x60))) as proof of (cNUMBER Xn)
% 260.37/260.81 Found (((fun (P:Type) (x8:(((and ((and (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 (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x8) x4)) (cNUMBER Xn)) (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x7 x60))) as proof of (cNUMBER Xn)
% 260.37/260.81 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (((fun (P:Type) (x8:(((and ((and (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 (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x8) x4)) (cNUMBER Xn)) (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x7 x60)))) as proof of (cNUMBER Xn)
% 262.18/262.59 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (((fun (P:Type) (x8:(((and ((and (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 (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x8) x4)) (cNUMBER Xn)) (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x7 x60)))) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 262.18/262.59 Found x50:=(x5 x40):(cNUMBER Xn00)
% 262.18/262.59 Instantiate: Xn0:=Xn00:fofType
% 262.18/262.59 Found (x5 x40) as proof of (cNUMBER Xn0)
% 262.18/262.59 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of (cNUMBER Xn0)
% 262.18/262.59 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn0))
% 262.18/262.59 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 262.18/262.59 Instantiate: Xn00:=Xn0:fofType
% 262.18/262.59 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 262.18/262.59 Found x70:(cNUMBER Xn00)
% 262.18/262.59 Instantiate: Xn00:=Xn:fofType
% 262.18/262.59 Found x70 as proof of (cNUMBER Xn)
% 262.18/262.59 Found x90:=(x9 x81):(cNUMBER Xn0)
% 262.18/262.59 Found (x9 x81) as proof of (cNUMBER Xn)
% 262.18/262.59 Found (x9 x81) as proof of (cNUMBER Xn)
% 262.18/262.59 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x9 x81)) as proof of (cNUMBER Xn)
% 262.18/262.59 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x9 x81)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 262.18/262.59 Found x30:(cNUMBER Xn0)
% 262.18/262.59 Instantiate: Xn00:=Xn0:fofType
% 262.18/262.59 Found x30 as proof of (cNUMBER Xn00)
% 262.18/262.59 Found x30:(cNUMBER Xn0)
% 262.18/262.59 Instantiate: Xn0:=Xn:fofType
% 262.18/262.59 Found x30 as proof of (cNUMBER Xn)
% 262.18/262.59 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 262.18/262.59 Instantiate: Xn0:=Xn00:fofType
% 262.18/262.59 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 262.18/262.59 Found x70:(cNUMBER Xn00)
% 262.18/262.59 Instantiate: Xn0:=Xn00:fofType
% 262.18/262.59 Found x70 as proof of (cNUMBER Xn0)
% 262.18/262.59 Found x40:=(x4 x50):((or (cEVEN Xn00)) (cODD Xn00))
% 262.18/262.59 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 262.18/262.59 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 262.18/262.59 Found (fun (x9:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x4 x50)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 262.18/262.59 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x9:(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)))
% 262.18/262.59 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x9:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x4 x50)) as proof of (((and ((and (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))))
% 262.18/262.59 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 262.18/262.59 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 262.18/262.59 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 262.18/262.59 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x2 x30)) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 262.18/262.59 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(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)))
% 262.18/262.59 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x2 x30)) as proof of (((and ((and (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))))
% 264.16/264.56 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 264.16/264.56 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 264.16/264.56 Found (x3 x20) as proof of (cNUMBER Xn)
% 264.16/264.56 Found (x3 x20) as proof of (cNUMBER Xn)
% 264.16/264.56 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 264.16/264.56 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 264.16/264.56 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 264.16/264.56 Instantiate: Xn0:=Xn:fofType
% 264.16/264.56 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 264.16/264.56 Found (x5 x20) as proof of (cNUMBER Xn)
% 264.16/264.56 Found (x5 x20) as proof of (cNUMBER Xn)
% 264.16/264.56 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x20)) as proof of (cNUMBER Xn)
% 264.16/264.56 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x20)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 264.16/264.56 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 264.16/264.56 Instantiate: Xn0:=Xn00:fofType
% 264.16/264.56 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 264.16/264.56 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 264.16/264.56 Instantiate: Xn00:=Xn0:fofType
% 264.16/264.56 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 264.16/264.56 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 264.16/264.56 Instantiate: Xn0:=Xn00:fofType
% 264.16/264.56 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 264.16/264.56 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 264.16/264.56 Instantiate: Xn00:=Xn0:fofType
% 264.16/264.56 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 264.16/264.56 Found x60:=(x6 x70):((or (cEVEN Xn00)) (cODD Xn00))
% 264.16/264.56 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 264.16/264.56 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 264.16/264.56 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 264.16/264.56 Found x30:(cNUMBER Xn0)
% 264.16/264.56 Instantiate: Xn0:=Xn:fofType
% 264.16/264.56 Found (fun (x13:(cODD (cS c0)))=> x30) as proof of (cNUMBER Xn)
% 264.16/264.56 Found (fun (x13:(cODD (cS c0)))=> x30) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 264.16/264.56 Found x50:(cNUMBER Xn00)
% 264.16/264.56 Instantiate: Xn0:=Xn00:fofType
% 264.16/264.56 Found x50 as proof of (cNUMBER Xn0)
% 264.16/264.56 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 264.16/264.56 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 264.16/264.56 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 264.16/264.56 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 264.16/264.56 Found x70:(cNUMBER Xn00)
% 264.16/264.56 Instantiate: Xn00:=Xn:fofType
% 264.16/264.56 Found (fun (x13:(cODD (cS c0)))=> x70) as proof of (cNUMBER Xn)
% 264.16/264.56 Found (fun (x13:(cODD (cS c0)))=> x70) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 264.16/264.56 Found x60:=(x6 x70):((or (cEVEN Xn00)) (cODD Xn00))
% 264.16/264.56 Instantiate: Xn00:=Xn:fofType
% 264.16/264.56 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 264.16/264.56 Found (fun (x9:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x6 x70)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 264.16/264.56 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x9:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x6 x70)) as proof of ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 264.16/264.56 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x9:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x6 x70)) as proof of (((and ((and (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))))
% 264.16/264.56 Found x40:=(x4 x50):((or (cEVEN Xn00)) (cODD Xn00))
% 264.16/264.56 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 264.16/264.56 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 264.16/264.56 Found (fun (x9:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x4 x50)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 264.16/264.56 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x9:(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)))
% 264.16/264.56 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x9:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x4 x50)) as proof of (((and ((and (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))))
% 264.89/265.27 Found x30:=(x3 x21):(cNUMBER Xn0)
% 264.89/265.27 Instantiate: Xn0:=Xn:fofType
% 264.89/265.27 Found (x3 x21) as proof of (cNUMBER Xn)
% 264.89/265.27 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21)) as proof of (cNUMBER Xn)
% 264.89/265.27 Found (fun (x6:((and ((and (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 x21)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 264.89/265.27 Found (fun (x6:((and ((and (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 x21)) as proof of (((and ((and (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)))
% 264.89/265.27 Found (and_rect30 (fun (x6:((and ((and (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 x21))) as proof of (cNUMBER Xn)
% 264.89/265.27 Found ((and_rect3 (cNUMBER Xn)) (fun (x6:((and ((and (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 x21))) as proof of (cNUMBER Xn)
% 264.89/265.27 Found (((fun (P:Type) (x6:(((and ((and (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 (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) x4)) (cNUMBER Xn)) (fun (x6:((and ((and (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 x21))) as proof of (cNUMBER Xn)
% 264.89/265.27 Found (((fun (P:Type) (x6:(((and ((and (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 (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) x4)) (cNUMBER Xn)) (fun (x6:((and ((and (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 x21))) as proof of (cNUMBER Xn)
% 264.89/265.27 Found x80:=(x8 x90):((or (cEVEN Xn00)) (cODD Xn00))
% 264.89/265.27 Found (x8 x90) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 264.89/265.27 Found (x8 x90) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 264.89/265.27 Found (x8 x90) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 264.89/265.27 Found x30:=(x3 x21):(cNUMBER Xn0)
% 264.89/265.27 Instantiate: Xn0:=Xn:fofType
% 264.89/265.27 Found (x3 x21) as proof of (cNUMBER Xn)
% 264.89/265.27 Found (fun (x4:(cEVEN Xn0))=> (x3 x21)) as proof of (cNUMBER Xn)
% 264.89/265.27 Found (fun (x4:(cEVEN Xn0))=> (x3 x21)) as proof of ((cEVEN Xn0)->(cNUMBER Xn))
% 264.89/265.27 Found x30:=(x3 x21):(cNUMBER Xn0)
% 264.89/265.27 Instantiate: Xn0:=Xn:fofType
% 264.89/265.27 Found (x3 x21) as proof of (cNUMBER Xn)
% 264.89/265.27 Found (fun (x4:(cODD Xn0))=> (x3 x21)) as proof of (cNUMBER Xn)
% 264.89/265.27 Found (fun (x4:(cODD Xn0))=> (x3 x21)) as proof of ((cODD Xn0)->(cNUMBER Xn))
% 264.89/265.27 Found ((or_ind00 (fun (x4:(cEVEN Xn0))=> (x3 x21))) (fun (x4:(cODD Xn0))=> (x3 x21))) as proof of (cNUMBER Xn)
% 264.89/265.27 Found (((or_ind0 (cNUMBER Xn)) (fun (x4:(cEVEN Xn0))=> (x3 x21))) (fun (x4:(cODD Xn0))=> (x3 x21))) as proof of (cNUMBER Xn)
% 264.89/265.27 Found ((((fun (P:Prop) (x4:((cEVEN Xn0)->P)) (x5:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x4) x5) x21)) (cNUMBER Xn)) (fun (x4:(cEVEN Xn0))=> (x3 x21))) (fun (x4:(cODD Xn0))=> (x3 x21))) as proof of (cNUMBER Xn)
% 266.99/267.40 Found ((((fun (P:Prop) (x4:((cEVEN Xn0)->P)) (x5:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x4) x5) x21)) (cNUMBER Xn)) (fun (x4:(cEVEN Xn0))=> (x3 x21))) (fun (x4:(cODD Xn0))=> (x3 x21))) as proof of (cNUMBER Xn)
% 266.99/267.40 Found x30:=(x3 x21):(cNUMBER Xn0)
% 266.99/267.40 Instantiate: Xn0:=Xn:fofType
% 266.99/267.40 Found (x3 x21) as proof of (cNUMBER Xn)
% 266.99/267.40 Found (fun (x4:(cEVEN Xn0))=> (x3 x21)) as proof of (cNUMBER Xn)
% 266.99/267.40 Found (fun (x4:(cEVEN Xn0))=> (x3 x21)) as proof of ((cEVEN Xn0)->(cNUMBER Xn))
% 266.99/267.40 Found x30:=(x3 x21):(cNUMBER Xn0)
% 266.99/267.40 Instantiate: Xn0:=Xn:fofType
% 266.99/267.40 Found (x3 x21) as proof of (cNUMBER Xn)
% 266.99/267.40 Found (fun (x4:(cODD Xn0))=> (x3 x21)) as proof of (cNUMBER Xn)
% 266.99/267.40 Found (fun (x4:(cODD Xn0))=> (x3 x21)) as proof of ((cODD Xn0)->(cNUMBER Xn))
% 266.99/267.40 Found ((or_ind00 (fun (x4:(cEVEN Xn0))=> (x3 x21))) (fun (x4:(cODD Xn0))=> (x3 x21))) as proof of (cNUMBER Xn)
% 266.99/267.40 Found (((or_ind0 (cNUMBER Xn)) (fun (x4:(cEVEN Xn0))=> (x3 x21))) (fun (x4:(cODD Xn0))=> (x3 x21))) as proof of (cNUMBER Xn)
% 266.99/267.40 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)
% 266.99/267.40 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)
% 266.99/267.40 Found x50:(cNUMBER Xn00)
% 266.99/267.40 Instantiate: Xn0:=Xn00:fofType
% 266.99/267.40 Found x50 as proof of (cNUMBER Xn0)
% 266.99/267.40 Found x30:(cNUMBER Xn0)
% 266.99/267.40 Instantiate: Xn00:=Xn0:fofType
% 266.99/267.40 Found x30 as proof of (cNUMBER Xn00)
% 266.99/267.40 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 266.99/267.40 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 266.99/267.40 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 266.99/267.40 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x2 x30)) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 266.99/267.40 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(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)))
