TSTP Solution File: SYO113^5 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SYO113^5 : TPTP v7.5.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.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 00:50:41 EDT 2022
% Result : Timeout 289.01s 289.37s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SYO113^5 : TPTP v7.5.0. Released v4.0.0.
% 0.03/0.12 % Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.32 % Computer : n013.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPUModel : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % RAMPerCPU : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % DateTime : Fri Mar 11 15:21:22 EST 2022
% 0.11/0.32 % CPUTime :
% 0.11/0.33 ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27'
% 0.11/0.34 Python 2.7.5
% 2.39/2.56 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox2/benchmark/', '/export/starexec/sandbox2/benchmark/']
% 2.39/2.56 FOF formula (<kernel.Constant object at 0x2b14191c65a8>, <kernel.DependentProduct object at 0x2b14116cc440>) of role type named cNUMBER
% 2.39/2.56 Using role type
% 2.39/2.56 Declaring cNUMBER:(fofType->Prop)
% 2.39/2.56 FOF formula (<kernel.Constant object at 0x2b14191c6d88>, <kernel.DependentProduct object at 0x2b14116ccef0>) of role type named cODD
% 2.39/2.56 Using role type
% 2.39/2.56 Declaring cODD:(fofType->Prop)
% 2.39/2.56 FOF formula (<kernel.Constant object at 0x914cf8>, <kernel.DependentProduct object at 0x2b14116cc4d0>) of role type named cEVEN
% 2.39/2.56 Using role type
% 2.39/2.56 Declaring cEVEN:(fofType->Prop)
% 2.39/2.56 FOF formula (<kernel.Constant object at 0x2b14191c6d88>, <kernel.DependentProduct object at 0x2b14116cc710>) of role type named cS
% 2.39/2.56 Using role type
% 2.39/2.56 Declaring cS:(fofType->fofType)
% 2.39/2.56 FOF formula (<kernel.Constant object at 0x2b14191c67e8>, <kernel.Single object at 0x2b14191c6d88>) of role type named c0
% 2.39/2.56 Using role type
% 2.39/2.56 Declaring c0:fofType
% 2.39/2.56 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))))))) (((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))) (forall (Xn:fofType), ((iff (cNUMBER Xn)) ((or (cEVEN Xn)) (cODD Xn)))))->(forall (Xn:fofType), (cNUMBER Xn))) of role conjecture named cTHM350
% 2.39/2.56 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))))))) (((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))) (forall (Xn:fofType), ((iff (cNUMBER Xn)) ((or (cEVEN Xn)) (cODD Xn)))))->(forall (Xn:fofType), (cNUMBER Xn))):Prop
% 2.39/2.56 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))))))) (((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))) (forall (Xn:fofType), ((iff (cNUMBER Xn)) ((or (cEVEN Xn)) (cODD Xn)))))->(forall (Xn:fofType), (cNUMBER Xn)))']
% 2.39/2.56 Parameter fofType:Type.
% 2.39/2.56 Parameter cNUMBER:(fofType->Prop).
% 2.39/2.56 Parameter cODD:(fofType->Prop).
% 2.39/2.56 Parameter cEVEN:(fofType->Prop).
% 2.39/2.56 Parameter cS:(fofType->fofType).
% 2.39/2.56 Parameter c0:fofType.
% 2.39/2.56 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))))))) (((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))) (forall (Xn:fofType), ((iff (cNUMBER Xn)) ((or (cEVEN Xn)) (cODD Xn)))))->(forall (Xn:fofType), (cNUMBER Xn)))
% 2.39/2.56 Found x30:(cNUMBER Xn0)
% 2.39/2.56 Instantiate: Xn0:=Xn:fofType
% 2.39/2.56 Found x30 as proof of (cNUMBER Xn)
% 2.39/2.56 Found x30:=(x3 x20):(cNUMBER Xn0)
% 2.39/2.56 Instantiate: Xn0:=Xn:fofType
% 2.39/2.56 Found (x3 x20) as proof of (cNUMBER Xn)
% 2.39/2.56 Found (x3 x20) as proof of (cNUMBER Xn)
% 2.39/2.56 Found x30:=(x3 x20):(cNUMBER Xn0)
% 2.39/2.56 Instantiate: Xn0:=Xn:fofType
% 2.39/2.56 Found (x3 x20) as proof of (cNUMBER Xn)
% 2.39/2.56 Found (fun (x3:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 2.39/2.56 Found (fun (x3:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x3 x20)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 2.39/2.56 Found x30:=(x3 x20):(cNUMBER Xn0)
% 2.39/2.56 Found (x3 x20) as proof of (cNUMBER Xn)
% 2.39/2.56 Found (x3 x20) as proof of (cNUMBER Xn)
% 2.39/2.56 Found (x3 x20) as proof of (cNUMBER Xn)
% 5.25/5.44 Found x30:=(x3 x20):(cNUMBER Xn0)
% 5.25/5.44 Found (x3 x20) as proof of (cNUMBER Xn)
% 5.25/5.44 Found (x3 x20) as proof of (cNUMBER Xn)
% 5.25/5.44 Found (fun (x3:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 5.25/5.44 Found (fun (x3:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x3 x20)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 5.25/5.44 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 5.25/5.44 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 5.25/5.44 Found (x3 x20) as proof of (cNUMBER Xn)
% 5.25/5.44 Found (x3 x20) as proof of (cNUMBER Xn)
% 5.25/5.44 Found (x3 x20) as proof of (cNUMBER Xn)
% 5.25/5.44 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 5.25/5.44 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 5.25/5.44 Found (x3 x20) as proof of (cNUMBER Xn)
% 5.25/5.44 Found (x3 x20) as proof of (cNUMBER Xn)
% 5.25/5.44 Found (fun (x3:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 5.25/5.44 Found (fun (x3:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x3 x20)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 5.25/5.44 Found x50:(cNUMBER Xn0)
% 5.25/5.44 Instantiate: Xn0:=Xn:fofType
% 5.25/5.44 Found x50 as proof of (cNUMBER Xn)
% 5.25/5.44 Found x30:(cNUMBER Xn0)
% 5.25/5.44 Instantiate: Xn0:=Xn:fofType
% 5.25/5.44 Found x30 as proof of (cNUMBER Xn)
% 5.25/5.44 Found x30:(cNUMBER Xn0)
% 5.25/5.44 Instantiate: Xn0:=Xn:fofType
% 5.25/5.44 Found (fun (x5:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> x30) as proof of (cNUMBER Xn)
% 5.25/5.44 Found (fun (x5:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> x30) as proof of ((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn))
% 5.25/5.44 Found x30:(cNUMBER Xn0)
% 5.25/5.44 Instantiate: Xn0:=Xn:fofType
% 5.25/5.44 Found (fun (x5:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> x30) as proof of (cNUMBER Xn)
% 5.25/5.44 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> x30) as proof of ((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn))
% 5.25/5.44 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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))))))->((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn)))
% 5.25/5.44 Found x50:=(x5 x40):(cNUMBER Xn0)
% 5.25/5.44 Instantiate: Xn0:=Xn:fofType
% 5.25/5.44 Found (x5 x40) as proof of (cNUMBER Xn)
% 5.25/5.44 Found (x5 x40) as proof of (cNUMBER Xn)
% 5.25/5.44 Found x30:=(x3 x20):(cNUMBER Xn0)
% 5.25/5.44 Instantiate: Xn0:=Xn:fofType
% 5.25/5.44 Found (x3 x20) as proof of (cNUMBER Xn)
% 6.68/6.90 Found (x3 x20) as proof of (cNUMBER Xn)
% 6.68/6.90 Found x50:=(x5 x40):(cNUMBER Xn0)
% 6.68/6.90 Instantiate: Xn0:=Xn:fofType
% 6.68/6.90 Found (x5 x40) as proof of (cNUMBER Xn)
% 6.68/6.90 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 6.68/6.90 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x5 x40)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 6.68/6.90 Found x30:=(x3 x20):(cNUMBER Xn0)
% 6.68/6.90 Instantiate: Xn0:=Xn:fofType
% 6.68/6.90 Found (x3 x20) as proof of (cNUMBER Xn)
% 6.68/6.90 Found (fun (x5:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 6.68/6.90 Found (fun (x5:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x3 x20)) as proof of ((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn))
% 6.68/6.90 Found x50:=(x5 x40):(cNUMBER Xn0)
% 6.68/6.90 Found (x5 x40) as proof of (cNUMBER Xn)
% 6.68/6.90 Found (x5 x40) as proof of (cNUMBER Xn)
% 6.68/6.90 Found (x5 x40) as proof of (cNUMBER Xn)
% 6.68/6.90 Found x30:=(x3 x20):(cNUMBER Xn0)
% 6.68/6.90 Instantiate: Xn0:=Xn:fofType
% 6.68/6.90 Found (x3 x20) as proof of (cNUMBER Xn)
% 6.68/6.90 Found (fun (x5:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 6.68/6.90 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x3 x20)) as proof of ((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn))
% 6.68/6.90 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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))))))->((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn)))
% 6.68/6.90 Found x30:=(x3 x20):(cNUMBER Xn0)
% 6.68/6.90 Found (x3 x20) as proof of (cNUMBER Xn)
% 6.68/6.90 Found (x3 x20) as proof of (cNUMBER Xn)
% 6.68/6.90 Found (x3 x20) as proof of (cNUMBER Xn)
% 6.68/6.90 Found x50:=(x5 x40):(cNUMBER Xn0)
% 6.68/6.90 Found (x5 x40) as proof of (cNUMBER Xn)
% 6.68/6.90 Found (x5 x40) as proof of (cNUMBER Xn)
% 6.68/6.90 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 6.68/6.90 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x5 x40)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 6.68/6.90 Found x30:=(x3 x20):(cNUMBER Xn0)
% 6.68/6.90 Found (x3 x20) as proof of (cNUMBER Xn)
% 6.68/6.90 Found (x3 x20) as proof of (cNUMBER Xn)
% 6.68/6.90 Found (fun (x5:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 8.10/8.30 Found (fun (x5:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x3 x20)) as proof of ((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn))
% 8.10/8.30 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 8.10/8.30 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 8.10/8.30 Found (x5 x40) as proof of (cNUMBER Xn)
% 8.10/8.30 Found (x5 x40) as proof of (cNUMBER Xn)
% 8.10/8.30 Found (x5 x40) as proof of (cNUMBER Xn)
% 8.10/8.30 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 8.10/8.30 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 8.10/8.30 Found (x3 x20) as proof of (cNUMBER Xn)
% 8.10/8.30 Found (x3 x20) as proof of (cNUMBER Xn)
% 8.10/8.30 Found (x3 x20) as proof of (cNUMBER Xn)
% 8.10/8.30 Found x30:=(x3 x20):(cNUMBER Xn0)
% 8.10/8.30 Found (x3 x20) as proof of (cNUMBER Xn)
% 8.10/8.30 Found (x3 x20) as proof of (cNUMBER Xn)
% 8.10/8.30 Found (fun (x5:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 8.10/8.30 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x3 x20)) as proof of ((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn))
% 8.10/8.30 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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))))))->((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn)))
% 8.10/8.30 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 8.10/8.30 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 8.10/8.30 Found (x5 x40) as proof of (cNUMBER Xn)
% 8.10/8.30 Found (x5 x40) as proof of (cNUMBER Xn)
% 8.10/8.30 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 8.10/8.30 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x5 x40)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 8.10/8.30 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 8.10/8.30 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 8.10/8.30 Found (x3 x20) as proof of (cNUMBER Xn)
% 8.10/8.30 Found (x3 x20) as proof of (cNUMBER Xn)
% 8.10/8.30 Found (fun (x5:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 8.10/8.30 Found (fun (x5:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x3 x20)) as proof of ((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn))
% 11.00/11.16 Found x30:(cNUMBER Xn0)
% 11.00/11.16 Instantiate: Xn0:=Xn:fofType
% 11.00/11.16 Found x30 as proof of (cNUMBER Xn)
% 11.00/11.16 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 11.00/11.16 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 11.00/11.16 Found (x3 x20) as proof of (cNUMBER Xn)
% 11.00/11.16 Found (x3 x20) as proof of (cNUMBER Xn)
% 11.00/11.16 Found (fun (x5:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 11.00/11.16 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x3 x20)) as proof of ((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn))
% 11.00/11.17 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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))))))->((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn)))
% 11.00/11.17 Found x30:(cNUMBER Xn0)
% 11.00/11.17 Instantiate: Xn0:=Xn:fofType
% 11.00/11.17 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of (cNUMBER Xn)
% 11.00/11.17 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))
% 11.00/11.17 Found x70:(cNUMBER Xn0)
% 11.00/11.17 Instantiate: Xn0:=Xn:fofType
% 11.00/11.17 Found x70 as proof of (cNUMBER Xn)
% 11.00/11.17 Found x50:(cNUMBER Xn0)
% 11.00/11.17 Instantiate: Xn0:=Xn:fofType
% 11.00/11.17 Found x50 as proof of (cNUMBER Xn)
% 11.00/11.17 Found x30:(cNUMBER Xn0)
% 11.00/11.17 Instantiate: Xn0:=Xn:fofType
% 11.00/11.17 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of (cNUMBER Xn)
% 11.00/11.17 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))))))=> x30) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 11.00/11.17 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))))))=> 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)))
% 11.00/11.17 Found x30:=(x3 x20):(cNUMBER Xn0)
% 11.00/11.17 Instantiate: Xn0:=Xn:fofType
% 11.00/11.17 Found (x3 x20) as proof of (cNUMBER Xn)
% 11.00/11.17 Found (fun (x5:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 11.00/11.17 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x3 x20)) as proof of ((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn))
% 11.00/11.17 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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))))))->((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn)))
% 11.00/11.17 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 11.00/11.17 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 11.00/11.17 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))))))->((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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))))))) (((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 11.00/11.17 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))))))->((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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))))))) (((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 12.50/12.70 Found x30:=(x3 x20):(cNUMBER Xn0)
% 12.50/12.70 Instantiate: Xn0:=Xn:fofType
% 12.50/12.70 Found (x3 x20) as proof of (cNUMBER Xn)
% 12.50/12.70 Found (x3 x20) as proof of (cNUMBER Xn)
% 12.50/12.70 Found x50:(cNUMBER Xn0)
% 12.50/12.70 Instantiate: Xn0:=Xn:fofType
% 12.50/12.70 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of (cNUMBER Xn)
% 12.50/12.70 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))
% 12.50/12.70 Found x30:=(x3 x20):(cNUMBER Xn0)
% 12.50/12.70 Instantiate: Xn0:=Xn:fofType
% 12.50/12.70 Found (x3 x20) as proof of (cNUMBER Xn)
% 12.50/12.70 Found (fun (x5:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 12.50/12.70 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x3 x20)) as proof of ((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn))
% 12.50/12.70 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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))))))->((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn)))
% 12.50/12.70 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 12.50/12.70 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 12.50/12.70 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))))))->((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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))))))) (((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 12.50/12.70 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))))))->((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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))))))) (((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x3 x20)))) as proof of (cNUMBER Xn)
% 12.50/12.70 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))))))->((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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))))))) (((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x3 x20)))) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 16.50/16.67 Found x30:=(x3 x20):(cNUMBER Xn0)
% 16.50/16.67 Instantiate: Xn0:=Xn:fofType
% 16.50/16.67 Found (x3 x20) as proof of (cNUMBER Xn)
% 16.50/16.67 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 16.50/16.67 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))
% 16.50/16.67 Found x50:(cNUMBER Xn0)
% 16.50/16.67 Instantiate: Xn0:=Xn:fofType
% 16.50/16.67 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of (cNUMBER Xn)
% 16.50/16.67 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))
% 16.50/16.67 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)))
% 16.50/16.67 Found x70:=(x7 x60):(cNUMBER Xn0)
% 16.50/16.67 Instantiate: Xn0:=Xn:fofType
% 16.50/16.67 Found (x7 x60) as proof of (cNUMBER Xn)
% 16.50/16.67 Found (x7 x60) as proof of (cNUMBER Xn)
% 16.50/16.67 Found x50:=(x5 x40):(cNUMBER Xn0)
% 16.50/16.67 Instantiate: Xn0:=Xn:fofType
% 16.50/16.67 Found (x5 x40) as proof of (cNUMBER Xn)
% 16.50/16.67 Found (x5 x40) as proof of (cNUMBER Xn)
% 16.50/16.67 Found x30:=(x3 x20):(cNUMBER Xn0)
% 16.50/16.67 Instantiate: Xn0:=Xn:fofType
% 16.50/16.67 Found (x3 x20) as proof of (cNUMBER Xn)
% 16.50/16.67 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 16.50/16.67 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))
% 16.50/16.67 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)))
% 16.50/16.67 Found x30:=(x3 x20):(cNUMBER Xn0)
% 16.50/16.67 Found (x3 x20) as proof of (cNUMBER Xn)
% 16.50/16.67 Found (x3 x20) as proof of (cNUMBER Xn)
% 16.50/16.67 Found (x3 x20) as proof of (cNUMBER Xn)
% 16.50/16.67 Found x70:=(x7 x60):(cNUMBER Xn0)
% 16.50/16.67 Instantiate: Xn0:=Xn:fofType
% 16.50/16.67 Found (x7 x60) as proof of (cNUMBER Xn)
% 16.50/16.67 Found (fun (x7:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x7 x60)) as proof of (cNUMBER Xn)
% 16.50/16.67 Found (fun (x7:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x7 x60)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 16.50/16.67 Found x50:=(x5 x40):(cNUMBER Xn0)
% 16.50/16.67 Instantiate: Xn0:=Xn:fofType
% 16.50/16.67 Found (x5 x40) as proof of (cNUMBER Xn)
% 16.50/16.67 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 16.50/16.67 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))
% 16.50/16.67 Found x30:=(x3 x20):(cNUMBER Xn0)
% 16.50/16.67 Found (x3 x20) as proof of (cNUMBER Xn)
% 16.50/16.67 Found (x3 x20) as proof of (cNUMBER Xn)
% 16.50/16.67 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 16.50/16.67 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))
% 16.50/16.67 Found x70:=(x7 x60):(cNUMBER Xn0)
% 16.50/16.67 Found (x7 x60) as proof of (cNUMBER Xn)
% 16.50/16.67 Found (x7 x60) as proof of (cNUMBER Xn)
% 20.34/20.54 Found (x7 x60) as proof of (cNUMBER Xn)
% 20.34/20.54 Found x50:=(x5 x40):(cNUMBER Xn0)
% 20.34/20.54 Instantiate: Xn0:=Xn:fofType
% 20.34/20.54 Found (x5 x40) as proof of (cNUMBER Xn)
% 20.34/20.54 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 20.34/20.54 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))))))=> (x5 x40)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 20.34/20.54 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))))))=> (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)))
% 20.34/20.54 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 20.34/20.54 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 20.34/20.54 Found (x3 x20) as proof of (cNUMBER Xn)
% 20.34/20.54 Found (x3 x20) as proof of (cNUMBER Xn)
% 20.34/20.54 Found (x3 x20) as proof of (cNUMBER Xn)
% 20.34/20.54 Found x30:=(x3 x20):(cNUMBER Xn0)
% 20.34/20.54 Found (x3 x20) as proof of (cNUMBER Xn)
% 20.34/20.54 Found (x3 x20) as proof of (cNUMBER Xn)
% 20.34/20.54 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 20.34/20.54 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))
% 20.34/20.54 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)))
% 20.34/20.54 Found x50:=(x5 x40):(cNUMBER Xn0)
% 20.34/20.54 Found (x5 x40) as proof of (cNUMBER Xn)
% 20.34/20.54 Found (x5 x40) as proof of (cNUMBER Xn)
% 20.34/20.54 Found (x5 x40) as proof of (cNUMBER Xn)
% 20.34/20.54 Found x70:=(x7 x60):(cNUMBER Xn0)
% 20.34/20.54 Found (x7 x60) as proof of (cNUMBER Xn)
% 20.34/20.54 Found (x7 x60) as proof of (cNUMBER Xn)
% 20.34/20.54 Found (fun (x7:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x7 x60)) as proof of (cNUMBER Xn)
% 20.34/20.54 Found (fun (x7:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x7 x60)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 20.34/20.54 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 20.34/20.54 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 20.34/20.54 Found (x3 x20) as proof of (cNUMBER Xn)
% 20.34/20.54 Found (x3 x20) as proof of (cNUMBER Xn)
% 20.34/20.54 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 20.34/20.54 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))
% 20.34/20.54 Found x50:=(x5 x40):(cNUMBER Xn0)
% 20.34/20.54 Found (x5 x40) as proof of (cNUMBER Xn)
% 20.34/20.54 Found (x5 x40) as proof of (cNUMBER Xn)
% 20.34/20.54 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 20.34/20.54 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))
% 20.34/20.54 Found x60:((or (cEVEN Xn0)) (cODD Xn0))
% 20.34/20.54 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 20.34/20.54 Found (x7 x60) as proof of (cNUMBER Xn)
% 20.34/20.54 Found (x7 x60) as proof of (cNUMBER Xn)
% 20.34/20.54 Found (x7 x60) as proof of (cNUMBER Xn)
% 20.34/20.54 Found x30:(cNUMBER Xn0)
% 20.34/20.54 Instantiate: Xn0:=Xn:fofType
% 20.34/20.54 Found x30 as proof of (cNUMBER Xn)
% 20.34/20.54 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 20.34/20.54 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 20.34/20.54 Found (x5 x40) as proof of (cNUMBER Xn)
% 20.34/20.54 Found (x5 x40) as proof of (cNUMBER Xn)
% 20.34/20.54 Found (x5 x40) as proof of (cNUMBER Xn)
% 20.34/20.54 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 20.34/20.54 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 20.34/20.54 Found (x3 x20) as proof of (cNUMBER Xn)
% 20.34/20.54 Found (x3 x20) as proof of (cNUMBER Xn)
% 22.79/22.95 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 22.79/22.95 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 x20)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 22.79/22.95 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 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)))
% 22.79/22.95 Found x50:=(x5 x40):(cNUMBER Xn0)
% 22.79/22.95 Found (x5 x40) as proof of (cNUMBER Xn)
% 22.79/22.95 Found (x5 x40) as proof of (cNUMBER Xn)
% 22.79/22.95 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 22.79/22.95 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))))))=> (x5 x40)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 22.79/22.95 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))))))=> (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)))
% 22.79/22.95 Found x30:=(x3 x20):(cNUMBER Xn0)
% 22.79/22.95 Found (x3 x20) as proof of (cNUMBER Xn0)
% 22.79/22.95 Found (x3 x20) as proof of (cNUMBER Xn0)
% 22.79/22.95 Found x30:=(x3 x21):(cNUMBER Xn0)
% 22.79/22.95 Instantiate: Xn0:=Xn:fofType
% 22.79/22.95 Found (x3 x21) as proof of (cNUMBER Xn)
% 22.79/22.95 Found (x3 x21) as proof of (cNUMBER Xn)
% 22.79/22.95 Found x30:=(x3 x21):(cNUMBER Xn0)
% 22.79/22.95 Found (x3 x21) as proof of (cNUMBER Xn)
% 22.79/22.95 Found (x3 x21) as proof of (cNUMBER Xn)
% 22.79/22.95 Found (x3 x21) as proof of (cNUMBER Xn)
% 22.79/22.95 Found x60:((or (cEVEN Xn0)) (cODD Xn0))
% 22.79/22.95 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 22.79/22.95 Found (x7 x60) as proof of (cNUMBER Xn)
% 22.79/22.95 Found (x7 x60) as proof of (cNUMBER Xn)
% 22.79/22.95 Found (fun (x7:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x7 x60)) as proof of (cNUMBER Xn)
% 22.79/22.95 Found (fun (x7:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x7 x60)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 22.79/22.95 Found x21:((or (cEVEN Xn0)) (cODD Xn0))
% 22.79/22.95 Found x21 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 22.79/22.95 Found (x3 x21) as proof of (cNUMBER Xn)
% 22.79/22.95 Found (x3 x21) as proof of (cNUMBER Xn)
% 22.79/22.95 Found (x3 x21) as proof of (cNUMBER Xn)
% 22.79/22.95 Found x30:(cNUMBER Xn0)
% 22.79/22.95 Instantiate: Xn0:=Xn:fofType
% 22.79/22.95 Found (fun (x9:(cODD (cS c0)))=> x30) as proof of (cNUMBER Xn)
% 22.79/22.95 Found (fun (x9:(cODD (cS c0)))=> x30) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 22.79/22.95 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 22.79/22.95 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 22.79/22.95 Found (x5 x40) as proof of (cNUMBER Xn)
% 22.79/22.95 Found (x5 x40) as proof of (cNUMBER Xn)
% 22.79/22.95 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 22.79/22.95 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))
% 22.79/22.95 Found x30:=(x3 x20):(cNUMBER Xn0)
% 22.79/22.95 Instantiate: Xn0:=Xn:fofType
% 22.79/22.95 Found (x3 x20) as proof of (cNUMBER Xn)
% 22.79/22.95 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 22.79/22.95 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 x20)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 22.79/22.95 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 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)))
% 24.81/25.02 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)
% 24.81/25.02 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)
% 24.81/25.02 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)
% 24.81/25.02 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)
% 24.81/25.02 Found x30:=(x3 x20):(cNUMBER Xn0)
% 24.81/25.02 Found (x3 x20) as proof of (cNUMBER Xn0)
% 24.81/25.02 Found (x3 x20) as proof of (cNUMBER Xn0)
% 24.81/25.02 Found x30:=(x3 x21):(cNUMBER Xn0)
% 24.81/25.02 Instantiate: Xn0:=Xn:fofType
% 24.81/25.02 Found (x3 x21) as proof of (cNUMBER Xn)
% 24.81/25.02 Found (x3 x21) as proof of (cNUMBER Xn)
% 24.81/25.02 Found x30:=(x3 x21):(cNUMBER Xn0)
% 24.81/25.02 Found (x3 x21) as proof of (cNUMBER Xn)
% 24.81/25.02 Found (x3 x21) as proof of (cNUMBER Xn)
% 24.81/25.02 Found (x3 x21) as proof of (cNUMBER Xn)
% 24.81/25.02 Found x21:((or (cEVEN Xn0)) (cODD Xn0))
% 24.81/25.02 Found x21 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 24.81/25.02 Found (x3 x21) as proof of (cNUMBER Xn)
% 24.81/25.02 Found (x3 x21) as proof of (cNUMBER Xn)
% 24.81/25.02 Found (x3 x21) as proof of (cNUMBER Xn)
% 24.81/25.02 Found x50:(cNUMBER Xn0)
% 24.81/25.02 Instantiate: Xn0:=Xn:fofType
% 24.81/25.02 Found x50 as proof of (cNUMBER Xn)
% 24.81/25.02 Found x30:(cNUMBER Xn0)
% 24.81/25.02 Instantiate: Xn0:=Xn:fofType
% 24.81/25.02 Found (fun (x9:(cODD (cS c0)))=> x30) as proof of (cNUMBER Xn)
% 24.81/25.02 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))
% 24.81/25.02 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)))
% 24.81/25.02 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 24.81/25.02 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 24.81/25.02 Found (x5 x40) as proof of (cNUMBER Xn)
% 24.81/25.02 Found (x5 x40) as proof of (cNUMBER Xn)
% 24.81/25.02 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 24.81/25.02 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))
% 24.81/25.02 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)))
% 25.82/26.02 Found x30:=(x3 x20):(cNUMBER Xn0)
% 25.82/26.02 Instantiate: Xn0:=Xn:fofType
% 25.82/26.02 Found (x3 x20) as proof of (cNUMBER Xn)
% 25.82/26.02 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 25.82/26.02 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))