% 266.99/267.40 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x2 x30)) as proof of (((and ((and (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))))
% 266.99/267.40 Found x60:=(x6 x70):((or (cEVEN Xn00)) (cODD Xn00))
% 266.99/267.40 Instantiate: Xn00:=Xn:fofType
% 266.99/267.40 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 266.99/267.40 Found (fun (x9:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x6 x70)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 266.99/267.40 Found (fun (x9:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x6 x70)) as proof of ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 266.99/267.40 Found x40:=(x4 x50):((or (cEVEN Xn0)) (cODD Xn0))
% 266.99/267.40 Instantiate: Xn0:=Xn:fofType
% 266.99/267.40 Found (x4 x50) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 266.99/267.40 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x4 x50)) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 266.99/267.40 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x4 x50)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->((or (cEVEN Xn00)) (cODD Xn00)))
% 266.99/267.40 Found x60:=(x6 x70):((or (cEVEN Xn00)) (cODD Xn00))
% 266.99/267.40 Instantiate: Xn00:=Xn:fofType
% 266.99/267.40 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 266.99/267.40 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 266.99/267.40 Found x30:(cNUMBER Xn0)
% 266.99/267.40 Found x30 as proof of (cNUMBER Xn0)
% 266.99/267.40 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 266.99/267.40 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 266.99/267.40 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 266.99/267.40 Found x60:=(x6 x70):((or (cEVEN Xn00)) (cODD Xn00))
% 266.99/267.40 Instantiate: Xn00:=Xn:fofType
% 267.19/267.59 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 267.19/267.59 Found (fun (x9:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x6 x70)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 267.19/267.59 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x9:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x6 x70)) as proof of ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 267.19/267.59 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x9:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x6 x70)) as proof of (((and ((and (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))))
% 267.19/267.59 Found x50:(cNUMBER Xn00)
% 267.19/267.59 Found x50 as proof of (cNUMBER Xn00)
% 267.19/267.59 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 267.19/267.59 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 267.19/267.59 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 267.19/267.59 Found x31:(cNUMBER Xn0)
% 267.19/267.59 Instantiate: Xn0:=Xn:fofType
% 267.19/267.59 Found (fun (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x31) as proof of (cNUMBER Xn)
% 267.19/267.59 Found (fun (x7:(cEVEN Xn0)) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x31) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 267.19/267.59 Found (fun (x7:(cEVEN Xn0)) (x8:(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)))
% 267.19/267.59 Found x31:(cNUMBER Xn0)
% 267.19/267.59 Instantiate: Xn0:=Xn:fofType
% 267.19/267.59 Found (fun (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x31) as proof of (cNUMBER Xn)
% 267.19/267.59 Found (fun (x7:(cODD Xn0)) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x31) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 267.19/267.59 Found (fun (x7:(cODD Xn0)) (x8:(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)))
% 267.19/267.59 Found ((or_ind00 (fun (x7:(cEVEN Xn0)) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x31)) (fun (x7:(cODD Xn0)) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x31)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 267.19/267.59 Found (((or_ind0 ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))) (fun (x7:(cEVEN Xn0)) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x31)) (fun (x7:(cODD Xn0)) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x31)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 267.19/267.59 Found ((((fun (P:Prop) (x7:((cEVEN Xn0)->P)) (x8:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x7) x8) x20)) ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->(cNUMBER Xn))) (fun (x7:(cEVEN Xn0)) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x31)) (fun (x7:(cODD Xn0)) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x31)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 267.19/267.59 Found ((((fun (P:Prop) (x7:((cEVEN Xn0)->P)) (x8:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x7) x8) (x2 x31))) ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->(cNUMBER Xn))) (fun (x7:(cEVEN Xn0)) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x31)) (fun (x7:(cODD Xn0)) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x31)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 267.19/267.59 Found ((((fun (P:Prop) (x7:((cEVEN Xn0)->P)) (x8:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x7) x8) (x2 x31))) ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->(cNUMBER Xn))) (fun (x7:(cEVEN Xn0)) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x31)) (fun (x7:(cODD Xn0)) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x31)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 267.37/267.75 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 267.37/267.75 Instantiate: Xn0:=Xn:fofType
% 267.37/267.75 Found x40 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 267.37/267.75 Found (x7 x40) as proof of (cNUMBER Xn)
% 267.37/267.75 Found (x7 x40) as proof of (cNUMBER Xn)
% 267.37/267.75 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x7 x40)) as proof of (cNUMBER Xn)
% 267.37/267.75 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x7 x40)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 267.37/267.75 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x7 x40)) as proof of (((and ((and (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)))
% 267.37/267.75 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 267.37/267.75 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 267.37/267.75 Found (x5 x40) as proof of (cNUMBER Xn)
% 267.37/267.75 Found (x5 x40) as proof of (cNUMBER Xn)
% 267.37/267.75 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 267.37/267.75 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(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))
% 267.37/267.75 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (((and ((and (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)))
% 267.37/267.75 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 267.37/267.75 Instantiate: Xn00:=Xn:fofType
% 267.37/267.75 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 267.37/267.75 Found (x5 x60) as proof of (cNUMBER Xn)
% 267.37/267.75 Found (x5 x60) as proof of (cNUMBER Xn)
% 267.37/267.75 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x60)) as proof of (cNUMBER Xn)
% 267.37/267.75 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x60)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 267.37/267.75 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x60)) as proof of (((and ((and (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)))
% 267.37/267.75 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 267.37/267.75 Found x60 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 267.37/267.75 Found (x7 x60) as proof of (cNUMBER Xn)
% 267.37/267.75 Found (x7 x60) as proof of (cNUMBER Xn)
% 267.37/267.75 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x7 x60)) as proof of (cNUMBER Xn)
% 267.37/267.75 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x7 x60)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 267.37/267.75 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x7 x60)) as proof of (((and ((and (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)))
% 267.77/268.17 Found x80:=(x8 x90):((or (cEVEN Xn00)) (cODD Xn00))
% 267.77/268.17 Found (x8 x90) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 267.77/268.17 Found (x8 x90) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 267.77/268.17 Found (x8 x90) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 267.77/268.17 Found x31:(cNUMBER Xn0)
% 267.77/268.17 Instantiate: Xn0:=Xn:fofType
% 267.77/268.17 Found (fun (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x31) as proof of (cNUMBER Xn)
% 267.77/268.17 Found (fun (x7:(cEVEN Xn0)) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x31) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 267.77/268.17 Found (fun (x7:(cEVEN Xn0)) (x8:(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)))
% 267.77/268.17 Found x31:(cNUMBER Xn0)
% 267.77/268.17 Instantiate: Xn0:=Xn:fofType
% 267.77/268.17 Found (fun (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x31) as proof of (cNUMBER Xn)
% 267.77/268.17 Found (fun (x7:(cODD Xn0)) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x31) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 267.77/268.17 Found (fun (x7:(cODD Xn0)) (x8:(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)))
% 267.77/268.17 Found ((or_ind00 (fun (x7:(cEVEN Xn0)) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x31)) (fun (x7:(cODD Xn0)) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x31)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 267.77/268.17 Found (((or_ind0 ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))) (fun (x7:(cEVEN Xn0)) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x31)) (fun (x7:(cODD Xn0)) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x31)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 267.77/268.17 Found ((((fun (P:Prop) (x7:((cEVEN Xn0)->P)) (x8:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x7) x8) x20)) ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->(cNUMBER Xn))) (fun (x7:(cEVEN Xn0)) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x31)) (fun (x7:(cODD Xn0)) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x31)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 267.77/268.17 Found ((((fun (P:Prop) (x7:((cEVEN Xn0)->P)) (x8:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x7) x8) (x2 x31))) ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->(cNUMBER Xn))) (fun (x7:(cEVEN Xn0)) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x31)) (fun (x7:(cODD Xn0)) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x31)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 267.77/268.17 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))))=> ((((fun (P:Prop) (x7:((cEVEN Xn0)->P)) (x8:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x7) x8) (x2 x31))) ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->(cNUMBER Xn))) (fun (x7:(cEVEN Xn0)) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x31)) (fun (x7:(cODD Xn0)) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x31))) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 267.77/268.17 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))))=> ((((fun (P:Prop) (x7:((cEVEN Xn0)->P)) (x8:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x7) x8) (x2 x31))) ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->(cNUMBER Xn))) (fun (x7:(cEVEN Xn0)) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x31)) (fun (x7:(cODD Xn0)) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x31))) as proof of (((and ((and (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)))
% 268.31/268.69 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 268.31/268.69 Instantiate: Xn00:=Xn0:fofType
% 268.31/268.69 Found x40 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 268.31/268.69 Found x30:=(x3 x20):(cNUMBER Xn0)
% 268.31/268.69 Instantiate: Xn0:=Xn:fofType
% 268.31/268.69 Found (x3 x20) as proof of (cNUMBER Xn)
% 268.31/268.69 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 268.31/268.69 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))
% 268.31/268.69 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)))
% 268.31/268.69 Found (and_rect40 (fun (x8:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20))) as proof of (cNUMBER Xn)
% 268.31/268.69 Found ((and_rect4 (cNUMBER Xn)) (fun (x8:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20))) as proof of (cNUMBER Xn)
% 268.31/268.69 Found (((fun (P:Type) (x8:(((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) x8) x11)) (cNUMBER Xn)) (fun (x8:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20))) as proof of (cNUMBER Xn)
% 268.31/268.69 Found x70:(cNUMBER Xn00)
% 268.31/268.69 Instantiate: Xn00:=Xn:fofType
% 268.31/268.69 Found x70 as proof of (cNUMBER Xn)
% 268.31/268.69 Found x9:(cEVEN c0)
% 268.31/268.69 Instantiate: Xn0:=c0:fofType