% 25.82/26.02 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)))
% 25.82/26.02 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)
% 25.82/26.02 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)
% 25.82/26.02 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)
% 25.82/26.02 Found (fun (x5:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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)
% 25.82/26.02 Found (fun (x5:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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 (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn))
% 25.82/26.02 Found x30:=(x3 x21):(cNUMBER Xn0)
% 25.82/26.02 Instantiate: Xn0:=Xn:fofType
% 25.82/26.02 Found (x3 x21) as proof of (cNUMBER Xn)
% 25.82/26.02 Found (fun (x3:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x3 x21)) as proof of (cNUMBER Xn)
% 25.92/26.07 Found (fun (x3:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x3 x21)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 25.92/26.07 Found x30:=(x3 x20):(cNUMBER Xn0)
% 25.92/26.07 Instantiate: Xn0:=Xn:fofType
% 25.92/26.07 Found (x3 x20) as proof of (cNUMBER Xn)
% 25.92/26.07 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 25.92/26.07 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))
% 25.92/26.07 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)))
% 25.92/26.07 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)
% 25.92/26.07 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)
% 25.92/26.07 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)
% 25.92/26.07 Found (fun (x5:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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)
% 25.92/26.07 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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 (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn))
% 27.78/27.95 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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))))))->((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn)))
% 27.78/27.95 Found x50:(cNUMBER Xn0)
% 27.78/27.95 Instantiate: Xn0:=Xn:fofType
% 27.78/27.95 Found (fun (x9:(cODD (cS c0)))=> x50) as proof of (cNUMBER Xn)
% 27.78/27.95 Found (fun (x9:(cODD (cS c0)))=> x50) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 27.78/27.95 Found x30:=(x3 x20):(cNUMBER Xn0)
% 27.78/27.95 Instantiate: Xn0:=Xn:fofType
% 27.78/27.95 Found (x3 x20) as proof of (cNUMBER Xn)
% 27.78/27.95 Found (x3 x20) as proof of (cNUMBER Xn)
% 27.78/27.95 Found x50:=(x5 x40):(cNUMBER Xn0)
% 27.78/27.95 Instantiate: Xn0:=Xn:fofType
% 27.78/27.95 Found (x5 x40) as proof of (cNUMBER Xn)
% 27.78/27.95 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 27.78/27.95 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))))))=> (x5 x40)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 27.78/27.95 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))))))=> (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)))
% 27.78/27.95 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))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 27.78/27.95 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))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 27.78/27.95 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) 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)
% 27.78/27.95 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) 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)
% 31.18/31.37 Found x90:(cNUMBER Xn0)
% 31.18/31.37 Instantiate: Xn0:=Xn:fofType
% 31.18/31.37 Found x90 as proof of (cNUMBER Xn)
% 31.18/31.37 Found x70:(cNUMBER Xn0)
% 31.18/31.37 Instantiate: Xn0:=Xn:fofType
% 31.18/31.37 Found x70 as proof of (cNUMBER Xn)
% 31.18/31.37 Found x50:(cNUMBER Xn0)
% 31.18/31.37 Instantiate: Xn0:=Xn:fofType
% 31.18/31.37 Found (fun (x9:(cODD (cS c0)))=> x50) as proof of (cNUMBER Xn)
% 31.18/31.37 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))
% 31.18/31.37 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)))
% 31.18/31.37 Found x30:=(x3 x20):(cNUMBER Xn0)
% 31.18/31.37 Instantiate: Xn0:=Xn:fofType
% 31.18/31.37 Found (x3 x20) as proof of (cNUMBER Xn)
% 31.18/31.37 Found (fun (x9:(cODD (cS c0)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 31.18/31.37 Found (fun (x9:(cODD (cS c0)))=> (x3 x20)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 31.18/31.37 Found x50:=(x5 x40):(cNUMBER Xn0)
% 31.18/31.37 Instantiate: Xn0:=Xn:fofType
% 31.18/31.37 Found (x5 x40) as proof of (cNUMBER Xn)
% 31.18/31.37 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 31.18/31.37 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))
% 31.18/31.37 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)))
% 31.18/31.37 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))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 31.18/31.37 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))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 31.18/31.37 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) 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)
% 31.18/31.37 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)
% 35.78/35.96 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))
% 35.78/35.96 Found x70:(cNUMBER Xn0)
% 35.78/35.96 Instantiate: Xn0:=Xn:fofType
% 35.78/35.96 Found (fun (x9:(cODD (cS c0)))=> x70) as proof of (cNUMBER Xn)
% 35.78/35.96 Found (fun (x9:(cODD (cS c0)))=> x70) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 35.78/35.96 Found x50:=(x5 x40):(cNUMBER Xn0)
% 35.78/35.96 Instantiate: Xn0:=Xn:fofType
% 35.78/35.96 Found (x5 x40) as proof of (cNUMBER Xn)
% 35.78/35.96 Found (x5 x40) as proof of (cNUMBER Xn)
% 35.78/35.96 Found x30:=(x3 x20):(cNUMBER Xn0)
% 35.78/35.96 Instantiate: Xn0:=Xn:fofType
% 35.78/35.96 Found (x3 x20) as proof of (cNUMBER Xn)
% 35.78/35.96 Found (fun (x9:(cODD (cS c0)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 35.78/35.96 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))
% 35.78/35.96 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)))
% 35.78/35.96 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 35.78/35.96 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 35.78/35.96 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 35.78/35.96 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 35.78/35.96 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)))
% 35.78/35.96 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))))
% 35.78/35.96 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))
% 35.78/35.96 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))
% 35.78/35.96 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))
% 35.78/35.96 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))
% 35.78/35.96 Found x30:=(x3 x21):(cNUMBER Xn0)
% 35.78/35.96 Found (x3 x21) as proof of (cNUMBER Xn)
% 35.78/35.96 Found (x3 x21) as proof of (cNUMBER Xn)
% 35.78/35.96 Found (fun (x3:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x3 x21)) as proof of (cNUMBER Xn)
% 41.80/41.99 Found (fun (x3:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x3 x21)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 41.80/41.99 Found x30:=(x3 x20):(cNUMBER Xn0)
% 41.80/41.99 Found (x3 x20) as proof of (cNUMBER Xn)
% 41.80/41.99 Found (x3 x20) as proof of (cNUMBER Xn)
% 41.80/41.99 Found (x3 x20) as proof of (cNUMBER Xn)
% 41.80/41.99 Found x50:(cNUMBER Xn0)
% 41.80/41.99 Instantiate: Xn0:=Xn:fofType
% 41.80/41.99 Found x50 as proof of (cNUMBER Xn)
% 41.80/41.99 Found x70:(cNUMBER Xn0)
% 41.80/41.99 Instantiate: Xn0:=Xn:fofType
% 41.80/41.99 Found (fun (x9:(cODD (cS c0)))=> x70) as proof of (cNUMBER Xn)
% 41.80/41.99 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))
% 41.80/41.99 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)))
% 41.80/41.99 Found x50:=(x5 x40):(cNUMBER Xn0)
% 41.80/41.99 Instantiate: Xn0:=Xn:fofType
% 41.80/41.99 Found (x5 x40) as proof of (cNUMBER Xn)
% 41.80/41.99 Found (fun (x9:(cODD (cS c0)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 41.80/41.99 Found (fun (x9:(cODD (cS c0)))=> (x5 x40)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 41.80/41.99 Found x30:(cNUMBER Xn0)
% 41.80/41.99 Instantiate: Xn0:=Xn:fofType
% 41.80/41.99 Found x30 as proof of (cNUMBER Xn)
% 41.80/41.99 Found x90:=(x9 x80):(cNUMBER Xn0)
% 41.80/41.99 Instantiate: Xn0:=Xn:fofType
% 41.80/41.99 Found (x9 x80) as proof of (cNUMBER Xn)
% 41.80/41.99 Found (x9 x80) as proof of (cNUMBER Xn)
% 41.80/41.99 Found x30:=(x3 x20):(cNUMBER Xn0)
% 41.80/41.99 Found (x3 x20) as proof of (cNUMBER Xn)
% 41.80/41.99 Found (x3 x20) as proof of (cNUMBER Xn)
% 41.80/41.99 Found (fun (x9:(cODD (cS c0)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 41.80/41.99 Found (fun (x9:(cODD (cS c0)))=> (x3 x20)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 41.80/41.99 Found x50:(cNUMBER Xn0)
% 41.80/41.99 Instantiate: Xn0:=Xn:fofType
% 41.80/41.99 Found x50 as proof of (cNUMBER Xn)
% 41.80/41.99 Found x70:=(x7 x60):(cNUMBER Xn0)
% 41.80/41.99 Instantiate: Xn0:=Xn:fofType
% 41.80/41.99 Found (x7 x60) as proof of (cNUMBER Xn)
% 41.80/41.99 Found (x7 x60) as proof of (cNUMBER Xn)
% 41.80/41.99 Found x50:=(x5 x40):(cNUMBER Xn0)
% 41.80/41.99 Instantiate: Xn0:=Xn:fofType
% 41.80/41.99 Found (x5 x40) as proof of (cNUMBER Xn)
% 41.80/41.99 Found (fun (x9:(cODD (cS c0)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 41.80/41.99 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))
% 41.80/41.99 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)))
% 41.80/41.99 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 41.80/41.99 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 41.80/41.99 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 41.80/41.99 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 41.80/41.99 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)))
% 41.80/41.99 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))))
% 41.80/41.99 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))
% 41.80/41.99 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))
% 41.80/41.99 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))
% 43.78/44.01 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))
% 43.78/44.01 Found x90:=(x9 x80):(cNUMBER Xn0)
% 43.78/44.01 Instantiate: Xn0:=Xn:fofType
% 43.78/44.01 Found (x9 x80) as proof of (cNUMBER Xn)
% 43.78/44.01 Found (fun (x9:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x9 x80)) as proof of (cNUMBER Xn)
% 43.78/44.01 Found (fun (x9:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x9 x80)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 43.78/44.01 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 43.78/44.01 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 43.78/44.01 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 43.78/44.01 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 43.78/44.01 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)))
% 43.78/44.01 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))))
% 43.78/44.01 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))
% 43.78/44.01 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))
% 43.78/44.01 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))
% 43.78/44.01 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))
% 43.78/44.01 Found x30:=(x3 x20):(cNUMBER Xn0)
% 43.78/44.01 Found (x3 x20) as proof of (cNUMBER Xn0)
% 43.78/44.01 Found (x3 x20) as proof of (cNUMBER Xn0)
% 43.78/44.01 Found x50:=(x5 x40):(cNUMBER Xn0)
% 43.78/44.01 Found (x5 x40) as proof of (cNUMBER Xn)
% 43.78/44.01 Found (x5 x40) as proof of (cNUMBER Xn)
% 43.78/44.01 Found (x5 x40) as proof of (cNUMBER Xn)
% 43.78/44.01 Found x30:=(x3 x20):(cNUMBER Xn0)
% 43.78/44.01 Found (x3 x20) as proof of (cNUMBER Xn)
% 43.78/44.01 Found (x3 x20) as proof of (cNUMBER Xn)
% 43.78/44.01 Found (fun (x9:(cODD (cS c0)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 43.78/44.01 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))
% 43.78/44.01 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)))
% 45.19/45.40 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 45.19/45.40 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 45.19/45.40 Found (x3 x20) as proof of (cNUMBER Xn)
% 45.19/45.40 Found (x3 x20) as proof of (cNUMBER Xn)
% 45.19/45.40 Found (x3 x20) as proof of (cNUMBER Xn)
% 45.19/45.40 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 45.19/45.40 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 45.19/45.40 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 45.19/45.40 Found x31:(cNUMBER Xn0)
% 45.19/45.40 Instantiate: Xn0:=Xn:fofType
% 45.19/45.40 Found (fun (x5:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> x31) as proof of (cNUMBER Xn)
% 45.19/45.40 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> x31) as proof of ((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn))
% 45.19/45.40 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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))))))->((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn)))
% 45.19/45.40 Found x300:=(x30 c0):((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 45.19/45.40 Found (x30 c0) as proof of ((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 45.19/45.40 Found (x30 c0) as proof of ((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 45.19/45.40 Found x50:(cNUMBER Xn0)
% 45.19/45.40 Instantiate: Xn0:=Xn:fofType
% 45.19/45.40 Found x50 as proof of (cNUMBER Xn)
% 45.19/45.40 Found x70:=(x7 x60):(cNUMBER Xn0)
% 45.19/45.40 Instantiate: Xn0:=Xn:fofType
% 45.19/45.40 Found (x7 x60) as proof of (cNUMBER Xn)
% 45.19/45.40 Found (fun (x9:(cODD (cS c0)))=> (x7 x60)) as proof of (cNUMBER Xn)
% 45.19/45.40 Found (fun (x9:(cODD (cS c0)))=> (x7 x60)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 45.19/45.40 Found x21:((or (cEVEN Xn0)) (cODD Xn0))
% 45.19/45.40 Found x21 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 45.19/45.40 Found (x3 x21) as proof of (cNUMBER Xn)
% 45.19/45.40 Found (x3 x21) as proof of (cNUMBER Xn)
% 45.19/45.40 Found (fun (x3:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x3 x21)) as proof of (cNUMBER Xn)
% 45.19/45.40 Found (fun (x3:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x3 x21)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 45.19/45.40 Found x31:(cNUMBER Xn0)
% 45.19/45.40 Instantiate: Xn0:=Xn:fofType
% 45.19/45.40 Found (fun (x5:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> x31) as proof of (cNUMBER Xn)
% 45.19/45.40 Found (fun (x5:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> x31) as proof of ((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn))
% 48.66/48.87 Found x30:=(x3 x21):(cNUMBER Xn0)
% 48.66/48.87 Instantiate: Xn0:=Xn:fofType
% 48.66/48.87 Found (x3 x21) as proof of (cNUMBER Xn)
% 48.66/48.87 Found (fun (x5:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x3 x21)) as proof of (cNUMBER Xn)
% 48.66/48.87 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x3 x21)) as proof of ((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn))
% 48.66/48.87 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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))))))->((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn)))
% 48.66/48.87 Found x50:=(x5 x40):(cNUMBER Xn0)
% 48.66/48.87 Found (x5 x40) as proof of (cNUMBER Xn)
% 48.66/48.87 Found (x5 x40) as proof of (cNUMBER Xn)
% 48.66/48.87 Found (fun (x9:(cODD (cS c0)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 48.66/48.87 Found (fun (x9:(cODD (cS c0)))=> (x5 x40)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 48.66/48.87 Found x30:=(x3 x20):(cNUMBER Xn0)
% 48.66/48.87 Found (x3 x20) as proof of (cNUMBER Xn0)
% 48.66/48.87 Found (x3 x20) as proof of (cNUMBER Xn0)
% 48.66/48.87 Found x30:=(x3 x21):(cNUMBER Xn0)
% 48.66/48.87 Instantiate: Xn0:=Xn:fofType
% 48.66/48.87 Found (x3 x21) as proof of (cNUMBER Xn)
% 48.66/48.87 Found (fun (x5:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x3 x21)) as proof of (cNUMBER Xn)
% 48.66/48.87 Found (fun (x5:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x3 x21)) as proof of ((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn))
% 48.66/48.87 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 48.66/48.87 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 48.66/48.87 Found (x3 x20) as proof of (cNUMBER Xn)
% 48.66/48.87 Found (x3 x20) as proof of (cNUMBER Xn)
% 48.66/48.87 Found (fun (x9:(cODD (cS c0)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 48.66/48.87 Found (fun (x9:(cODD (cS c0)))=> (x3 x20)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 48.66/48.87 Found x30:(cNUMBER Xn0)
% 48.66/48.87 Instantiate: Xn0:=Xn:fofType
% 48.66/48.87 Found x30 as proof of (cNUMBER Xn)
% 48.66/48.87 Found x50:(cNUMBER Xn00)
% 48.66/48.87 Instantiate: Xn00:=Xn:fofType
% 48.66/48.87 Found x50 as proof of (cNUMBER Xn)
% 48.66/48.87 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 48.66/48.87 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 48.66/48.87 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 48.66/48.87 Found x90:=(x9 x80):(cNUMBER Xn0)
% 48.66/48.87 Found (x9 x80) as proof of (cNUMBER Xn)
% 48.66/48.87 Found (x9 x80) as proof of (cNUMBER Xn)
% 48.66/48.87 Found (x9 x80) as proof of (cNUMBER Xn)
% 48.66/48.87 Found x70:=(x7 x60):(cNUMBER Xn0)
% 48.66/48.87 Instantiate: Xn0:=Xn:fofType
% 50.17/50.40 Found (x7 x60) as proof of (cNUMBER Xn)
% 50.17/50.40 Found (fun (x9:(cODD (cS c0)))=> (x7 x60)) as proof of (cNUMBER Xn)
% 50.17/50.40 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))
% 50.17/50.40 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)))
% 50.17/50.40 Found x31:(cNUMBER Xn0)
% 50.17/50.40 Instantiate: Xn0:=Xn:fofType
% 50.17/50.40 Found (fun (x5:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> x31) as proof of (cNUMBER Xn)
% 50.17/50.40 Found (fun (x5:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> x31) as proof of ((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn))
% 50.17/50.40 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 50.17/50.40 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 50.17/50.40 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 50.17/50.40 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 50.17/50.40 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)))
% 50.17/50.40 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))))
% 50.17/50.40 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))
% 50.17/50.40 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))
% 50.17/50.40 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))
% 50.17/50.40 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))
% 50.17/50.40 Found x50:=(x5 x40):(cNUMBER Xn0)
% 50.17/50.40 Found (x5 x40) as proof of (cNUMBER Xn0)
% 50.17/50.40 Found (x5 x40) as proof of (cNUMBER Xn0)
% 50.17/50.40 Found x50:=(x5 x41):(cNUMBER Xn0)
% 50.17/50.40 Instantiate: Xn0:=Xn:fofType
% 50.17/50.40 Found (x5 x41) as proof of (cNUMBER Xn)
% 50.17/50.40 Found (x5 x41) as proof of (cNUMBER Xn)
% 50.17/50.40 Found x50:=(x5 x40):(cNUMBER Xn0)
% 50.17/50.40 Found (x5 x40) as proof of (cNUMBER Xn)
% 50.17/50.40 Found (x5 x40) as proof of (cNUMBER Xn)
% 50.17/50.40 Found (x5 x40) as proof of (cNUMBER Xn)
% 50.17/50.40 Found x50:=(x5 x40):(cNUMBER Xn0)
% 50.17/50.40 Instantiate: Xn0:=Xn:fofType
% 52.07/52.26 Found (x5 x40) as proof of (cNUMBER Xn)
% 52.07/52.26 Found (x5 x40) as proof of (cNUMBER Xn)
% 52.07/52.26 Found x50:=(x5 x40):(cNUMBER Xn0)
% 52.07/52.26 Instantiate: Xn0:=Xn:fofType
% 52.07/52.26 Found (x5 x40) as proof of (cNUMBER Xn)
% 52.07/52.26 Found (x5 x40) as proof of (cNUMBER Xn)
% 52.07/52.26 Found x70:=(x7 x60):(cNUMBER Xn0)
% 52.07/52.26 Found (x7 x60) as proof of (cNUMBER Xn)
% 52.07/52.26 Found (x7 x60) as proof of (cNUMBER Xn)
% 52.07/52.26 Found (x7 x60) as proof of (cNUMBER Xn)
% 52.07/52.26 Found x50:=(x5 x40):(cNUMBER Xn0)
% 52.07/52.26 Found (x5 x40) as proof of (cNUMBER Xn)
% 52.07/52.26 Found (x5 x40) as proof of (cNUMBER Xn)
% 52.07/52.26 Found (fun (x9:(cODD (cS c0)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 52.07/52.26 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))
% 52.07/52.26 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)))
% 52.07/52.26 Found x30:(cNUMBER Xn0)
% 52.07/52.26 Instantiate: Xn0:=Xn:fofType
% 52.07/52.26 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30) as proof of (cNUMBER Xn)
% 52.07/52.26 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 52.07/52.26 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 52.07/52.26 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 52.07/52.26 Found (x3 x20) as proof of (cNUMBER Xn)
% 52.07/52.26 Found (x3 x20) as proof of (cNUMBER Xn)
% 52.07/52.26 Found (fun (x9:(cODD (cS c0)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 52.07/52.26 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))
% 52.07/52.26 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)))
% 52.07/52.26 Found x30:=(x3 x20):(cNUMBER Xn0)
% 52.07/52.26 Found (x3 x20) as proof of (cNUMBER Xn)
% 52.07/52.26 Found (x3 x20) as proof of (cNUMBER Xn)
% 52.07/52.26 Found (fun (x5:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 52.07/52.26 Found (fun (x5:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x3 x20)) as proof of ((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn))
% 52.07/52.26 Found x30:=(x3 x20):(cNUMBER Xn0)
% 52.07/52.26 Found (x3 x20) as proof of (cNUMBER Xn0)
% 52.07/52.26 Found (x3 x20) as proof of (cNUMBER Xn0)
% 52.07/52.26 Found x30:=(x3 x21):(cNUMBER Xn0)
% 52.07/52.26 Instantiate: Xn0:=Xn:fofType
% 52.07/52.26 Found (x3 x21) as proof of (cNUMBER Xn)
% 52.07/52.26 Found (fun (x5:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x3 x21)) as proof of (cNUMBER Xn)
% 52.07/52.26 Found (fun (x5:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x3 x21)) as proof of ((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn))
% 52.07/52.26 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 52.07/52.26 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 52.07/52.26 Found (x5 x40) as proof of (cNUMBER Xn)
% 52.07/52.26 Found (x5 x40) as proof of (cNUMBER Xn)
% 52.07/52.26 Found (x5 x40) as proof of (cNUMBER Xn)
% 52.07/52.26 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 54.66/54.87 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 54.66/54.87 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 54.66/54.87 Found x90:=(x9 x80):(cNUMBER Xn0)
% 54.66/54.87 Found (x9 x80) as proof of (cNUMBER Xn)
% 54.66/54.87 Found (x9 x80) as proof of (cNUMBER Xn)
% 54.66/54.87 Found (fun (x9:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x9 x80)) as proof of (cNUMBER Xn)
% 54.66/54.87 Found (fun (x9:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x9 x80)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 54.66/54.87 Found x30:=(x3 x20):(cNUMBER Xn0)
% 54.66/54.87 Found (x3 x20) as proof of (cNUMBER Xn0)
% 54.66/54.87 Found (x3 x20) as proof of (cNUMBER Xn0)
% 54.66/54.87 Found x30:=(x3 x21):(cNUMBER Xn0)
% 54.66/54.87 Instantiate: Xn0:=Xn:fofType
% 54.66/54.87 Found (x3 x21) as proof of (cNUMBER Xn)
% 54.66/54.87 Found (x3 x21) as proof of (cNUMBER Xn)
% 54.66/54.87 Found x30:=(x3 x20):(cNUMBER Xn0)
% 54.66/54.87 Found (x3 x20) as proof of (cNUMBER Xn)
% 54.66/54.87 Found (x3 x20) as proof of (cNUMBER Xn)
% 54.66/54.87 Found (x3 x20) as proof of (cNUMBER Xn)
% 54.66/54.87 Found x30:=(x3 x20):(cNUMBER Xn0)
% 54.66/54.87 Instantiate: Xn0:=Xn:fofType
% 54.66/54.87 Found (x3 x20) as proof of (cNUMBER Xn)
% 54.66/54.87 Found (x3 x20) as proof of (cNUMBER Xn)
% 54.66/54.87 Found x30:=(x3 x20):(cNUMBER Xn0)
% 54.66/54.87 Instantiate: Xn0:=Xn:fofType
% 54.66/54.87 Found (x3 x20) as proof of (cNUMBER Xn)
% 54.66/54.87 Found (x3 x20) as proof of (cNUMBER Xn)
% 54.66/54.87 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 54.66/54.87 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 54.66/54.87 Found (x5 x40) as proof of (cNUMBER Xn)
% 54.66/54.87 Found (x5 x40) as proof of (cNUMBER Xn)
% 54.66/54.87 Found (x5 x40) as proof of (cNUMBER Xn)
% 54.66/54.87 Found x30:(cNUMBER Xn0)
% 54.66/54.87 Instantiate: Xn0:=Xn:fofType
% 54.66/54.87 Found x30 as proof of (cNUMBER Xn)
% 54.66/54.87 Found x30:=(x3 x20):(cNUMBER Xn0)
% 54.66/54.87 Instantiate: Xn0:=Xn:fofType
% 54.66/54.87 Found (x3 x20) as proof of (cNUMBER Xn)
% 54.66/54.87 Found (fun (x9:(cODD (cS c0)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 54.66/54.87 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))
% 54.66/54.87 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)))
% 54.66/54.87 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)
% 54.66/54.87 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)
% 54.66/54.87 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)
% 54.66/54.87 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)
% 54.66/54.87 Found x50:=(x5 x40):(cNUMBER Xn0)
% 54.66/54.87 Found (x5 x40) as proof of (cNUMBER Xn0)
% 54.66/54.87 Found (x5 x40) as proof of (cNUMBER Xn0)
% 54.66/54.87 Found x50:=(x5 x41):(cNUMBER Xn0)
% 54.66/54.87 Instantiate: Xn0:=Xn:fofType
% 54.66/54.87 Found (x5 x41) as proof of (cNUMBER Xn)
% 54.66/54.87 Found (x5 x41) as proof of (cNUMBER Xn)
% 54.66/54.87 Found x50:=(x5 x40):(cNUMBER Xn0)
% 54.66/54.87 Found (x5 x40) as proof of (cNUMBER Xn)
% 54.66/54.87 Found (x5 x40) as proof of (cNUMBER Xn)
% 54.66/54.87 Found (x5 x40) as proof of (cNUMBER Xn)
% 54.66/54.87 Found x50:=(x5 x40):(cNUMBER Xn0)
% 54.66/54.87 Instantiate: Xn0:=Xn:fofType
% 54.66/54.87 Found (x5 x40) as proof of (cNUMBER Xn)
% 54.66/54.87 Found (x5 x40) as proof of (cNUMBER Xn)
% 54.66/54.87 Found x50:=(x5 x40):(cNUMBER Xn0)
% 54.66/54.87 Instantiate: Xn0:=Xn:fofType
% 54.66/54.87 Found (x5 x40) as proof of (cNUMBER Xn)
% 54.66/54.87 Found (x5 x40) as proof of (cNUMBER Xn)
% 54.66/54.87 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 54.66/54.87 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 54.66/54.87 Found (x3 x20) as proof of (cNUMBER Xn)
% 55.57/55.77 Found (x3 x20) as proof of (cNUMBER Xn)
% 55.57/55.77 Found (x3 x20) as proof of (cNUMBER Xn)
% 55.57/55.77 Found x70:=(x7 x60):(cNUMBER Xn0)
% 55.57/55.77 Found (x7 x60) as proof of (cNUMBER Xn)
% 55.57/55.77 Found (x7 x60) as proof of (cNUMBER Xn)
% 55.57/55.77 Found (fun (x9:(cODD (cS c0)))=> (x7 x60)) as proof of (cNUMBER Xn)
% 55.57/55.77 Found (fun (x9:(cODD (cS c0)))=> (x7 x60)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 55.57/55.77 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 55.57/55.77 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 55.57/55.77 Found (x5 x40) as proof of (cNUMBER Xn)
% 55.57/55.77 Found (x5 x40) as proof of (cNUMBER Xn)
% 55.57/55.77 Found (fun (x9:(cODD (cS c0)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 55.57/55.77 Found (fun (x9:(cODD (cS c0)))=> (x5 x40)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 55.57/55.77 Found x30:(cNUMBER Xn0)
% 55.57/55.77 Instantiate: Xn0:=Xn:fofType
% 55.57/55.77 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30) as proof of (cNUMBER Xn)
% 55.57/55.77 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))
% 55.57/55.77 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)))
% 55.57/55.77 Found x30:(cNUMBER Xn0)
% 55.57/55.77 Instantiate: Xn0:=Xn:fofType
% 55.57/55.77 Found (fun (x6:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> x30) as proof of (cNUMBER Xn)