% 268.31/268.69 Found x9 as proof of (cEVEN Xn0)
% 268.31/268.69 Found (or_intror00 x9) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 268.31/268.69 Found ((or_intror0 (cEVEN Xn0)) x9) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 268.31/268.69 Found (((or_intror (cODD Xn0)) (cEVEN Xn0)) x9) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 268.31/268.69 Found (fun (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_intror (cODD Xn0)) (cEVEN Xn0)) x9)) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 268.31/268.69 Found (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_intror (cODD Xn0)) (cEVEN Xn0)) x9)) as proof of ((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->((or (cODD Xn0)) (cEVEN Xn0)))
% 268.31/268.69 Found (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_intror (cODD Xn0)) (cEVEN Xn0)) x9)) as proof of ((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->((or (cODD Xn0)) (cEVEN Xn0))))
% 268.31/268.69 Found (and_rect50 (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_intror (cODD Xn0)) (cEVEN Xn0)) x9))) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 268.31/268.69 Found ((and_rect5 ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_intror (cODD Xn0)) (cEVEN Xn0)) x9))) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 268.31/268.69 Found (((fun (P:Type) (x9:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x9) x8)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_intror (cODD Xn0)) (cEVEN Xn0)) x9))) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 268.31/268.69 Found (((fun (P:Type) (x9:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x9) x8)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_intror (cODD Xn0)) (cEVEN Xn0)) x9))) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 270.01/270.44 Found (or_comm_i00 (((fun (P:Type) (x9:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x9) x8)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_intror (cODD Xn0)) (cEVEN Xn0)) x9)))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 270.01/270.44 Found ((or_comm_i0 (cEVEN Xn0)) (((fun (P:Type) (x9:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x9) x8)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_intror (cODD Xn0)) (cEVEN Xn0)) x9)))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 270.01/270.44 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((fun (P:Type) (x9:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x9) x8)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_intror (cODD Xn0)) (cEVEN Xn0)) x9)))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 270.01/270.44 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((fun (P:Type) (x9:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x9) x8)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x9:(cEVEN c0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_intror (cODD Xn0)) (cEVEN Xn0)) x9)))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 270.01/270.44 Found x50:(cNUMBER Xn0)
% 270.01/270.44 Instantiate: Xn0:=Xn:fofType
% 270.01/270.44 Found x50 as proof of (cNUMBER Xn)
% 270.01/270.44 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 270.01/270.44 Instantiate: Xn0:=Xn00:fofType
% 270.01/270.44 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 270.01/270.44 Found x30:(cNUMBER Xn0)
% 270.01/270.44 Found x30 as proof of (cNUMBER Xn0)
% 270.01/270.44 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 270.01/270.44 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 270.01/270.44 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 270.01/270.44 Found x50:=(x5 x41):(cNUMBER Xn0)
% 270.01/270.44 Instantiate: Xn0:=Xn:fofType
% 270.01/270.44 Found (x5 x41) as proof of (cNUMBER Xn)
% 270.01/270.44 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x41)) as proof of (cNUMBER Xn)
% 270.01/270.44 Found (fun (x11:(cEVEN c0)) (x12:(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))
% 270.01/270.44 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x41)) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 270.01/270.44 Found (and_rect50 (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x41))) as proof of (cNUMBER Xn)
% 270.01/270.44 Found ((and_rect5 (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x41))) as proof of (cNUMBER Xn)
% 270.01/270.44 Found (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x41))) as proof of (cNUMBER Xn)
% 270.01/270.44 Found (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x41))) as proof of (cNUMBER Xn)
% 270.01/270.44 Found x61:((or (cEVEN Xn0)) (cODD Xn0))
% 270.01/270.44 Found x61 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 270.01/270.44 Found (x7 x61) as proof of (cNUMBER Xn)
% 270.01/270.44 Found (x7 x61) as proof of (cNUMBER Xn)
% 273.85/274.26 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x61)) as proof of (cNUMBER Xn)
% 273.85/274.26 Found (fun (x12:(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))
% 273.85/274.26 Found x50:(cNUMBER Xn00)
% 273.85/274.26 Found x50 as proof of (cNUMBER Xn00)
% 273.85/274.26 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 273.85/274.26 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 273.85/274.26 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 273.85/274.26 Found x50:=(x5 x40):(cNUMBER Xn0)
% 273.85/274.26 Found (x5 x40) as proof of (cNUMBER Xn0)
% 273.85/274.26 Found (x5 x40) as proof of (cNUMBER Xn0)
% 273.85/274.26 Found x130:(cNUMBER Xn00)
% 273.85/274.26 Instantiate: Xn00:=Xn:fofType
% 273.85/274.26 Found x130 as proof of (cNUMBER Xn)
% 273.85/274.26 Found x30:(cNUMBER Xn0)
% 273.85/274.26 Instantiate: Xn0:=Xn:fofType
% 273.85/274.26 Found x30 as proof of (cNUMBER Xn)
% 273.85/274.26 Found x61:((or (cEVEN Xn0)) (cODD Xn0))
% 273.85/274.26 Found x61 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 273.85/274.26 Found (x7 x61) as proof of (cNUMBER Xn)
% 273.85/274.26 Found (x7 x61) as proof of (cNUMBER Xn)
% 273.85/274.26 Found (x7 x61) as proof of (cNUMBER Xn)
% 273.85/274.26 Found x80:=(x8 x90):((or (cEVEN Xn00)) (cODD Xn00))
% 273.85/274.26 Found (x8 x90) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 273.85/274.26 Found (x8 x90) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 273.85/274.26 Found (x8 x90) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 273.85/274.26 Found x40:=(x4 x50):((or (cEVEN Xn0)) (cODD Xn0))
% 273.85/274.26 Found (x4 x50) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 273.85/274.26 Found (x4 x50) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 273.85/274.26 Found (x4 x50) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 273.85/274.26 Found x90:=(x9 x80):(cNUMBER Xn0)
% 273.85/274.26 Found (x9 x80) as proof of (cNUMBER Xn0)
% 273.85/274.26 Found (x9 x80) as proof of (cNUMBER Xn0)
% 273.85/274.26 Found x90:=(x9 x81):(cNUMBER Xn0)
% 273.85/274.26 Instantiate: Xn0:=Xn:fofType
% 273.85/274.26 Found (x9 x81) as proof of (cNUMBER Xn)
% 273.85/274.26 Found (x9 x81) as proof of (cNUMBER Xn)
% 273.85/274.26 Found x90:=(x9 x81):(cNUMBER Xn0)
% 273.85/274.26 Found (x9 x81) as proof of (cNUMBER Xn)
% 273.85/274.26 Found (x9 x81) as proof of (cNUMBER Xn)
% 273.85/274.26 Found (x9 x81) as proof of (cNUMBER Xn)
% 273.85/274.26 Found x40:=(x4 x30):(cNUMBER Xn00)
% 273.85/274.26 Found (x4 x30) as proof of (cNUMBER Xn0)
% 273.85/274.26 Found (x4 x30) as proof of (cNUMBER Xn0)
% 273.85/274.26 Found (x4 x30) as proof of (cNUMBER Xn0)
% 273.85/274.26 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 273.85/274.26 Instantiate: Xn00:=Xn0:fofType
% 273.85/274.26 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 273.85/274.26 Found x30:(cNUMBER Xn0)
% 273.85/274.26 Instantiate: Xn0:=Xn:fofType
% 273.85/274.26 Found x30 as proof of (cNUMBER Xn)
% 273.85/274.26 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 273.85/274.26 Instantiate: Xn0:=Xn00:fofType
% 273.85/274.26 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 273.85/274.26 Found x50:(cNUMBER Xn00)
% 273.85/274.26 Instantiate: Xn0:=Xn00:fofType
% 273.85/274.26 Found x50 as proof of (cNUMBER Xn0)
% 273.85/274.26 Found x40:=(x4 x50):((or (cEVEN Xn0)) (cODD Xn0))
% 273.85/274.26 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 273.85/274.26 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 273.85/274.26 Found x51:(cNUMBER Xn0)
% 273.85/274.26 Instantiate: Xn0:=Xn:fofType
% 273.85/274.26 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x51) as proof of (cNUMBER Xn)
% 273.85/274.26 Found (fun (x6:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x51) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 273.85/274.26 Found (fun (x6:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x51) as proof of (((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))->((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn)))
% 273.85/274.26 Found x50:(cNUMBER Xn00)
% 273.85/274.26 Instantiate: Xn00:=Xn:fofType
% 273.85/274.26 Found x50 as proof of (cNUMBER Xn)
% 273.85/274.26 Found x30:(cNUMBER Xn0)
% 273.85/274.26 Instantiate: Xn00:=Xn0:fofType
% 273.85/274.26 Found x30 as proof of (cNUMBER Xn00)
% 273.85/274.26 Found x70:=(x7 x60):(cNUMBER Xn0)
% 273.85/274.26 Instantiate: Xn0:=Xn:fofType
% 273.85/274.26 Found (x7 x60) as proof of (cNUMBER Xn)
% 273.85/274.26 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x7 x60)) as proof of (cNUMBER Xn)
% 273.85/274.26 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))
% 273.85/274.26 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)))
% 274.30/274.68 Found (and_rect40 (fun (x8:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x7 x60))) as proof of (cNUMBER Xn)
% 274.30/274.68 Found ((and_rect4 (cNUMBER Xn)) (fun (x8:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x7 x60))) as proof of (cNUMBER Xn)
% 274.30/274.68 Found (((fun (P:Type) (x8:(((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) x8) x11)) (cNUMBER Xn)) (fun (x8:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x7 x60))) as proof of (cNUMBER Xn)
% 274.30/274.68 Found x80:=(x8 x90):((or (cEVEN Xn00)) (cODD Xn00))
% 274.30/274.68 Found (x8 x90) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 274.30/274.68 Found (x8 x90) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 274.30/274.68 Found (x8 x90) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 274.30/274.68 Found x30:=(x3 x21):(cNUMBER Xn0)
% 274.30/274.68 Instantiate: Xn0:=Xn:fofType
% 274.30/274.68 Found (x3 x21) as proof of (cNUMBER Xn)
% 274.30/274.68 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21)) as proof of (cNUMBER Xn)
% 274.30/274.68 Found (fun (x6:((and ((and (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 x21)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 274.30/274.68 Found (fun (x6:((and ((and (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 x21)) as proof of (((and ((and (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)))
% 274.30/274.68 Found (and_rect30 (fun (x6:((and ((and (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 x21))) as proof of (cNUMBER Xn)
% 274.30/274.68 Found ((and_rect3 (cNUMBER Xn)) (fun (x6:((and ((and (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 x21))) as proof of (cNUMBER Xn)
% 274.30/274.68 Found (((fun (P:Type) (x6:(((and ((and (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 (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) x4)) (cNUMBER Xn)) (fun (x6:((and ((and (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 x21))) as proof of (cNUMBER Xn)
% 274.30/274.68 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (((fun (P:Type) (x6:(((and ((and (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 (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) x4)) (cNUMBER Xn)) (fun (x6:((and ((and (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 x21)))) as proof of (cNUMBER Xn)
% 274.30/274.68 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (((fun (P:Type) (x6:(((and ((and (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 (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) x4)) (cNUMBER Xn)) (fun (x6:((and ((and (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 x21)))) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 275.05/275.46 Found x11:(cEVEN c0)
% 275.05/275.46 Instantiate: Xn0:=c0:fofType
% 275.05/275.46 Found (fun (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11) as proof of (cEVEN Xn0)
% 275.05/275.46 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11) as proof of ((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->(cEVEN Xn0))
% 275.05/275.46 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11) as proof of ((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->(cEVEN Xn0)))
% 275.05/275.46 Found (and_rect50 (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11)) as proof of (cEVEN Xn0)
% 275.05/275.46 Found ((and_rect5 (cEVEN Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11)) as proof of (cEVEN Xn0)