% 55.57/55.77 Found (fun (x5:(cODD Xn0)) (x6:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> x30) as proof of ((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn))
% 55.57/55.77 Found (fun (x5:(cODD Xn0)) (x6:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> x30) as proof of ((cODD Xn0)->((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn)))
% 55.57/55.77 Found x30:(cNUMBER Xn0)
% 55.57/55.77 Instantiate: Xn0:=Xn:fofType
% 55.57/55.77 Found (fun (x6:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> x30) as proof of (cNUMBER Xn)
% 55.57/55.77 Found (fun (x5:(cEVEN Xn0)) (x6:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> x30) as proof of ((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn))
% 55.57/55.77 Found (fun (x5:(cEVEN Xn0)) (x6:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> x30) as proof of ((cEVEN Xn0)->((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn)))
% 55.57/55.77 Found ((or_ind00 (fun (x5:(cEVEN Xn0)) (x6:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> x30)) (fun (x5:(cODD Xn0)) (x6:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> x30)) as proof of ((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn))
% 55.57/55.77 Found (((or_ind0 ((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn))) (fun (x5:(cEVEN Xn0)) (x6:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> x30)) (fun (x5:(cODD Xn0)) (x6:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> x30)) as proof of ((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn))
% 55.57/55.77 Found ((((fun (P:Prop) (x5:((cEVEN Xn0)->P)) (x6:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x5) x6) x20)) ((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn))) (fun (x5:(cEVEN Xn0)) (x6:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> x30)) (fun (x5:(cODD Xn0)) (x6:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> x30)) as proof of ((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn))
% 55.57/55.77 Found ((((fun (P:Prop) (x5:((cEVEN Xn0)->P)) (x6:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x5) x6) (x2 x30))) ((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn))) (fun (x5:(cEVEN Xn0)) (x6:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> x30)) (fun (x5:(cODD Xn0)) (x6:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> x30)) as proof of ((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn))
% 56.27/56.51 Found ((((fun (P:Prop) (x5:((cEVEN Xn0)->P)) (x6:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x5) x6) (x2 x30))) ((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn))) (fun (x5:(cEVEN Xn0)) (x6:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> x30)) (fun (x5:(cODD Xn0)) (x6:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> x30)) as proof of ((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn))
% 56.27/56.51 Found x30:=(x3 x20):(cNUMBER Xn0)
% 56.27/56.51 Found (x3 x20) as proof of (cNUMBER Xn)
% 56.27/56.51 Found (x3 x20) as proof of (cNUMBER Xn)
% 56.27/56.51 Found (fun (x5:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 56.27/56.51 Found (fun (x5:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x3 x20)) as proof of ((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn))
% 56.27/56.51 Found x30:=(x3 x20):(cNUMBER Xn0)
% 56.27/56.51 Found (x3 x20) as proof of (cNUMBER Xn)
% 56.27/56.51 Found (x3 x20) as proof of (cNUMBER Xn)
% 56.27/56.51 Found (fun (x5:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 56.27/56.51 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x3 x20)) as proof of ((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn))
% 56.27/56.51 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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))))))->((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn)))
% 56.27/56.51 Found x30:=(x3 x20):(cNUMBER Xn0)
% 56.27/56.51 Found (x3 x20) as proof of (cNUMBER Xn0)
% 56.27/56.51 Found (x3 x20) as proof of (cNUMBER Xn0)
% 56.82/57.00 Found x30:=(x3 x21):(cNUMBER Xn0)
% 56.82/57.00 Instantiate: Xn0:=Xn:fofType
% 56.82/57.00 Found (x3 x21) as proof of (cNUMBER Xn)
% 56.82/57.00 Found (x3 x21) as proof of (cNUMBER Xn)
% 56.82/57.00 Found x30:=(x3 x20):(cNUMBER Xn0)
% 56.82/57.00 Found (x3 x20) as proof of (cNUMBER Xn)
% 56.82/57.00 Found (x3 x20) as proof of (cNUMBER Xn)
% 56.82/57.00 Found (x3 x20) as proof of (cNUMBER Xn)
% 56.82/57.00 Found x300:=(x30 (cS Xx)):((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))
% 56.82/57.00 Found (x30 (cS Xx)) as proof of ((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))
% 56.82/57.00 Found (fun (x4:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx))) as proof of ((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))
% 56.82/57.00 Found (fun (Xx:fofType) (x4:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx))) as proof of (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))
% 56.82/57.00 Found (fun (Xx:fofType) (x4:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx))) as proof of (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))
% 56.82/57.00 Found ((conj00 (x30 c0)) (fun (Xx:fofType) (x4:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 56.82/57.00 Found (((conj0 (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))) (x30 c0)) (fun (Xx:fofType) (x4:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 56.82/57.00 Found ((((conj ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))) (x30 c0)) (fun (Xx:fofType) (x4:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 56.82/57.00 Found ((((conj ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))) (x30 c0)) (fun (Xx:fofType) (x4:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 56.82/57.00 Found x30:=(x3 x20):(cNUMBER Xn0)
% 56.82/57.00 Instantiate: Xn0:=Xn:fofType
% 56.82/57.00 Found (x3 x20) as proof of (cNUMBER Xn)
% 56.82/57.00 Found (x3 x20) as proof of (cNUMBER Xn)
% 56.82/57.00 Found x80:((or (cEVEN Xn0)) (cODD Xn0))
% 56.82/57.00 Found x80 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 56.82/57.00 Found (x9 x80) as proof of (cNUMBER Xn)
% 56.82/57.00 Found (x9 x80) as proof of (cNUMBER Xn)
% 56.82/57.00 Found (x9 x80) as proof of (cNUMBER Xn)
% 56.82/57.00 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 56.82/57.00 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 56.82/57.00 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 56.82/57.00 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 56.82/57.00 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)))
% 56.82/57.00 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))))
% 56.82/57.00 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))
% 56.82/57.00 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))
% 57.62/57.84 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))
% 57.62/57.84 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))
% 57.62/57.84 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)
% 57.62/57.84 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)
% 57.62/57.84 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 57.62/57.84 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 57.62/57.84 Found (x5 x40) as proof of (cNUMBER Xn)
% 57.62/57.84 Found (x5 x40) as proof of (cNUMBER Xn)
% 57.62/57.84 Found (x5 x40) as proof of (cNUMBER Xn)
% 57.62/57.84 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 57.62/57.84 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 57.62/57.84 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 57.62/57.84 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 57.62/57.84 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)))
% 57.62/57.84 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))))
% 57.62/57.84 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))
% 57.62/57.84 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))
% 57.62/57.84 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))
% 57.62/57.84 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))
% 58.66/58.90 Found x30:(cNUMBER Xn0)
% 58.66/58.90 Instantiate: Xn0:=Xn:fofType
% 58.66/58.90 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x30) as proof of (cNUMBER Xn)
% 58.66/58.90 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))
% 58.66/58.90 Found x30:=(x3 x20):(cNUMBER Xn0)
% 58.66/58.90 Instantiate: Xn0:=Xn:fofType
% 58.66/58.90 Found (x3 x20) as proof of (cNUMBER Xn)
% 58.66/58.90 Found (fun (x9:(cODD (cS c0)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 58.66/58.90 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))
% 58.66/58.90 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)))
% 58.66/58.90 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)
% 58.66/58.90 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)
% 58.66/58.90 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)) (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)
% 58.66/58.90 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)
% 58.66/58.90 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))
% 58.66/58.90 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 58.66/58.90 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 58.66/58.90 Found (x3 x20) as proof of (cNUMBER Xn)
% 58.66/58.90 Found (x3 x20) as proof of (cNUMBER Xn)
% 58.66/58.90 Found (fun (x5:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 58.66/58.90 Found (fun (x5:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x3 x20)) as proof of ((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn))
% 58.66/58.90 Found x50:=(x5 x40):(cNUMBER Xn0)
% 58.66/58.90 Instantiate: Xn0:=Xn:fofType
% 58.66/58.90 Found (x5 x40) as proof of (cNUMBER Xn)
% 59.67/59.87 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 59.67/59.87 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x5 x40)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 59.67/59.87 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 59.67/59.87 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 59.67/59.87 Found (x3 x20) as proof of (cNUMBER Xn)
% 59.67/59.87 Found (x3 x20) as proof of (cNUMBER Xn)
% 59.67/59.87 Found (x3 x20) as proof of (cNUMBER Xn)
% 59.67/59.87 Found x50:=(x5 x40):(cNUMBER Xn00)
% 59.67/59.87 Instantiate: Xn00:=Xn:fofType
% 59.67/59.87 Found (x5 x40) as proof of (cNUMBER Xn)
% 59.67/59.87 Found (x5 x40) as proof of (cNUMBER Xn)
% 59.67/59.87 Found x30:=(x3 x20):(cNUMBER Xn0)
% 59.67/59.87 Instantiate: Xn0:=Xn:fofType
% 59.67/59.87 Found (x3 x20) as proof of (cNUMBER Xn)
% 59.67/59.87 Found (x3 x20) as proof of (cNUMBER Xn)
% 59.67/59.87 Found x50:=(x5 x40):(cNUMBER Xn0)
% 59.67/59.87 Instantiate: Xn0:=Xn:fofType
% 59.67/59.87 Found (x5 x40) as proof of (cNUMBER Xn)
% 59.67/59.87 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 59.67/59.87 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x5 x40)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 59.67/59.87 Found x50:=(x5 x41):(cNUMBER Xn0)
% 59.67/59.87 Instantiate: Xn0:=Xn:fofType
% 59.67/59.87 Found (x5 x41) as proof of (cNUMBER Xn)
% 59.67/59.87 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x5 x41)) as proof of (cNUMBER Xn)
% 59.67/59.87 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x5 x41)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 59.67/59.87 Found x50:=(x5 x40):(cNUMBER Xn0)
% 59.67/59.87 Instantiate: Xn0:=Xn:fofType
% 59.67/59.87 Found (x5 x40) as proof of (cNUMBER Xn)
% 59.67/59.87 Found (x5 x40) as proof of (cNUMBER Xn)
% 59.67/59.87 Found x70:=(x7 x60):(cNUMBER Xn0)
% 59.67/59.87 Found (x7 x60) as proof of (cNUMBER Xn)
% 59.67/59.87 Found (x7 x60) as proof of (cNUMBER Xn)
% 59.67/59.87 Found (fun (x9:(cODD (cS c0)))=> (x7 x60)) as proof of (cNUMBER Xn)
% 59.67/59.87 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))
% 59.67/59.87 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)))
% 59.67/59.87 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 59.67/59.87 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 59.67/59.87 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 59.67/59.87 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 59.67/59.87 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)))
% 59.67/59.87 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))))
% 59.67/59.87 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))
% 59.67/59.87 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))
% 59.67/59.87 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))
% 59.67/59.87 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))
% 59.67/59.88 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)))
% 59.67/59.88 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))))
% 59.67/59.88 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))
% 59.67/59.88 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))
% 59.67/59.88 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))
% 59.80/60.01 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))
% 59.80/60.01 Found x60:((or (cEVEN Xn0)) (cODD Xn0))
% 59.80/60.01 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 59.80/60.01 Found (x7 x60) as proof of (cNUMBER Xn)
% 59.80/60.01 Found (x7 x60) as proof of (cNUMBER Xn)
% 59.80/60.01 Found (x7 x60) as proof of (cNUMBER Xn)
% 59.80/60.01 Found x30:=(x3 x20):(cNUMBER Xn0)
% 59.80/60.01 Instantiate: Xn0:=Xn:fofType
% 59.80/60.01 Found (x3 x20) as proof of (cNUMBER Xn)
% 59.80/60.01 Found (fun (x9:(cODD (cS c0)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 59.80/60.01 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))
% 59.80/60.01 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)))
% 59.80/60.01 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)
% 59.80/60.01 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)
% 59.80/60.01 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)
% 59.80/60.01 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)
% 59.80/60.01 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))
% 60.48/60.72 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)))
% 60.48/60.72 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 60.48/60.72 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 60.48/60.72 Found (x5 x40) as proof of (cNUMBER Xn)
% 60.48/60.72 Found (x5 x40) as proof of (cNUMBER Xn)
% 60.48/60.72 Found (fun (x9:(cODD (cS c0)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 60.48/60.72 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))
% 60.48/60.72 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)))
% 60.48/60.72 Found x30:(cNUMBER Xn0)
% 60.48/60.72 Instantiate: Xn0:=Xn:fofType
% 60.48/60.72 Found (fun (x6:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> x30) as proof of (cNUMBER Xn)
% 60.48/60.72 Found (fun (x5:(cEVEN Xn0)) (x6:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> x30) as proof of ((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn))
% 60.48/60.72 Found (fun (x5:(cEVEN Xn0)) (x6:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> x30) as proof of ((cEVEN Xn0)->((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn)))
% 60.48/60.72 Found x30:(cNUMBER Xn0)
% 60.48/60.72 Instantiate: Xn0:=Xn:fofType
% 60.48/60.72 Found (fun (x6:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> x30) as proof of (cNUMBER Xn)
% 60.48/60.72 Found (fun (x5:(cODD Xn0)) (x6:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> x30) as proof of ((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn))
% 60.48/60.72 Found (fun (x5:(cODD Xn0)) (x6:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> x30) as proof of ((cODD Xn0)->((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn)))
% 60.48/60.72 Found ((or_ind00 (fun (x5:(cEVEN Xn0)) (x6:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> x30)) (fun (x5:(cODD Xn0)) (x6:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> x30)) as proof of ((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn))
% 60.48/60.72 Found (((or_ind0 ((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn))) (fun (x5:(cEVEN Xn0)) (x6:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> x30)) (fun (x5:(cODD Xn0)) (x6:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> x30)) as proof of ((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn))
% 60.48/60.72 Found ((((fun (P:Prop) (x5:((cEVEN Xn0)->P)) (x6:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x5) x6) x20)) ((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn))) (fun (x5:(cEVEN Xn0)) (x6:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> x30)) (fun (x5:(cODD Xn0)) (x6:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> x30)) as proof of ((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn))
% 60.48/60.72 Found ((((fun (P:Prop) (x5:((cEVEN Xn0)->P)) (x6:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x5) x6) (x2 x30))) ((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn))) (fun (x5:(cEVEN Xn0)) (x6:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> x30)) (fun (x5:(cODD Xn0)) (x6:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> x30)) as proof of ((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn))
% 61.75/61.95 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)))))))=> ((((fun (P:Prop) (x5:((cEVEN Xn0)->P)) (x6:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x5) x6) (x2 x30))) ((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn))) (fun (x5:(cEVEN Xn0)) (x6:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> x30)) (fun (x5:(cODD Xn0)) (x6:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> x30))) as proof of ((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn))
% 61.75/61.95 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)))))))=> ((((fun (P:Prop) (x5:((cEVEN Xn0)->P)) (x6:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x5) x6) (x2 x30))) ((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn))) (fun (x5:(cEVEN Xn0)) (x6:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> x30)) (fun (x5:(cODD Xn0)) (x6:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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))))))->((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn)))
% 61.75/61.95 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 61.75/61.95 Instantiate: Xn00:=Xn:fofType
% 61.75/61.95 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 61.75/61.95 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 61.75/61.95 Instantiate: Xn0:=Xn:fofType
% 61.75/61.95 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 61.75/61.95 Found x30:=(x3 x20):(cNUMBER Xn0)
% 61.75/61.95 Found (x3 x20) as proof of (cNUMBER Xn0)
% 61.75/61.95 Found (x3 x20) as proof of (cNUMBER Xn0)
% 61.75/61.95 Found x30:=(x3 x21):(cNUMBER Xn0)
% 61.75/61.95 Instantiate: Xn0:=Xn:fofType
% 61.75/61.95 Found (x3 x21) as proof of (cNUMBER Xn)
% 61.75/61.95 Found (x3 x21) as proof of (cNUMBER Xn)
% 61.75/61.95 Found x30:=(x3 x20):(cNUMBER Xn0)
% 61.75/61.95 Found (x3 x20) as proof of (cNUMBER Xn)
% 61.75/61.95 Found (x3 x20) as proof of (cNUMBER Xn)
% 61.75/61.95 Found (x3 x20) as proof of (cNUMBER Xn)
% 61.75/61.95 Found x80:((or (cEVEN Xn0)) (cODD Xn0))
% 61.75/61.95 Found x80 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 61.75/61.95 Found (x9 x80) as proof of (cNUMBER Xn)
% 61.75/61.95 Found (x9 x80) as proof of (cNUMBER Xn)
% 61.75/61.95 Found (fun (x9:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x9 x80)) as proof of (cNUMBER Xn)
% 61.75/61.95 Found (fun (x9:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x9 x80)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 64.54/64.78 Found x30:=(x3 x20):(cNUMBER Xn0)
% 64.54/64.78 Instantiate: Xn0:=Xn:fofType
% 64.54/64.78 Found (x3 x20) as proof of (cNUMBER Xn)
% 64.54/64.78 Found (x3 x20) as proof of (cNUMBER Xn)
% 64.54/64.78 Found x50:(cNUMBER Xn0)
% 64.54/64.78 Instantiate: Xn0:=Xn:fofType
% 64.54/64.78 Found x50 as proof of (cNUMBER Xn)
% 64.54/64.78 Found x30:(cNUMBER Xn0)
% 64.54/64.78 Instantiate: Xn0:=Xn:fofType
% 64.54/64.78 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x30) as proof of (cNUMBER Xn)
% 64.54/64.78 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))
% 64.54/64.78 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)))
% 64.54/64.78 Found x50:=(x5 x40):(cNUMBER Xn0)
% 64.54/64.78 Instantiate: Xn0:=Xn:fofType
% 64.54/64.78 Found (x5 x40) as proof of (cNUMBER Xn)
% 64.54/64.78 Found (fun (x9:(cODD (cS c0)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 64.54/64.78 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))
% 64.54/64.78 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)))
% 64.54/64.78 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)
% 64.54/64.78 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)
% 64.54/64.78 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)
% 64.54/64.78 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)
% 64.54/64.78 Found x30:=(x3 x20):(cNUMBER Xn0)
% 64.54/64.78 Instantiate: Xn0:=Xn:fofType
% 64.54/64.78 Found (x3 x20) as proof of (cNUMBER Xn)
% 64.54/64.78 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 64.54/64.78 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 64.54/64.78 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 64.54/64.78 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 64.54/64.78 Found (x3 x20) as proof of (cNUMBER Xn)
% 64.54/64.78 Found (x3 x20) as proof of (cNUMBER Xn)
% 64.54/64.78 Found (fun (x5:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 64.54/64.78 Found (fun (x5:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x3 x20)) as proof of ((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn))
% 64.54/64.78 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 64.54/64.78 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 64.54/64.78 Found (x3 x20) as proof of (cNUMBER Xn)
% 64.54/64.78 Found (x3 x20) as proof of (cNUMBER Xn)
% 64.54/64.78 Found (fun (x5:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 64.91/65.16 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x3 x20)) as proof of ((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn))
% 64.91/65.16 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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))))))->((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn)))
% 64.91/65.16 Found x50:=(x5 x40):(cNUMBER Xn00)
% 64.91/65.16 Instantiate: Xn00:=Xn:fofType
% 64.91/65.16 Found (x5 x40) as proof of (cNUMBER Xn)
% 64.91/65.16 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 64.91/65.16 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 64.91/65.16 Found x30:(cNUMBER Xn0)
% 64.91/65.16 Instantiate: Xn0:=Xn:fofType
% 64.91/65.16 Found (fun (x6:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> x30) as proof of (cNUMBER Xn)
% 64.91/65.16 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> x30) as proof of ((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn))
% 64.91/65.16 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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))))))->((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn)))
% 64.91/65.16 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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))))))->((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn))))
% 64.97/65.20 Found x30:(cNUMBER Xn0)
% 64.97/65.20 Instantiate: Xn0:=Xn:fofType
% 64.97/65.20 Found (fun (x6:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> x30) as proof of (cNUMBER Xn)
% 64.97/65.20 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> x30) as proof of ((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn))
% 64.97/65.20 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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))))))->((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn)))
% 64.97/65.20 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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))))))->((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn))))
% 64.97/65.20 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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))))))->((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn)))
% 64.97/65.20 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))))))->((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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))))))->((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn)))
% 64.97/65.20 Found ((((fun (P:Prop) (x4:((cEVEN Xn0)->P)) (x5:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x4) x5) x20)) (((and ((and ((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))->((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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))))))->((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn)))
% 65.06/65.28 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))))))->((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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))))))->((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn)))
% 65.06/65.28 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))))))->((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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))))))->((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn)))
% 65.06/65.28 Found x50:=(x5 x40):(cNUMBER Xn0)
% 65.06/65.28 Instantiate: Xn0:=Xn:fofType
% 65.06/65.28 Found (x5 x40) as proof of (cNUMBER Xn)
% 67.94/68.15 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 67.94/68.15 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x5 x40)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 67.94/68.15 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 67.94/68.15 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 67.94/68.15 Found (x3 x20) as proof of (cNUMBER Xn)
% 67.94/68.15 Found (x3 x20) as proof of (cNUMBER Xn)
% 67.94/68.15 Found (x3 x20) as proof of (cNUMBER Xn)
% 67.94/68.15 Found x60:((or (cEVEN Xn0)) (cODD Xn0))
% 67.94/68.15 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 67.94/68.15 Found (x7 x60) as proof of (cNUMBER Xn)
% 67.94/68.15 Found (x7 x60) as proof of (cNUMBER Xn)
% 67.94/68.15 Found (fun (x9:(cODD (cS c0)))=> (x7 x60)) as proof of (cNUMBER Xn)
% 67.94/68.15 Found (fun (x9:(cODD (cS c0)))=> (x7 x60)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 67.94/68.15 Found x300:=(x30 c0):((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 67.94/68.15 Found (x30 c0) as proof of ((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 67.94/68.15 Found (x30 c0) as proof of ((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 67.94/68.15 Found x50:=(x5 x40):(cNUMBER Xn0)
% 67.94/68.15 Found (x5 x40) as proof of (cNUMBER Xn)
% 67.94/68.15 Found (x5 x40) as proof of (cNUMBER Xn)
% 67.94/68.15 Found (x5 x40) as proof of (cNUMBER Xn)
% 67.94/68.15 Found x50:=(x5 x40):(cNUMBER Xn0)
% 67.94/68.15 Found (x5 x40) as proof of (cNUMBER Xn)
% 67.94/68.15 Found (x5 x40) as proof of (cNUMBER Xn)
% 67.94/68.15 Found (x5 x40) as proof of (cNUMBER Xn)
% 67.94/68.15 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 67.94/68.15 Instantiate: Xn00:=Xn:fofType
% 67.94/68.15 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 67.94/68.15 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 67.94/68.15 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 67.94/68.15 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 67.94/68.15 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 67.94/68.15 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)))