% 275.05/275.46 Found (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x11) x8)) (cEVEN Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11)) as proof of (cEVEN Xn0)
% 275.05/275.46 Found (fun (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x11) x8)) (cEVEN Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11))) as proof of (cEVEN Xn0)
% 275.05/275.46 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x11) x8)) (cEVEN Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11))) as proof of ((cODD (cS c0))->(cEVEN Xn0))
% 275.05/275.46 Found (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x11) x8)) (cEVEN Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->(cEVEN Xn0)))
% 275.05/275.46 Found (and_rect40 (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x11) x8)) (cEVEN Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11)))) as proof of (cEVEN Xn0)
% 275.05/275.46 Found ((and_rect4 (cEVEN Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x11) x8)) (cEVEN Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11)))) as proof of (cEVEN Xn0)
% 275.05/275.46 Found (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) (cEVEN Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x11) x8)) (cEVEN Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11)))) as proof of (cEVEN Xn0)
% 275.05/275.46 Found (fun (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) (cEVEN Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x11) x8)) (cEVEN Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11))))) as proof of (cEVEN Xn0)
% 275.05/275.46 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) (cEVEN Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x11) x8)) (cEVEN Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11))))) as proof of ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->(cEVEN Xn0))
% 275.05/275.46 Found (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) (cEVEN Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x11) x8)) (cEVEN Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11))))) as proof of (((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))->((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->(cEVEN Xn0)))
% 275.05/275.46 Found (and_rect30 (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) (cEVEN Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x11) x8)) (cEVEN Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11)))))) as proof of (cEVEN Xn0)
% 275.05/275.46 Found ((and_rect3 (cEVEN Xn0)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) (cEVEN Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x11) x8)) (cEVEN Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11)))))) as proof of (cEVEN Xn0)
% 275.05/275.46 Found (((fun (P:Type) (x6:(((and ((and (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 (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) x4)) (cEVEN Xn0)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) (cEVEN Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x11) x8)) (cEVEN Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11)))))) as proof of (cEVEN Xn0)
% 275.05/275.46 Found (((fun (P:Type) (x6:(((and ((and (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 (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) x4)) (cEVEN Xn0)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) (cEVEN Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x11) x8)) (cEVEN Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11)))))) as proof of (cEVEN Xn0)
% 275.05/275.47 Found (or_introl00 (((fun (P:Type) (x6:(((and ((and (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 (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) x4)) (cEVEN Xn0)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) (cEVEN Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x11) x8)) (cEVEN Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 275.05/275.47 Found ((or_introl0 (cODD Xn0)) (((fun (P:Type) (x6:(((and ((and (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 (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x4)) (cEVEN Xn0)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) (cEVEN Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x11) x8)) (cEVEN Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 275.05/275.47 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) (((fun (P:Type) (x6:(((and ((and (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 (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x4)) (cEVEN Xn0)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) (cEVEN Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x11) x8)) (cEVEN Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 275.52/275.95 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) (((fun (P:Type) (x6:(((and ((and (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 (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x6) x4)) (cEVEN Xn0)) (fun (x6:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x8:(((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x8) x6)) (cEVEN Xn0)) (fun (x8:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x11) x8)) (cEVEN Xn0)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x11))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 275.52/275.95 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 275.52/275.95 Instantiate: Xn0:=Xn00:fofType
% 275.52/275.95 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 275.52/275.95 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 275.52/275.95 Instantiate: Xn00:=Xn0:fofType
% 275.52/275.95 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 275.52/275.95 Found x111:((or (cEVEN Xn0)) (cODD Xn0))
% 275.52/275.95 Found x111 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 275.52/275.95 Found (x12 x111) as proof of (cNUMBER Xn)
% 275.52/275.95 Found (x12 x111) as proof of (cNUMBER Xn)
% 275.52/275.95 Found (x12 x111) as proof of (cNUMBER Xn)
% 275.52/275.95 Found x30:=(x3 x21):(cNUMBER Xn0)
% 275.52/275.95 Instantiate: Xn0:=Xn:fofType
% 275.52/275.95 Found (x3 x21) as proof of (cNUMBER Xn)
% 275.52/275.95 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21)) as proof of (cNUMBER Xn)
% 275.52/275.95 Found (fun (x6:((and ((and (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 x21)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 275.52/275.95 Found (fun (x6:((and ((and (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 x21)) as proof of (((and ((and (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)))
% 275.52/275.95 Found (and_rect30 (fun (x6:((and ((and (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 x21))) as proof of (cNUMBER Xn)
% 275.52/275.95 Found ((and_rect3 (cNUMBER Xn)) (fun (x6:((and ((and (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 x21))) as proof of (cNUMBER Xn)
% 275.52/275.95 Found (((fun (P:Type) (x6:(((and ((and (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 (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) x4)) (cNUMBER Xn)) (fun (x6:((and ((and (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 x21))) as proof of (cNUMBER Xn)
% 278.00/278.38 Found (((fun (P:Type) (x6:(((and ((and (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 (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) x4)) (cNUMBER Xn)) (fun (x6:((and ((and (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 x21))) as proof of (cNUMBER Xn)
% 278.00/278.38 Found x30:=(x3 x20):(cNUMBER Xn0)
% 278.00/278.38 Instantiate: Xn0:=Xn:fofType
% 278.00/278.38 Found (x3 x20) as proof of (cNUMBER Xn)
% 278.00/278.38 Found (x3 x20) as proof of (cNUMBER Xn)
% 278.00/278.38 Found x50:=(x5 x40):(cNUMBER Xn00)
% 278.00/278.38 Instantiate: Xn00:=Xn:fofType
% 278.00/278.38 Found (x5 x40) as proof of (cNUMBER Xn)
% 278.00/278.38 Found (x5 x40) as proof of (cNUMBER Xn)
% 278.00/278.38 Found x30:(cNUMBER Xn0)
% 278.00/278.38 Found x30 as proof of (cNUMBER Xn0)
% 278.00/278.38 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 278.00/278.38 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 278.00/278.38 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 278.00/278.38 Found x90:(cNUMBER Xn00)
% 278.00/278.38 Found x90 as proof of (cNUMBER Xn00)
% 278.00/278.38 Found (x8 x90) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 278.00/278.38 Found (x8 x90) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 278.00/278.38 Found (x8 x90) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 278.00/278.38 Found x60:=(x6 x70):((or (cEVEN Xn00)) (cODD Xn00))
% 278.00/278.38 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 278.00/278.38 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 278.00/278.38 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 278.00/278.38 Found x40:=(x4 x50):((or (cEVEN Xn00)) (cODD Xn00))
% 278.00/278.38 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 278.00/278.38 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 278.00/278.38 Found (fun (x9:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x4 x50)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 278.00/278.38 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x9:(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)))
% 278.00/278.38 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x9:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x4 x50)) as proof of (((and ((and (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))))
% 278.00/278.38 Found x30:=(x3 x20):(cNUMBER Xn0)
% 278.00/278.38 Found (x3 x20) as proof of (cNUMBER Xn0)
% 278.00/278.38 Found (x3 x20) as proof of (cNUMBER Xn0)
% 278.00/278.38 Found x30:=(x3 x20):(cNUMBER Xn0)
% 278.00/278.38 Found (x3 x20) as proof of (cNUMBER Xn0)
% 278.00/278.38 Found (x3 x20) as proof of (cNUMBER Xn0)
% 278.00/278.38 Found x70:(cNUMBER Xn00)
% 278.00/278.38 Instantiate: Xn00:=Xn:fofType
% 278.00/278.38 Found x70 as proof of (cNUMBER Xn)
% 278.00/278.38 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 278.00/278.38 Instantiate: Xn00:=Xn0:fofType
% 278.00/278.38 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 278.00/278.38 Found x50:=(x5 x40):(cNUMBER Xn0)
% 278.00/278.38 Instantiate: Xn0:=Xn:fofType
% 278.00/278.38 Found (x5 x40) as proof of (cNUMBER Xn)
% 278.00/278.38 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 278.00/278.38 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(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))
% 278.00/278.38 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (((and ((and (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)))
% 278.00/278.40 Found (and_rect40 (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 278.00/278.40 Found ((and_rect4 (cNUMBER Xn)) (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 278.00/278.40 Found (((fun (P:Type) (x8:(((and ((and (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 (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x8) x2)) (cNUMBER Xn)) (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 278.00/278.40 Found (((fun (P:Type) (x8:(((and ((and (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 (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x8) x2)) (cNUMBER Xn)) (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 278.00/278.40 Found x70:=(x7 x60):(cNUMBER Xn00)
% 278.00/278.40 Instantiate: Xn00:=Xn:fofType
% 278.00/278.40 Found (x7 x60) as proof of (cNUMBER Xn)
% 278.00/278.40 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x7 x60)) as proof of (cNUMBER Xn)
% 278.00/278.40 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x7 x60)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 278.00/278.40 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x7 x60)) as proof of (((and ((and (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)))
% 278.00/278.40 Found (and_rect40 (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x7 x60))) as proof of (cNUMBER Xn)
% 278.00/278.40 Found ((and_rect4 (cNUMBER Xn)) (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x7 x60))) as proof of (cNUMBER Xn)
% 278.00/278.40 Found (((fun (P:Type) (x8:(((and ((and (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 (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x8) x2)) (cNUMBER Xn)) (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x7 x60))) as proof of (cNUMBER Xn)
% 278.00/278.40 Found (((fun (P:Type) (x8:(((and ((and (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 (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x8) x2)) (cNUMBER Xn)) (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x7 x60))) as proof of (cNUMBER Xn)
% 278.00/278.41 Found x30:=(x3 x20):(cNUMBER Xn0)
% 278.00/278.41 Instantiate: Xn0:=Xn:fofType
% 278.00/278.41 Found (x3 x20) as proof of (cNUMBER Xn)
% 278.00/278.41 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 278.00/278.41 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(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))
% 278.00/278.41 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (((and ((and (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)))