% 67.94/68.15 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))))
% 67.94/68.15 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))
% 67.94/68.15 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))
% 67.94/68.15 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) 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))
% 67.94/68.15 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) 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))
% 67.94/68.15 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)
% 69.39/69.59 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)
% 69.39/69.59 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 69.39/69.59 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 69.39/69.59 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 69.39/69.59 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 69.39/69.59 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)))
% 69.39/69.59 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))))
% 69.39/69.59 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))
% 69.39/69.59 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))
% 69.39/69.59 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))
% 69.39/69.59 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))
% 69.39/69.59 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)
% 69.39/69.59 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)
% 69.39/69.59 Found x50:(cNUMBER Xn0)
% 69.39/69.59 Instantiate: Xn0:=Xn:fofType
% 69.39/69.59 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x50) as proof of (cNUMBER Xn)
% 69.39/69.59 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))
% 69.39/69.59 Found x30:=(x3 x20):(cNUMBER Xn0)
% 69.39/69.59 Found (x3 x20) as proof of (cNUMBER Xn)
% 69.39/69.59 Found (x3 x20) as proof of (cNUMBER Xn)
% 72.02/72.21 Found (x3 x20) as proof of (cNUMBER Xn)
% 72.02/72.21 Found x9:(cODD (cS c0))
% 72.02/72.21 Instantiate: Xn0:=(cS c0):fofType
% 72.02/72.21 Found x9 as proof of (cODD Xn0)
% 72.02/72.21 Found (or_intror00 x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 72.02/72.21 Found ((or_intror0 (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 72.02/72.21 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 72.02/72.21 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 72.02/72.21 Found x30:=(x3 x20):(cNUMBER Xn0)
% 72.02/72.21 Found (x3 x20) as proof of (cNUMBER Xn)
% 72.02/72.21 Found (x3 x20) as proof of (cNUMBER Xn)
% 72.02/72.21 Found (x3 x20) as proof of (cNUMBER Xn)
% 72.02/72.21 Found x50:=(x5 x40):(cNUMBER Xn0)
% 72.02/72.21 Instantiate: Xn0:=Xn:fofType
% 72.02/72.21 Found (x5 x40) as proof of (cNUMBER Xn)
% 72.02/72.21 Found (fun (x9:(cODD (cS c0)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 72.02/72.21 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))
% 72.02/72.21 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)))
% 72.02/72.21 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)
% 72.02/72.21 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)
% 72.02/72.21 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)
% 72.02/72.21 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)
% 72.02/72.21 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))
% 72.02/72.21 Found x30:=(x3 x20):(cNUMBER Xn0)
% 72.02/72.21 Instantiate: Xn0:=Xn:fofType
% 72.02/72.21 Found (x3 x20) as proof of (cNUMBER Xn)
% 72.02/72.21 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 72.02/72.21 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))
% 72.02/72.21 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)))
% 72.02/72.21 Found x30:=(x3 x20):(cNUMBER Xn0)
% 72.02/72.21 Instantiate: Xn0:=Xn:fofType
% 72.02/72.21 Found (x3 x20) as proof of (cNUMBER Xn)
% 72.02/72.21 Found (x3 x20) as proof of (cNUMBER Xn)
% 72.02/72.21 Found x50:=(x5 x40):(cNUMBER Xn00)
% 72.02/72.21 Found (x5 x40) as proof of (cNUMBER Xn)
% 72.02/72.21 Found (x5 x40) as proof of (cNUMBER Xn)
% 72.02/72.21 Found (x5 x40) as proof of (cNUMBER Xn)
% 72.02/72.21 Found x30:=(x3 x20):(cNUMBER Xn0)
% 72.02/72.21 Found (x3 x20) as proof of (cNUMBER Xn)
% 72.02/72.21 Found (x3 x20) as proof of (cNUMBER Xn)
% 72.53/72.73 Found (x3 x20) as proof of (cNUMBER Xn)
% 72.53/72.73 Found x60:((or (cEVEN Xn0)) (cODD Xn0))
% 72.53/72.73 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 72.53/72.73 Found (x7 x60) as proof of (cNUMBER Xn)
% 72.53/72.73 Found (x7 x60) as proof of (cNUMBER Xn)
% 72.53/72.73 Found (fun (x9:(cODD (cS c0)))=> (x7 x60)) as proof of (cNUMBER Xn)
% 72.53/72.73 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))
% 72.53/72.73 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)))
% 72.53/72.73 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 72.53/72.73 Instantiate: Xn00:=Xn:fofType
% 72.53/72.73 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x40) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 72.53/72.73 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)))
% 72.53/72.73 Found x50:=(x5 x40):(cNUMBER Xn0)
% 72.53/72.73 Instantiate: Xn0:=Xn:fofType
% 72.53/72.73 Found (x5 x40) as proof of (cNUMBER Xn)
% 72.53/72.73 Found (fun (x9:(cODD (cS c0)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 72.53/72.73 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))
% 72.53/72.73 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)))
% 72.53/72.73 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)
% 72.53/72.73 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)
% 72.53/72.73 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)
% 72.53/72.73 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)
% 72.53/72.73 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))))))=> (((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))
% 72.53/72.73 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))))))=> (((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)))
% 72.74/72.96 Found x50:=(x5 x40):(cNUMBER Xn0)
% 72.74/72.96 Found (x5 x40) as proof of (cNUMBER Xn)
% 72.74/72.96 Found (x5 x40) as proof of (cNUMBER Xn)
% 72.74/72.96 Found (x5 x40) as proof of (cNUMBER Xn)
% 72.74/72.96 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 72.74/72.96 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 72.74/72.96 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 72.74/72.96 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 72.74/72.96 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)))
% 72.74/72.96 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))))
% 72.74/72.96 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))
% 72.74/72.96 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))
% 72.74/72.96 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))
% 72.74/72.96 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))
% 72.74/72.96 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)))
% 72.74/72.96 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))))
% 74.16/74.36 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))
% 74.16/74.36 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))
% 74.16/74.36 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))
% 74.16/74.36 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))
% 74.16/74.36 Found x50:=(x5 x40):(cNUMBER Xn0)
% 74.16/74.36 Found (x5 x40) as proof of (cNUMBER Xn)
% 74.16/74.36 Found (x5 x40) as proof of (cNUMBER Xn)
% 74.16/74.36 Found (x5 x40) as proof of (cNUMBER Xn)
% 74.16/74.36 Found x300:=(x30 c0):((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 74.16/74.36 Found (x30 c0) as proof of ((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 74.16/74.36 Found (x30 c0) as proof of ((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 74.16/74.36 Found x50:(cNUMBER Xn0)
% 77.34/77.58 Instantiate: Xn0:=Xn:fofType
% 77.34/77.58 Found x50 as proof of (cNUMBER Xn)
% 77.34/77.58 Found x70:(cNUMBER Xn0)
% 77.34/77.58 Instantiate: Xn0:=Xn:fofType
% 77.34/77.58 Found x70 as proof of (cNUMBER Xn)
% 77.34/77.58 Found x30:(cNUMBER Xn0)
% 77.34/77.58 Found (fun (x5:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> x30) as proof of (cNUMBER Xn0)
% 77.34/77.58 Found (fun (x5:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> x30) as proof of ((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn0))
% 77.34/77.58 Found x30:=(x3 x20):(cNUMBER Xn0)
% 77.34/77.58 Found (x3 x20) as proof of (cNUMBER Xn)
% 77.34/77.58 Found (x3 x20) as proof of (cNUMBER Xn)
% 77.34/77.58 Found (x3 x20) as proof of (cNUMBER Xn)
% 77.34/77.58 Found x30:(cNUMBER Xn0)
% 77.34/77.58 Instantiate: Xn0:=Xn:fofType
% 77.34/77.58 Found x30 as proof of (cNUMBER Xn)
% 77.34/77.58 Found x50:(cNUMBER Xn0)
% 77.34/77.58 Instantiate: Xn0:=Xn:fofType
% 77.34/77.58 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x50) as proof of (cNUMBER Xn)
% 77.34/77.58 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))
% 77.34/77.58 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)))
% 77.34/77.58 Found x70:=(x7 x60):(cNUMBER Xn0)
% 77.34/77.58 Instantiate: Xn0:=Xn:fofType
% 77.34/77.58 Found (x7 x60) as proof of (cNUMBER Xn)
% 77.34/77.58 Found (fun (x9:(cODD (cS c0)))=> (x7 x60)) as proof of (cNUMBER Xn)
% 77.34/77.58 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))
% 77.34/77.58 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)))
% 77.34/77.58 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)
% 77.34/77.58 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)
% 77.34/77.58 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)
% 77.34/77.58 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)
% 77.34/77.58 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 77.34/77.58 Found (fun (x5:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> x20) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 77.34/77.58 Found (fun (x5:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> x20) as proof of ((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 79.38/79.59 Found x30:=(x3 x20):(cNUMBER Xn0)
% 79.38/79.59 Instantiate: Xn0:=Xn:fofType
% 79.38/79.59 Found (x3 x20) as proof of (cNUMBER Xn)
% 79.38/79.59 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 79.38/79.59 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))
% 79.38/79.59 Found x30:=(x3 x20):(cNUMBER Xn0)
% 79.38/79.59 Found (x3 x20) as proof of (cNUMBER Xn)
% 79.38/79.59 Found (x3 x20) as proof of (cNUMBER Xn)
% 79.38/79.59 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 79.38/79.59 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 79.38/79.59 Found x50:=(x5 x40):(cNUMBER Xn00)
% 79.38/79.59 Found (x5 x40) as proof of (cNUMBER Xn)
% 79.38/79.59 Found (x5 x40) as proof of (cNUMBER Xn)
% 79.38/79.59 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 79.38/79.59 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 79.38/79.59 Found x30:=(x3 x20):(cNUMBER Xn0)
% 79.38/79.59 Instantiate: Xn0:=Xn:fofType
% 79.38/79.59 Found (x3 x20) as proof of (cNUMBER Xn)
% 79.38/79.59 Found (fun (x5:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 79.38/79.59 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x3 x20)) as proof of ((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn))
% 79.38/79.59 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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))))))->((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn)))
% 79.38/79.59 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 79.38/79.59 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 80.46/80.66 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))))))->((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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))))))) (((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 80.46/80.66 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))))))->((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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))))))) (((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 80.46/80.66 Found x50:=(x5 x40):(cNUMBER Xn0)
% 80.46/80.66 Found (x5 x40) as proof of (cNUMBER Xn)
% 80.46/80.66 Found (x5 x40) as proof of (cNUMBER Xn)
% 80.46/80.66 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 80.46/80.66 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x5 x40)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 80.46/80.66 Found x50:=(x5 x40):(cNUMBER Xn0)
% 80.46/80.66 Found (x5 x40) as proof of (cNUMBER Xn)
% 80.46/80.66 Found (x5 x40) as proof of (cNUMBER Xn)
% 80.46/80.66 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 80.46/80.66 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x5 x40)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 80.46/80.66 Found x50:=(x5 x40):(cNUMBER Xn0)
% 80.46/80.66 Found (x5 x40) as proof of (cNUMBER Xn)
% 80.46/80.66 Found (x5 x40) as proof of (cNUMBER Xn)
% 80.46/80.66 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 80.46/80.66 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x5 x40)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 80.46/80.66 Found x50:=(x5 x40):(cNUMBER Xn0)
% 80.46/80.66 Found (x5 x40) as proof of (cNUMBER Xn)
% 80.46/80.66 Found (x5 x40) as proof of (cNUMBER Xn)
% 80.46/80.66 Found (x5 x40) as proof of (cNUMBER Xn)
% 82.87/83.10 Found x40:=(x4 x50):((or (cEVEN Xn00)) (cODD Xn00))
% 82.87/83.10 Instantiate: Xn00:=Xn:fofType
% 82.87/83.10 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 82.87/83.10 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 82.87/83.10 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 82.87/83.10 Instantiate: Xn0:=Xn:fofType