% 278.00/278.41 Found (and_rect40 (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 278.00/278.41 Found ((and_rect4 (cNUMBER Xn)) (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 278.00/278.41 Found (((fun (P:Type) (x8:(((and ((and (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 (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x8) x4)) (cNUMBER Xn)) (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 278.00/278.41 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (((fun (P:Type) (x8:(((and ((and (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 (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x8) x4)) (cNUMBER Xn)) (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)))) as proof of (cNUMBER Xn)
% 278.00/278.41 Found (fun (x6:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (((fun (P:Type) (x8:(((and ((and (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 (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x8) x4)) (cNUMBER Xn)) (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)))) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 278.00/278.41 Found (fun (x6:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (((fun (P:Type) (x8:(((and ((and (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 (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x8) x4)) (cNUMBER Xn)) (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(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)))
% 278.50/278.90 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 278.50/278.90 Instantiate: Xn0:=Xn00:fofType
% 278.50/278.90 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 278.50/278.90 Found x120:=(x12 x111):(cNUMBER Xn0)
% 278.50/278.90 Instantiate: Xn0:=Xn:fofType
% 278.50/278.90 Found (x12 x111) as proof of (cNUMBER Xn)
% 278.50/278.90 Found (fun (x12:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x12 x111)) as proof of (cNUMBER Xn)
% 278.50/278.90 Found (fun (x12:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x12 x111)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 278.50/278.90 Found x30:(cNUMBER Xn0)
% 278.50/278.90 Instantiate: Xn0:=Xn:fofType
% 278.50/278.90 Found x30 as proof of (cNUMBER Xn)
% 278.50/278.90 Found x60:=(x6 x70):((or (cEVEN Xn00)) (cODD Xn00))
% 278.50/278.90 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 278.50/278.90 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 278.50/278.90 Found (fun (x9:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x6 x70)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 278.50/278.90 Found (fun (x9:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x6 x70)) as proof of ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 278.50/278.90 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 278.50/278.90 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 278.50/278.90 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 278.50/278.90 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x2 x30)) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 278.50/278.90 Found (fun (x9:(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)))
% 278.50/278.90 Found x60:=(x6 x70):((or (cEVEN Xn00)) (cODD Xn00))
% 278.50/278.90 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 278.50/278.90 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 278.50/278.90 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 278.50/278.90 Found x50:=(x5 x41):(cNUMBER Xn0)
% 278.50/278.90 Instantiate: Xn0:=Xn:fofType
% 278.50/278.90 Found (x5 x41) as proof of (cNUMBER Xn)
% 278.50/278.90 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x41)) as proof of (cNUMBER Xn)
% 278.50/278.90 Found (fun (x11:(cEVEN c0)) (x12:(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))
% 278.50/278.90 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x41)) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 278.50/278.90 Found (and_rect50 (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x41))) as proof of (cNUMBER Xn)
% 278.50/278.90 Found ((and_rect5 (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x41))) as proof of (cNUMBER Xn)
% 278.50/278.90 Found (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x41))) as proof of (cNUMBER Xn)
% 278.50/278.90 Found (fun (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x41)))) as proof of (cNUMBER Xn)
% 278.50/278.90 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x41)))) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 280.23/280.62 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x41)))) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 280.23/280.62 Found x31:(cNUMBER Xn0)
% 280.23/280.62 Instantiate: Xn0:=Xn:fofType
% 280.23/280.62 Found (fun (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x31) as proof of (cNUMBER Xn)
% 280.23/280.62 Found (fun (x7:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x31) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 280.23/280.62 Found (fun (x6:(cODD Xn0)) (x7:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x31) as proof of (((and ((and (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)))
% 280.23/280.62 Found (fun (x6:(cODD Xn0)) (x7:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x31) as proof of ((cODD Xn0)->(((and ((and (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))))
% 280.23/280.62 Found x31:(cNUMBER Xn0)
% 280.23/280.62 Instantiate: Xn0:=Xn:fofType
% 280.23/280.62 Found (fun (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x31) as proof of (cNUMBER Xn)
% 280.23/280.62 Found (fun (x7:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x31) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 280.23/280.62 Found (fun (x6:(cEVEN Xn0)) (x7:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x31) as proof of (((and ((and (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)))
% 280.23/280.62 Found (fun (x6:(cEVEN Xn0)) (x7:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x31) as proof of ((cEVEN Xn0)->(((and ((and (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))))
% 280.23/280.62 Found ((or_ind00 (fun (x6:(cEVEN Xn0)) (x7:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x31)) (fun (x6:(cODD Xn0)) (x7:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x31)) as proof of (((and ((and (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)))
% 280.23/280.62 Found (((or_ind0 (((and ((and (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 (x6:(cEVEN Xn0)) (x7:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x31)) (fun (x6:(cODD Xn0)) (x7:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x31)) as proof of (((and ((and (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)))
% 280.47/280.91 Found ((((fun (P:Prop) (x6:((cEVEN Xn0)->P)) (x7:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x6) x7) x20)) (((and ((and (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 (x6:(cEVEN Xn0)) (x7:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x31)) (fun (x6:(cODD Xn0)) (x7:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x31)) as proof of (((and ((and (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)))
% 280.47/280.91 Found ((((fun (P:Prop) (x6:((cEVEN Xn0)->P)) (x7:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x6) x7) (x2 x31))) (((and ((and (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 (x6:(cEVEN Xn0)) (x7:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x31)) (fun (x6:(cODD Xn0)) (x7:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x31)) as proof of (((and ((and (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)))
% 280.47/280.91 Found ((((fun (P:Prop) (x6:((cEVEN Xn0)->P)) (x7:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x6) x7) (x2 x31))) (((and ((and (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 (x6:(cEVEN Xn0)) (x7:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x31)) (fun (x6:(cODD Xn0)) (x7:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x31)) as proof of (((and ((and (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)))
% 280.47/280.91 Found x90:=(x9 x81):(cNUMBER Xn0)
% 280.47/280.91 Found (x9 x81) as proof of (cNUMBER Xn)
% 280.47/280.91 Found (x9 x81) as proof of (cNUMBER Xn)
% 280.47/280.91 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x9 x81)) as proof of (cNUMBER Xn)
% 280.47/280.91 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x9 x81)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 280.47/280.91 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x9 x81)) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 280.47/280.91 Found x90:=(x9 x81):(cNUMBER Xn0)
% 280.47/280.91 Found (x9 x81) as proof of (cNUMBER Xn)
% 280.78/281.19 Found (x9 x81) as proof of (cNUMBER Xn)
% 280.78/281.19 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x9 x81)) as proof of (cNUMBER Xn)
% 280.78/281.19 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x9 x81)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 280.78/281.19 Found x30:=(x3 x21):(cNUMBER Xn0)
% 280.78/281.19 Instantiate: Xn0:=Xn:fofType
% 280.78/281.19 Found (x3 x21) as proof of (cNUMBER Xn)
% 280.78/281.19 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21)) as proof of (cNUMBER Xn)
% 280.78/281.19 Found (fun (x6:((and ((and (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 x21)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 280.78/281.19 Found (fun (x6:((and ((and (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 x21)) as proof of (((and ((and (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)))
% 280.78/281.19 Found (and_rect30 (fun (x6:((and ((and (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 x21))) as proof of (cNUMBER Xn)
% 280.78/281.19 Found ((and_rect3 (cNUMBER Xn)) (fun (x6:((and ((and (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 x21))) as proof of (cNUMBER Xn)
% 280.78/281.19 Found (((fun (P:Type) (x6:(((and ((and (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 (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) x4)) (cNUMBER Xn)) (fun (x6:((and ((and (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 x21))) as proof of (cNUMBER Xn)
% 280.78/281.19 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (((fun (P:Type) (x6:(((and ((and (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 (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) x4)) (cNUMBER Xn)) (fun (x6:((and ((and (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 x21)))) as proof of (cNUMBER Xn)
% 280.78/281.19 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (((fun (P:Type) (x6:(((and ((and (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 (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) x4)) (cNUMBER Xn)) (fun (x6:((and ((and (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 x21)))) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 282.20/282.65 Found x30:=(x3 x20):(cNUMBER Xn0)
% 282.20/282.65 Found (x3 x20) as proof of (cNUMBER Xn0)
% 282.20/282.65 Found (x3 x20) as proof of (cNUMBER Xn0)
% 282.20/282.65 Found x60:=(x6 x70):((or (cEVEN Xn00)) (cODD Xn00))
% 282.20/282.65 Instantiate: Xn00:=Xn:fofType
% 282.20/282.65 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 282.20/282.65 Found (fun (x9:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x6 x70)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 282.20/282.65 Found (fun (x9:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x6 x70)) as proof of ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 282.20/282.65 Found x60:=(x6 x70):((or (cEVEN Xn00)) (cODD Xn00))
% 282.20/282.65 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 282.20/282.65 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 282.20/282.65 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 282.20/282.65 Found x50:(cNUMBER Xn00)
% 282.20/282.65 Found x50 as proof of (cNUMBER Xn00)
% 282.20/282.65 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 282.20/282.65 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 282.20/282.65 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 282.20/282.65 Found x30:(cNUMBER Xn0)
% 282.20/282.65 Instantiate: Xn0:=Xn:fofType
% 282.20/282.65 Found x30 as proof of (cNUMBER Xn)
% 282.20/282.65 Found x70:(cNUMBER Xn00)
% 282.20/282.65 Instantiate: Xn00:=Xn:fofType
% 282.20/282.65 Found x70 as proof of (cNUMBER Xn)
% 282.20/282.65 Found x50:(cNUMBER Xn0)
% 282.20/282.65 Instantiate: Xn0:=Xn:fofType
% 282.20/282.65 Found x50 as proof of (cNUMBER Xn)
% 282.20/282.65 Found x40:=(x4 x50):((or (cEVEN Xn0)) (cODD Xn0))
% 282.20/282.65 Found (x4 x50) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 282.20/282.65 Found (x4 x50) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 282.20/282.65 Found (x4 x50) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 282.20/282.65 Found x90:(cNUMBER Xn00)
% 282.20/282.65 Instantiate: Xn00:=Xn:fofType
% 282.20/282.65 Found x90 as proof of (cNUMBER Xn)
% 282.20/282.65 Found x50:(cNUMBER Xn00)
% 282.20/282.65 Found x50 as proof of (cNUMBER Xn00)
% 282.20/282.65 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 282.20/282.65 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 282.20/282.65 Found (fun (x9:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x4 x50)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 282.20/282.65 Found (fun (x9:(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)))
% 282.20/282.65 Found x30:=(x3 x21):(cNUMBER Xn0)
% 282.20/282.65 Instantiate: Xn0:=Xn:fofType
% 282.20/282.65 Found (x3 x21) as proof of (cNUMBER Xn)
% 282.20/282.65 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21)) as proof of (cNUMBER Xn)
% 282.20/282.65 Found (fun (x6:((and ((and (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 x21)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 282.20/282.65 Found (fun (x6:((and ((and (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 x21)) as proof of (((and ((and (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)))
% 282.20/282.65 Found (and_rect30 (fun (x6:((and ((and (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 x21))) as proof of (cNUMBER Xn)
% 282.20/282.65 Found ((and_rect3 (cNUMBER Xn)) (fun (x6:((and ((and (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 x21))) as proof of (cNUMBER Xn)
% 282.20/282.65 Found (((fun (P:Type) (x6:(((and ((and (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 (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) x4)) (cNUMBER Xn)) (fun (x6:((and ((and (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 x21))) as proof of (cNUMBER Xn)
% 282.33/282.71 Found (((fun (P:Type) (x6:(((and ((and (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 (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) x4)) (cNUMBER Xn)) (fun (x6:((and ((and (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 x21))) as proof of (cNUMBER Xn)
% 282.33/282.71 Found x30:=(x3 x21):(cNUMBER Xn0)
% 282.33/282.71 Instantiate: Xn0:=Xn:fofType
% 282.33/282.71 Found (x3 x21) as proof of (cNUMBER Xn)
% 282.33/282.71 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21)) as proof of (cNUMBER Xn)
% 282.33/282.71 Found (fun (x6:((and ((and (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 x21)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 282.33/282.71 Found (fun (x6:((and ((and (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 x21)) as proof of (((and ((and (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)))
% 282.33/282.71 Found (and_rect30 (fun (x6:((and ((and (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 x21))) as proof of (cNUMBER Xn)
% 282.33/282.71 Found ((and_rect3 (cNUMBER Xn)) (fun (x6:((and ((and (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 x21))) as proof of (cNUMBER Xn)
% 282.33/282.71 Found (((fun (P:Type) (x6:(((and ((and (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 (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) x4)) (cNUMBER Xn)) (fun (x6:((and ((and (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 x21))) as proof of (cNUMBER Xn)
% 282.33/282.71 Found (((fun (P:Type) (x6:(((and ((and (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 (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) x4)) (cNUMBER Xn)) (fun (x6:((and ((and (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 x21))) as proof of (cNUMBER Xn)
% 282.33/282.71 Found x30:=(x3 x21):(cNUMBER Xn0)
% 282.33/282.71 Instantiate: Xn0:=Xn:fofType
% 282.33/282.71 Found (x3 x21) as proof of (cNUMBER Xn)
% 282.33/282.71 Found (fun (x4:(cODD Xn0))=> (x3 x21)) as proof of (cNUMBER Xn)
% 282.33/282.71 Found (fun (x4:(cODD Xn0))=> (x3 x21)) as proof of ((cODD Xn0)->(cNUMBER Xn))
% 282.33/282.71 Found x30:=(x3 x21):(cNUMBER Xn0)
% 282.33/282.71 Instantiate: Xn0:=Xn:fofType
% 282.33/282.71 Found (x3 x21) as proof of (cNUMBER Xn)
% 282.33/282.71 Found (fun (x4:(cEVEN Xn0))=> (x3 x21)) as proof of (cNUMBER Xn)
% 282.33/282.71 Found (fun (x4:(cEVEN Xn0))=> (x3 x21)) as proof of ((cEVEN Xn0)->(cNUMBER Xn))
% 282.33/282.71 Found ((or_ind00 (fun (x4:(cEVEN Xn0))=> (x3 x21))) (fun (x4:(cODD Xn0))=> (x3 x21))) as proof of (cNUMBER Xn)
% 282.33/282.71 Found (((or_ind0 (cNUMBER Xn)) (fun (x4:(cEVEN Xn0))=> (x3 x21))) (fun (x4:(cODD Xn0))=> (x3 x21))) as proof of (cNUMBER Xn)
% 282.37/282.79 Found ((((fun (P:Prop) (x4:((cEVEN Xn0)->P)) (x5:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x4) x5) x21)) (cNUMBER Xn)) (fun (x4:(cEVEN Xn0))=> (x3 x21))) (fun (x4:(cODD Xn0))=> (x3 x21))) as proof of (cNUMBER Xn)
% 282.37/282.79 Found ((((fun (P:Prop) (x4:((cEVEN Xn0)->P)) (x5:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x4) x5) x21)) (cNUMBER Xn)) (fun (x4:(cEVEN Xn0))=> (x3 x21))) (fun (x4:(cODD Xn0))=> (x3 x21))) as proof of (cNUMBER Xn)
% 282.37/282.79 Found x30:=(x3 x21):(cNUMBER Xn0)
% 282.37/282.79 Instantiate: Xn0:=Xn:fofType
% 282.37/282.79 Found (x3 x21) as proof of (cNUMBER Xn)
% 282.37/282.79 Found (fun (x4:(cEVEN Xn0))=> (x3 x21)) as proof of (cNUMBER Xn)
% 282.37/282.79 Found (fun (x4:(cEVEN Xn0))=> (x3 x21)) as proof of ((cEVEN Xn0)->(cNUMBER Xn))
% 282.37/282.79 Found x30:=(x3 x21):(cNUMBER Xn0)
% 282.37/282.79 Instantiate: Xn0:=Xn:fofType
% 282.37/282.79 Found (x3 x21) as proof of (cNUMBER Xn)
% 282.37/282.79 Found (fun (x4:(cODD Xn0))=> (x3 x21)) as proof of (cNUMBER Xn)
% 282.37/282.79 Found (fun (x4:(cODD Xn0))=> (x3 x21)) as proof of ((cODD Xn0)->(cNUMBER Xn))
% 282.37/282.79 Found ((or_ind00 (fun (x4:(cEVEN Xn0))=> (x3 x21))) (fun (x4:(cODD Xn0))=> (x3 x21))) as proof of (cNUMBER Xn)
% 282.37/282.79 Found (((or_ind0 (cNUMBER Xn)) (fun (x4:(cEVEN Xn0))=> (x3 x21))) (fun (x4:(cODD Xn0))=> (x3 x21))) as proof of (cNUMBER Xn)
% 282.37/282.79 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)
% 282.37/282.79 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)
% 282.37/282.79 Found x50:(cNUMBER Xn0)
% 282.37/282.79 Instantiate: Xn0:=Xn:fofType
% 282.37/282.79 Found (fun (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of (cNUMBER Xn)
% 282.37/282.79 Found (fun (x7:(cEVEN Xn0)) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 282.37/282.79 Found (fun (x7:(cEVEN Xn0)) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of ((cEVEN Xn0)->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 282.37/282.79 Found x50:(cNUMBER Xn0)
% 282.37/282.79 Instantiate: Xn0:=Xn:fofType
% 282.37/282.79 Found (fun (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of (cNUMBER Xn)
% 282.37/282.79 Found (fun (x7:(cODD Xn0)) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 282.37/282.79 Found (fun (x7:(cODD Xn0)) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of ((cODD Xn0)->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 282.37/282.79 Found ((or_ind00 (fun (x7:(cEVEN Xn0)) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50)) (fun (x7:(cODD Xn0)) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 282.37/282.79 Found (((or_ind0 ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))) (fun (x7:(cEVEN Xn0)) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50)) (fun (x7:(cODD Xn0)) (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 282.37/282.79 Found ((((fun (P:Prop) (x7:((cEVEN Xn0)->P)) (x8:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x7) x8) x40)) ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->(cNUMBER Xn))) (fun (x7:(cEVEN Xn0)) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x50)) (fun (x7:(cODD Xn0)) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x50)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 282.37/282.79 Found ((((fun (P:Prop) (x7:((cEVEN Xn0)->P)) (x8:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x7) x8) (x4 x51))) ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->(cNUMBER Xn))) (fun (x7:(cEVEN Xn0)) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x50)) (fun (x7:(cODD Xn0)) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x50)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 285.14/285.54 Found ((((fun (P:Prop) (x7:((cEVEN Xn0)->P)) (x8:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x7) x8) (x4 x51))) ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->(cNUMBER Xn))) (fun (x7:(cEVEN Xn0)) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x50)) (fun (x7:(cODD Xn0)) (x8:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x50)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 285.14/285.54 Found x30:(cNUMBER Xn0)
% 285.14/285.54 Found x30 as proof of (cNUMBER Xn0)
% 285.14/285.54 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 285.14/285.54 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 285.14/285.54 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x2 x30)) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 285.14/285.54 Found (fun (x9:(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)))
% 285.14/285.54 Found x70:(cNUMBER Xn00)
% 285.14/285.54 Instantiate: Xn00:=Xn:fofType
% 285.14/285.54 Found (fun (x13:(cODD (cS c0)))=> x70) as proof of (cNUMBER Xn)
% 285.14/285.54 Found (fun (x12:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x13:(cODD (cS c0)))=> x70) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 285.14/285.54 Found (fun (x12:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x13:(cODD (cS c0)))=> x70) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 285.14/285.54 Found x30:(cNUMBER Xn0)
% 285.14/285.54 Instantiate: Xn0:=Xn:fofType
% 285.14/285.54 Found (fun (x13:(cODD (cS c0)))=> x30) as proof of (cNUMBER Xn)
% 285.14/285.54 Found (fun (x12:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x13:(cODD (cS c0)))=> x30) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 285.14/285.54 Found (fun (x12:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x13:(cODD (cS c0)))=> x30) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 285.14/285.54 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 285.14/285.54 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 285.14/285.54 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 285.14/285.54 Found x31:(cNUMBER Xn0)
% 285.14/285.54 Instantiate: Xn0:=Xn:fofType
% 285.14/285.54 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x31) as proof of (cNUMBER Xn)
% 285.14/285.54 Found (fun (x6:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x31) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 285.14/285.54 Found (fun (x6:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x7:(((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)))
% 285.14/285.54 Found x50:=(x5 x40):(cNUMBER Xn0)
% 285.14/285.54 Instantiate: Xn0:=Xn:fofType
% 285.14/285.54 Found (x5 x40) as proof of (cNUMBER Xn)
% 285.14/285.54 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 285.14/285.54 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))
% 285.14/285.54 Found (fun (x8:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x9:(((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)))
% 285.14/285.54 Found (and_rect40 (fun (x8:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40))) as proof of (cNUMBER Xn)
% 285.14/285.54 Found ((and_rect4 (cNUMBER Xn)) (fun (x8:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40))) as proof of (cNUMBER Xn)
% 287.22/287.64 Found (((fun (P:Type) (x8:(((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) x8) x11)) (cNUMBER Xn)) (fun (x8:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40))) as proof of (cNUMBER Xn)
% 287.22/287.64 Found x30:=(x3 x21):(cNUMBER Xn0)
% 287.22/287.64 Found (x3 x21) as proof of (cNUMBER Xn0)
% 287.22/287.64 Found (x3 x21) as proof of (cNUMBER Xn0)
% 287.22/287.64 Found x30:(cNUMBER Xn0)
% 287.22/287.64 Found x30 as proof of (cNUMBER Xn0)
% 287.22/287.64 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 287.22/287.64 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 287.22/287.64 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x2 x30)) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 287.22/287.64 Found (fun (x9:(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)))
% 287.22/287.64 Found x50:(cNUMBER Xn0)
% 287.22/287.64 Instantiate: Xn0:=Xn:fofType
% 287.22/287.64 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x50) as proof of (cNUMBER Xn)
% 287.22/287.64 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x50) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 287.22/287.64 Found x50:(cNUMBER Xn0)
% 287.22/287.64 Instantiate: Xn0:=Xn:fofType
% 287.22/287.64 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x50) as proof of (cNUMBER Xn)
% 287.22/287.64 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x50) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 287.22/287.64 Found x51:(cNUMBER Xn0)
% 287.22/287.64 Instantiate: Xn0:=Xn:fofType
% 287.22/287.64 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x51) as proof of (cNUMBER Xn)
% 287.22/287.64 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x51) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 287.22/287.64 Found x50:(cNUMBER Xn00)
% 287.22/287.64 Found x50 as proof of (cNUMBER Xn00)
% 287.22/287.64 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 287.22/287.64 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 287.22/287.64 Found (fun (x9:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x4 x50)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 287.22/287.64 Found (fun (x9:(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)))
% 287.22/287.64 Found x80:=(x8 x90):((or (cEVEN Xn00)) (cODD Xn00))
% 287.22/287.64 Found (x8 x90) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 287.22/287.64 Found (x8 x90) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 287.22/287.64 Found (x8 x90) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 287.22/287.64 Found x70:(cNUMBER Xn00)
% 287.22/287.64 Instantiate: Xn00:=Xn:fofType
% 287.22/287.64 Found x70 as proof of (cNUMBER Xn)
% 287.22/287.64 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 287.22/287.64 Instantiate: Xn00:=Xn0:fofType
% 287.22/287.64 Found x40 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 287.22/287.64 Found x60:=(x6 x70):((or (cEVEN Xn00)) (cODD Xn00))
% 287.22/287.64 Instantiate: Xn00:=Xn:fofType
% 287.22/287.64 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 287.22/287.64 Found (fun (x9:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x6 x70)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 287.22/287.64 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x9:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x6 x70)) as proof of ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 287.22/287.64 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x9:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x6 x70)) as proof of (((and ((and (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))))
% 287.22/287.64 Found x40:=(x4 x50):((or (cEVEN Xn0)) (cODD Xn0))
% 287.22/287.64 Instantiate: Xn0:=Xn:fofType
% 287.22/287.64 Found (x4 x50) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 288.17/288.59 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x4 x50)) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 288.17/288.59 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x4 x50)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->((or (cEVEN Xn00)) (cODD Xn00)))
% 288.17/288.59 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x4 x50)) as proof of (((and ((and (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))))
% 288.17/288.59 Found x30:(cNUMBER Xn0)
% 288.17/288.59 Instantiate: Xn0:=Xn:fofType
% 288.17/288.59 Found (fun (x13:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30) as proof of (cNUMBER Xn)
% 288.17/288.59 Found (fun (x13:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 288.17/288.59 Found x30:=(x3 x20):(cNUMBER Xn0)
% 288.17/288.59 Instantiate: Xn0:=Xn:fofType
% 288.17/288.59 Found (x3 x20) as proof of (cNUMBER Xn)
% 288.17/288.59 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 288.17/288.59 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))
% 288.17/288.59 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)))
% 288.17/288.59 Found (and_rect40 (fun (x8:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20))) as proof of (cNUMBER Xn)
% 288.17/288.59 Found ((and_rect4 (cNUMBER Xn)) (fun (x8:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20))) as proof of (cNUMBER Xn)
% 288.17/288.59 Found (((fun (P:Type) (x8:(((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) x8) x11)) (cNUMBER Xn)) (fun (x8:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20))) as proof of (cNUMBER Xn)
% 288.17/288.59 Found x20:=(x2 x31):((or (cEVEN Xn0)) (cODD Xn0))
% 288.17/288.59 Found (x2 x31) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 288.17/288.59 Found (x2 x31) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 288.17/288.59 Found x32:(cNUMBER Xn0)
% 288.17/288.59 Instantiate: Xn0:=Xn:fofType
% 288.17/288.59 Found (fun (x9:(cODD (cS c0)))=> x32) as proof of (cNUMBER Xn)
% 288.17/288.59 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> x32) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 288.17/288.59 Found (fun (x8:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> x32) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 288.17/288.59 Found x50:=(x5 x41):(cNUMBER Xn0)
% 288.17/288.59 Instantiate: Xn0:=Xn:fofType
% 288.17/288.59 Found (x5 x41) as proof of (cNUMBER Xn)
% 288.17/288.59 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x41)) as proof of (cNUMBER Xn)
% 288.17/288.59 Found (fun (x11:(cEVEN c0)) (x12:(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))
% 288.17/288.59 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x41)) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 288.17/288.59 Found (and_rect50 (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x41))) as proof of (cNUMBER Xn)
% 288.17/288.59 Found ((and_rect5 (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x41))) as proof of (cNUMBER Xn)
% 288.66/289.05 Found (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x41))) as proof of (cNUMBER Xn)
% 288.66/289.05 Found (fun (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x41)))) as proof of (cNUMBER Xn)
% 288.66/289.05 Found (fun (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x41)))) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 288.66/289.05 Found x30:(cNUMBER Xn0)
% 288.66/289.05 Found x30 as proof of (cNUMBER Xn0)
% 288.66/289.05 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 288.66/289.05 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 288.66/289.05 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 288.66/289.05 Found x81:((or (cEVEN Xn0)) (cODD Xn0))
% 288.66/289.05 Found x81 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 288.66/289.05 Found (x9 x81) as proof of (cNUMBER Xn)
% 288.66/289.05 Found (x9 x81) as proof of (cNUMBER Xn)
% 288.66/289.05 Found (x9 x81) as proof of (cNUMBER Xn)
% 288.66/289.05 Found x30:=(x3 x21):(cNUMBER Xn0)
% 288.66/289.05 Instantiate: Xn0:=Xn:fofType
% 288.66/289.05 Found (x3 x21) as proof of (cNUMBER Xn)
% 288.66/289.05 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21)) as proof of (cNUMBER Xn)
% 288.66/289.05 Found (fun (x6:((and ((and (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 x21)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 288.66/289.05 Found (fun (x6:((and ((and (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 x21)) as proof of (((and ((and (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)))
% 288.66/289.05 Found (and_rect30 (fun (x6:((and ((and (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 x21))) as proof of (cNUMBER Xn)
% 288.66/289.05 Found ((and_rect3 (cNUMBER Xn)) (fun (x6:((and ((and (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 x21))) as proof of (cNUMBER Xn)
% 288.66/289.05 Found (((fun (P:Type) (x6:(((and ((and (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 (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) x4)) (cNUMBER Xn)) (fun (x6:((and ((and (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 x21))) as proof of (cNUMBER Xn)
% 288.66/289.05 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (((fun (P:Type) (x6:(((and ((and (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 (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) x4)) (cNUMBER Xn)) (fun (x6:((and ((and (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 x21)))) as proof of (cNUMBER Xn)
% 290.77/291.22 Found (fun (x5:(forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx))))))=> (((fun (P:Type) (x6:(((and ((and (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 (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) x4)) (cNUMBER Xn)) (fun (x6:((and ((and (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 x21)))) as proof of ((forall (P:(fofType->Prop)) (Q:(fofType->Prop)), (((and ((and (P c0)) (Q c0))) (forall (Xx:fofType), (((and (P Xx)) (Q Xx))->((and (P (cS Xx))) (Q (cS Xx))))))->(forall (Xx:fofType), ((and (P Xx)) (Q Xx)))))->(cNUMBER Xn))
% 290.77/291.22 Found x70:(cNUMBER Xn00)
% 290.77/291.22 Found x70 as proof of (cNUMBER Xn00)
% 290.77/291.22 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 290.77/291.22 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 290.77/291.22 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 290.77/291.22 Found x50:=(x5 x41):(cNUMBER Xn0)
% 290.77/291.22 Instantiate: Xn0:=Xn:fofType
% 290.77/291.22 Found (x5 x41) as proof of (cNUMBER Xn)
% 290.77/291.22 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x41)) as proof of (cNUMBER Xn)
% 290.77/291.22 Found (fun (x11:(cEVEN c0)) (x12:(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))
% 290.77/291.22 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x41)) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 290.77/291.22 Found (and_rect50 (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x41))) as proof of (cNUMBER Xn)
% 290.77/291.22 Found ((and_rect5 (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x41))) as proof of (cNUMBER Xn)
% 290.77/291.22 Found (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x41))) as proof of (cNUMBER Xn)
% 290.77/291.22 Found (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x41))) as proof of (cNUMBER Xn)
% 290.77/291.22 Found x30:=(x3 x21):(cNUMBER Xn0)
% 290.77/291.22 Instantiate: Xn0:=Xn:fofType
% 290.77/291.22 Found (x3 x21) as proof of (cNUMBER Xn)
% 290.77/291.22 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21)) as proof of (cNUMBER Xn)
% 290.77/291.22 Found (fun (x6:((and ((and (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 x21)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 290.77/291.22 Found (fun (x6:((and ((and (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 x21)) as proof of (((and ((and (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)))
% 290.84/291.24 Found (and_rect30 (fun (x6:((and ((and (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 x21))) as proof of (cNUMBER Xn)
% 290.84/291.24 Found ((and_rect3 (cNUMBER Xn)) (fun (x6:((and ((and (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 x21))) as proof of (cNUMBER Xn)
% 290.84/291.24 Found (((fun (P:Type) (x6:(((and ((and (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 (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) x4)) (cNUMBER Xn)) (fun (x6:((and ((and (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 x21))) as proof of (cNUMBER Xn)
% 290.84/291.24 Found (((fun (P:Type) (x6:(((and ((and (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 (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) x4)) (cNUMBER Xn)) (fun (x6:((and ((and (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 x21))) as proof of (cNUMBER Xn)
% 290.84/291.24 Found x30:=(x3 x21):(cNUMBER Xn0)
% 290.84/291.24 Instantiate: Xn0:=Xn:fofType
% 290.84/291.24 Found (x3 x21) as proof of (cNUMBER Xn)
% 290.84/291.24 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21)) as proof of (cNUMBER Xn)
% 290.84/291.24 Found (fun (x6:((and ((and (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 x21)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 290.84/291.24 Found (fun (x6:((and ((and (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 x21)) as proof of (((and ((and (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)))
% 290.84/291.24 Found (and_rect30 (fun (x6:((and ((and (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 x21))) as proof of (cNUMBER Xn)
% 290.84/291.24 Found ((and_rect3 (cNUMBER Xn)) (fun (x6:((and ((and (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 x21))) as proof of (cNUMBER Xn)
% 290.84/291.24 Found (((fun (P:Type) (x6:(((and ((and (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 (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) x4)) (cNUMBER Xn)) (fun (x6:((and ((and (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 x21))) as proof of (cNUMBER Xn)
% 290.84/291.24 Found (((fun (P:Type) (x6:(((and ((and (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 (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) x4)) (cNUMBER Xn)) (fun (x6:((and ((and (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 x21))) as proof of (cNUMBER Xn)
% 295.06/295.48 Found x61:((or (cEVEN Xn0)) (cODD Xn0))
% 295.06/295.48 Found x61 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 295.06/295.48 Found (x7 x61) as proof of (cNUMBER Xn)
% 295.06/295.48 Found (x7 x61) as proof of (cNUMBER Xn)
% 295.06/295.48 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x61)) as proof of (cNUMBER Xn)
% 295.06/295.48 Found (fun (x12:(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))
% 295.06/295.48 Found x61:((or (cEVEN Xn0)) (cODD Xn0))
% 295.06/295.48 Found x61 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 295.06/295.48 Found (x7 x61) as proof of (cNUMBER Xn)
% 295.06/295.48 Found (x7 x61) as proof of (cNUMBER Xn)
% 295.06/295.48 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x61)) as proof of (cNUMBER Xn)
% 295.06/295.48 Found (fun (x11:(cEVEN c0)) (x12:(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))
% 295.06/295.48 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x61)) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 295.06/295.48 Found x61:((or (cEVEN Xn0)) (cODD Xn0))
% 295.06/295.48 Found x61 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 295.06/295.48 Found (x7 x61) as proof of (cNUMBER Xn)
% 295.06/295.48 Found (x7 x61) as proof of (cNUMBER Xn)
% 295.06/295.48 Found (x7 x61) as proof of (cNUMBER Xn)
% 295.06/295.48 Found x30:(cNUMBER Xn0)
% 295.06/295.48 Instantiate: Xn0:=Xn:fofType
% 295.06/295.48 Found x30 as proof of (cNUMBER Xn)
% 295.06/295.48 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 295.06/295.48 Instantiate: Xn0:=Xn00:fofType
% 295.06/295.48 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 295.06/295.48 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 295.06/295.48 Instantiate: Xn00:=Xn0:fofType
% 295.06/295.48 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 295.06/295.48 Found x50:(cNUMBER Xn00)
% 295.06/295.48 Instantiate: Xn00:=Xn:fofType
% 295.06/295.48 Found x50 as proof of (cNUMBER Xn)
% 295.06/295.48 Found x40:=(x4 x30):(cNUMBER Xn00)
% 295.06/295.48 Found (x4 x30) as proof of (cNUMBER Xn0)
% 295.06/295.48 Found (x4 x30) as proof of (cNUMBER Xn0)
% 295.06/295.48 Found (fun (x4:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x4 x30)) as proof of (cNUMBER Xn0)
% 295.06/295.48 Found (fun (x4:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x4 x30)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn0))
% 295.06/295.48 Found x90:(cNUMBER Xn00)
% 295.06/295.48 Found x90 as proof of (cNUMBER Xn00)
% 295.06/295.48 Found (x8 x90) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 295.06/295.48 Found (x8 x90) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 295.06/295.48 Found (x8 x90) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 295.06/295.48 Found x90:=(x9 x80):(cNUMBER Xn0)
% 295.06/295.48 Found (x9 x80) as proof of (cNUMBER Xn0)
% 295.06/295.48 Found (x9 x80) as proof of (cNUMBER Xn0)
% 295.06/295.48 Found x90:=(x9 x81):(cNUMBER Xn0)
% 295.06/295.48 Instantiate: Xn0:=Xn:fofType
% 295.06/295.48 Found (x9 x81) as proof of (cNUMBER Xn)
% 295.06/295.48 Found (x9 x81) as proof of (cNUMBER Xn)
% 295.06/295.48 Found x90:=(x9 x81):(cNUMBER Xn0)
% 295.06/295.48 Found (x9 x81) as proof of (cNUMBER Xn)
% 295.06/295.48 Found (x9 x81) as proof of (cNUMBER Xn)
% 295.06/295.48 Found (x9 x81) as proof of (cNUMBER Xn)
% 295.06/295.48 Found x70:=(x7 x60):(cNUMBER Xn0)
% 295.06/295.48 Instantiate: Xn0:=Xn:fofType
% 295.06/295.48 Found (x7 x60) as proof of (cNUMBER Xn)
% 295.06/295.48 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x7 x60)) as proof of (cNUMBER Xn)
% 295.06/295.48 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))
% 295.06/295.48 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)))
% 295.06/295.48 Found (and_rect40 (fun (x8:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x7 x60))) as proof of (cNUMBER Xn)
% 295.06/295.48 Found ((and_rect4 (cNUMBER Xn)) (fun (x8:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x7 x60))) as proof of (cNUMBER Xn)
% 296.65/297.06 Found (((fun (P:Type) (x8:(((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) x8) x11)) (cNUMBER Xn)) (fun (x8:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x7 x60))) as proof of (cNUMBER Xn)
% 296.65/297.06 Found x50:=(x5 x40):(cNUMBER Xn00)
% 296.65/297.06 Instantiate: Xn00:=Xn:fofType
% 296.65/297.06 Found (x5 x40) as proof of (cNUMBER Xn)
% 296.65/297.06 Found (fun (x13:(cODD (cS c0)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 296.65/297.06 Found (fun (x13:(cODD (cS c0)))=> (x5 x40)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 296.65/297.06 Found x30:=(x3 x20):(cNUMBER Xn0)
% 296.65/297.06 Instantiate: Xn0:=Xn:fofType
% 296.65/297.06 Found (x3 x20) as proof of (cNUMBER Xn)
% 296.65/297.06 Found (fun (x13:(cODD (cS c0)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 296.65/297.06 Found (fun (x13:(cODD (cS c0)))=> (x3 x20)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 296.65/297.06 Found x50:=(x5 x41):(cNUMBER Xn0)
% 296.65/297.06 Instantiate: Xn0:=Xn:fofType
% 296.65/297.06 Found (x5 x41) as proof of (cNUMBER Xn)
% 296.65/297.06 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x41)) as proof of (cNUMBER Xn)
% 296.65/297.06 Found (fun (x11:(cEVEN c0)) (x12:(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))
% 296.65/297.06 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x41)) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 296.65/297.06 Found (and_rect50 (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x41))) as proof of (cNUMBER Xn)
% 296.65/297.06 Found ((and_rect5 (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x41))) as proof of (cNUMBER Xn)
% 296.65/297.06 Found (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x41))) as proof of (cNUMBER Xn)
% 296.65/297.06 Found (fun (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x41)))) as proof of (cNUMBER Xn)
% 296.65/297.06 Found (fun (x9:(cODD (cS c0)))=> (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x41)))) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 296.65/297.06 Found x60:=(x6 x70):((or (cEVEN Xn00)) (cODD Xn00))
% 296.65/297.06 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 296.65/297.06 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 296.65/297.06 Found (fun (x9:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x6 x70)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 296.65/297.06 Found (fun (x9:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x6 x70)) as proof of ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 296.65/297.06 Found x50:=(x5 x41):(cNUMBER Xn0)
% 296.65/297.06 Instantiate: Xn0:=Xn:fofType
% 296.65/297.06 Found (x5 x41) as proof of (cNUMBER Xn)
% 296.65/297.06 Found (fun (x6:(cEVEN Xn0))=> (x5 x41)) as proof of (cNUMBER Xn)
% 296.65/297.06 Found (fun (x6:(cEVEN Xn0))=> (x5 x41)) as proof of ((cEVEN Xn0)->(cNUMBER Xn))
% 296.65/297.06 Found x50:=(x5 x41):(cNUMBER Xn0)
% 296.65/297.06 Instantiate: Xn0:=Xn:fofType
% 296.65/297.06 Found (x5 x41) as proof of (cNUMBER Xn)
% 296.65/297.06 Found (fun (x6:(cODD Xn0))=> (x5 x41)) as proof of (cNUMBER Xn)
% 296.65/297.06 Found (fun (x6:(cODD Xn0))=> (x5 x41)) as proof of ((cODD Xn0)->(cNUMBER Xn))
% 298.35/298.83 Found ((or_ind00 (fun (x6:(cEVEN Xn0))=> (x5 x41))) (fun (x6:(cODD Xn0))=> (x5 x41))) as proof of (cNUMBER Xn)
% 298.35/298.83 Found (((or_ind0 (cNUMBER Xn)) (fun (x6:(cEVEN Xn0))=> (x5 x41))) (fun (x6:(cODD Xn0))=> (x5 x41))) as proof of (cNUMBER Xn)
% 298.35/298.83 Found ((((fun (P:Prop) (x6:((cEVEN Xn0)->P)) (x7:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x6) x7) x40)) (cNUMBER Xn)) (fun (x6:(cEVEN Xn0))=> (x5 x41))) (fun (x6:(cODD Xn0))=> (x5 x41))) as proof of (cNUMBER Xn)
% 298.35/298.83 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> ((((fun (P:Prop) (x6:((cEVEN Xn0)->P)) (x7:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x6) x7) x40)) (cNUMBER Xn)) (fun (x6:(cEVEN Xn0))=> (x5 x41))) (fun (x6:(cODD Xn0))=> (x5 x41)))) as proof of (cNUMBER Xn)
% 298.35/298.83 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> ((((fun (P:Prop) (x6:((cEVEN Xn0)->P)) (x7:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x6) x7) x40)) (cNUMBER Xn)) (fun (x6:(cEVEN Xn0))=> (x5 x41))) (fun (x6:(cODD Xn0))=> (x5 x41)))) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 298.35/298.83 Found x30:=(x3 x20):(cNUMBER Xn0)
% 298.35/298.83 Instantiate: Xn00:=Xn0:fofType
% 298.35/298.83 Found (x3 x20) as proof of (cNUMBER Xn00)
% 298.35/298.83 Found (x3 x20) as proof of (cNUMBER Xn00)
% 298.35/298.83 Found x111:((or (cEVEN Xn0)) (cODD Xn0))
% 298.35/298.83 Found x111 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 298.35/298.83 Found (x12 x111) as proof of (cNUMBER Xn)
% 298.35/298.83 Found (x12 x111) as proof of (cNUMBER Xn)
% 298.35/298.83 Found (x12 x111) as proof of (cNUMBER Xn)
% 298.35/298.83 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 298.35/298.83 Instantiate: Xn0:=Xn00:fofType
% 298.35/298.83 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 298.35/298.83 Found (x3 x40) as proof of (cNUMBER Xn0)
% 298.35/298.83 Found (x3 x40) as proof of (cNUMBER Xn0)
% 298.35/298.83 Found x50:=(x5 x41):(cNUMBER Xn0)
% 298.35/298.83 Instantiate: Xn0:=Xn:fofType
% 298.35/298.83 Found (x5 x41) as proof of (cNUMBER Xn)
% 298.35/298.83 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x41)) as proof of (cNUMBER Xn)
% 298.35/298.83 Found (fun (x11:(cEVEN c0)) (x12:(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))
% 298.35/298.83 Found (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x41)) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 298.35/298.83 Found (and_rect50 (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x41))) as proof of (cNUMBER Xn)
% 298.35/298.83 Found ((and_rect5 (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x41))) as proof of (cNUMBER Xn)
% 298.35/298.83 Found (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x41))) as proof of (cNUMBER Xn)
% 298.35/298.83 Found (((fun (P:Type) (x11:((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x11) x8)) (cNUMBER Xn)) (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x41))) as proof of (cNUMBER Xn)
% 298.35/298.83 Found x50:=(x5 x40):(cNUMBER Xn00)
% 298.35/298.83 Instantiate: Xn0:=Xn00:fofType
% 298.35/298.83 Found (x5 x40) as proof of (cNUMBER Xn0)
% 298.35/298.83 Found (x5 x40) as proof of (cNUMBER Xn0)
% 298.35/298.83 Found x30:=(x3 x20):(cNUMBER Xn0)
% 298.35/298.83 Instantiate: Xn00:=Xn0:fofType
% 298.35/298.83 Found (x3 x20) as proof of (cNUMBER Xn00)
% 298.35/298.83 Found (x3 x20) as proof of (cNUMBER Xn00)
% 298.35/298.83 Found x50:=(x5 x40):(cNUMBER Xn00)
% 298.35/298.83 Instantiate: Xn0:=Xn00:fofType
% 298.35/298.83 Found (x5 x40) as proof of (cNUMBER Xn0)
% 298.35/298.83 Found (x5 x40) as proof of (cNUMBER Xn0)
% 298.35/298.83 Found x50:=(x5 x40):(cNUMBER Xn00)
% 298.35/298.83 Found (x5 x40) as proof of (cNUMBER Xn00)
% 298.35/298.83 Found (x5 x40) as proof of (cNUMBER Xn00)
% 298.35/298.83 Found x60:=(x6 x70):((or (cEVEN Xn00)) (cODD Xn00))
% 298.35/298.83 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 298.35/298.83 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 298.35/298.83 Found (fun (x9:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x6 x70)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 299.16/299.56 Found (fun (x9:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x6 x70)) as proof of ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 299.16/299.56 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 299.16/299.56 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 299.16/299.56 Found (x3 x20) as proof of (cNUMBER Xn00)
% 299.16/299.56 Found (x3 x20) as proof of (cNUMBER Xn00)
% 299.16/299.56 Found (x3 x20) as proof of (cNUMBER Xn00)
% 299.16/299.56 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 299.16/299.56 Found x40 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 299.16/299.56 Found (x5 x40) as proof of (cNUMBER Xn0)
% 299.16/299.56 Found (x5 x40) as proof of (cNUMBER Xn0)
% 299.16/299.56 Found (x5 x40) as proof of (cNUMBER Xn0)
% 299.16/299.56 Found x30:=(x3 x20):(cNUMBER Xn0)
% 299.16/299.56 Found (x3 x20) as proof of (cNUMBER Xn0)
% 299.16/299.56 Found (x3 x20) as proof of (cNUMBER Xn0)
% 299.16/299.56 Found x50:=(x5 x40):(cNUMBER Xn0)
% 299.16/299.56 Instantiate: Xn0:=Xn:fofType
% 299.16/299.56 Found (x5 x40) as proof of (cNUMBER Xn)
% 299.16/299.56 Found (fun (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 299.16/299.56 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(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))
% 299.16/299.56 Found (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (((and ((and (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)))
% 299.16/299.56 Found (and_rect40 (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 299.16/299.56 Found ((and_rect4 (cNUMBER Xn)) (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 299.16/299.56 Found (((fun (P:Type) (x8:(((and ((and (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 (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x8) x2)) (cNUMBER Xn)) (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 299.16/299.56 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (((fun (P:Type) (x8:(((and ((and (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 (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x8) x2)) (cNUMBER Xn)) (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x9:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)))) as proof of (cNUMBER Xn)
% 299.16/299.56 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (((fun (P:Type) (x8:(((and ((and (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 (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x8) x2)) (cNUMBER Xn)) (fun (x8:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (
%------------------------------------------------------------------------------