% 82.87/83.10 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 82.87/83.10 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 82.87/83.10 Found x300:=(x30 c0):((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 82.87/83.10 Found (x30 c0) as proof of ((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 82.87/83.10 Found (x30 c0) as proof of ((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 82.87/83.10 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 82.87/83.10 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 82.87/83.10 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 82.87/83.10 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 82.87/83.10 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)))
% 82.87/83.10 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))))
% 82.87/83.10 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))
% 82.87/83.10 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))
% 82.87/83.10 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))
% 82.87/83.10 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))
% 82.87/83.10 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)
% 82.87/83.10 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)
% 82.87/83.10 Found x300:=(x30 c0):((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 82.87/83.10 Found (x30 c0) as proof of ((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 82.87/83.10 Found (x30 c0) as proof of ((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 82.87/83.10 Found x70:(cNUMBER Xn0)
% 82.87/83.10 Instantiate: Xn0:=Xn:fofType
% 82.87/83.10 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x70) as proof of (cNUMBER Xn)
% 83.93/84.18 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))
% 83.93/84.18 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 83.93/84.18 Instantiate: Xn0:=Xn:fofType
% 83.93/84.18 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 83.93/84.18 Found (x5 x20) as proof of (cNUMBER Xn)
% 83.93/84.18 Found (x5 x20) as proof of (cNUMBER Xn)
% 83.93/84.18 Found (x5 x20) as proof of (cNUMBER Xn)
% 83.93/84.18 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 83.93/84.18 Instantiate: Xn00:=Xn:fofType
% 83.93/84.18 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 83.93/84.18 Found (x3 x40) as proof of (cNUMBER Xn)
% 83.93/84.18 Found (x3 x40) as proof of (cNUMBER Xn)
% 83.93/84.18 Found (x3 x40) as proof of (cNUMBER Xn)
% 83.93/84.18 Found x30:=(x3 x20):(cNUMBER Xn0)
% 83.93/84.18 Found (x3 x20) as proof of (cNUMBER Xn)
% 83.93/84.18 Found (x3 x20) as proof of (cNUMBER Xn)
% 83.93/84.18 Found (x3 x20) as proof of (cNUMBER Xn)
% 83.93/84.18 Found x30:(cNUMBER Xn0)
% 83.93/84.18 Instantiate: Xn0:=Xn:fofType
% 83.93/84.18 Found x30 as proof of (cNUMBER Xn)
% 83.93/84.18 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 83.93/84.18 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 83.93/84.18 Found (x3 x20) as proof of (cNUMBER Xn)
% 83.93/84.18 Found (x3 x20) as proof of (cNUMBER Xn)
% 83.93/84.18 Found (x3 x20) as proof of (cNUMBER Xn)
% 83.93/84.18 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 83.93/84.18 Found x40 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 83.93/84.18 Found (x5 x40) as proof of (cNUMBER Xn)
% 83.93/84.18 Found (x5 x40) as proof of (cNUMBER Xn)
% 83.93/84.18 Found (x5 x40) as proof of (cNUMBER Xn)
% 83.93/84.18 Found x70:=(x7 x60):(cNUMBER Xn0)
% 83.93/84.18 Instantiate: Xn0:=Xn:fofType
% 83.93/84.18 Found (x7 x60) as proof of (cNUMBER Xn)
% 83.93/84.18 Found (fun (x9:(cODD (cS c0)))=> (x7 x60)) as proof of (cNUMBER Xn)
% 83.93/84.18 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))
% 83.93/84.18 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)))
% 83.93/84.18 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)
% 83.93/84.18 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)
% 83.93/84.18 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)) (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)
% 83.93/84.18 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)
% 83.93/84.18 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))
% 83.93/84.18 Found x9:(cODD (cS c0))
% 83.93/84.18 Instantiate: Xn0:=(cS c0):fofType
% 83.93/84.18 Found x9 as proof of (cODD Xn0)
% 83.93/84.18 Found (or_intror00 x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 83.93/84.18 Found ((or_intror0 (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 83.93/84.18 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 83.93/84.18 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 85.76/85.97 Found x30:(cNUMBER Xn0)
% 85.76/85.97 Found (fun (x5:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> x30) as proof of (cNUMBER Xn0)
% 85.76/85.97 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> x30) as proof of ((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn0))
% 85.76/85.97 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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))))))->((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn0)))
% 85.76/85.97 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 85.76/85.97 Found (fun (x5:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> x20) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 85.76/85.97 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> x20) as proof of ((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 85.76/85.97 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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))))))->((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->((or (cEVEN Xn0)) (cODD Xn0))))
% 85.76/85.97 Found x120:(cNUMBER Xn0)
% 85.76/85.97 Instantiate: Xn0:=Xn:fofType
% 85.76/85.97 Found x120 as proof of (cNUMBER Xn)
% 85.76/85.97 Found x30:=(x3 x20):(cNUMBER Xn0)
% 85.76/85.97 Found (x3 x20) as proof of (cNUMBER Xn0)
% 85.76/85.97 Found (x3 x20) as proof of (cNUMBER Xn0)
% 85.76/85.97 Found x50:=(x5 x40):(cNUMBER Xn0)
% 85.76/85.97 Instantiate: Xn0:=Xn:fofType
% 85.76/85.97 Found (x5 x40) as proof of (cNUMBER Xn)
% 85.76/85.97 Found (x5 x40) as proof of (cNUMBER Xn)
% 87.29/87.50 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 87.29/87.50 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 87.29/87.50 Found (x5 x40) as proof of (cNUMBER Xn)
% 87.29/87.50 Found (x5 x40) as proof of (cNUMBER Xn)
% 87.29/87.50 Found (x5 x40) as proof of (cNUMBER Xn)
% 87.29/87.50 Found x30:=(x3 x20):(cNUMBER Xn0)
% 87.29/87.50 Instantiate: Xn0:=Xn:fofType
% 87.29/87.50 Found (x3 x20) as proof of (cNUMBER Xn)
% 87.29/87.50 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 87.29/87.50 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))
% 87.29/87.50 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)))
% 87.29/87.50 Found x30:=(x3 x20):(cNUMBER Xn0)
% 87.29/87.50 Found (x3 x20) as proof of (cNUMBER Xn)
% 87.29/87.50 Found (x3 x20) as proof of (cNUMBER Xn)
% 87.29/87.50 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 87.29/87.50 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))
% 87.29/87.50 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)))
% 87.29/87.50 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 87.29/87.50 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 87.29/87.50 Found (x5 x40) as proof of (cNUMBER Xn)
% 87.29/87.50 Found (x5 x40) as proof of (cNUMBER Xn)
% 87.29/87.50 Found (x5 x40) as proof of (cNUMBER Xn)
% 87.29/87.50 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 87.29/87.50 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 87.29/87.50 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 87.29/87.50 Found x31:(cNUMBER Xn0)
% 87.29/87.50 Instantiate: Xn0:=Xn:fofType
% 87.29/87.50 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x31) as proof of (cNUMBER Xn)
% 87.29/87.50 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))
% 87.29/87.50 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)))
% 87.29/87.50 Found x30:=(x3 x20):(cNUMBER Xn0)
% 87.29/87.50 Instantiate: Xn0:=Xn:fofType
% 87.29/87.50 Found (x3 x20) as proof of (cNUMBER Xn)
% 87.29/87.50 Found (fun (x5:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 87.29/87.50 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x3 x20)) as proof of ((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn))
% 87.29/87.50 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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))))))->((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn)))
% 87.29/87.50 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 87.29/87.50 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 87.29/87.50 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))))))->((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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))))))) (((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 87.29/87.50 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))))))->((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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))))))) (((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 88.47/88.71 Found x70:(cNUMBER Xn0)
% 88.47/88.71 Instantiate: Xn0:=Xn:fofType
% 88.47/88.71 Found x70 as proof of (cNUMBER Xn)
% 88.47/88.71 Found x40:=(x4 x50):((or (cEVEN Xn00)) (cODD Xn00))
% 88.47/88.71 Instantiate: Xn00:=Xn:fofType
% 88.47/88.71 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 88.47/88.71 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 88.47/88.71 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 88.47/88.71 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 88.47/88.71 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 88.47/88.71 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 88.47/88.71 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)))
% 88.47/88.71 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))))
% 88.47/88.71 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))
% 88.47/88.71 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))
% 88.47/88.71 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))
% 88.47/88.71 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))
% 88.47/88.71 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)))
% 88.47/88.71 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))))
% 90.41/90.64 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))
% 90.41/90.64 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))
% 90.41/90.64 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))
% 90.41/90.64 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))
% 90.41/90.64 Found x50:=(x5 x40):(cNUMBER Xn0)
% 90.41/90.64 Found (x5 x40) as proof of (cNUMBER Xn)
% 90.41/90.64 Found (x5 x40) as proof of (cNUMBER Xn)
% 90.41/90.64 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 90.41/90.64 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x5 x40)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 90.41/90.64 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 90.41/90.64 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 92.24/92.44 Found (x3 x20) as proof of (cNUMBER Xn)
% 92.24/92.44 Found (x3 x20) as proof of (cNUMBER Xn)
% 92.24/92.44 Found (x3 x20) as proof of (cNUMBER Xn)
% 92.24/92.44 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 92.24/92.44 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 92.24/92.44 Found (x3 x20) as proof of (cNUMBER Xn)
% 92.24/92.44 Found (x3 x20) as proof of (cNUMBER Xn)
% 92.24/92.44 Found (x3 x20) as proof of (cNUMBER Xn)
% 92.24/92.44 Found x90:(cNUMBER Xn0)
% 92.24/92.44 Instantiate: Xn0:=Xn:fofType
% 92.24/92.44 Found x90 as proof of (cNUMBER Xn)
% 92.24/92.44 Found x300:=(x30 c0):((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 92.24/92.44 Found (x30 c0) as proof of ((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 92.24/92.44 Found (x30 c0) as proof of ((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 92.24/92.44 Found x300:=(x30 (cS Xx)):((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))
% 92.24/92.44 Found (x30 (cS Xx)) as proof of ((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))
% 92.24/92.44 Found (fun (x4:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx))) as proof of ((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))
% 92.24/92.44 Found (fun (Xx:fofType) (x4:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx))) as proof of (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))
% 92.24/92.44 Found (fun (Xx:fofType) (x4:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx))) as proof of (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))
% 92.24/92.44 Found ((conj00 (x30 c0)) (fun (Xx:fofType) (x4:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 92.24/92.44 Found (((conj0 (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))) (x30 c0)) (fun (Xx:fofType) (x4:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 92.24/92.44 Found ((((conj ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))) (x30 c0)) (fun (Xx:fofType) (x4:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 92.24/92.44 Found ((((conj ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))) (x30 c0)) (fun (Xx:fofType) (x4:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 92.24/92.44 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 92.24/92.44 Instantiate: Xn0:=Xn:fofType
% 92.24/92.44 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 92.24/92.44 Found (x5 x20) as proof of (cNUMBER Xn)
% 92.24/92.44 Found (x5 x20) as proof of (cNUMBER Xn)
% 92.24/92.44 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x20)) as proof of (cNUMBER Xn)
% 92.24/92.44 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x20)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 92.24/92.44 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 92.24/92.44 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 92.24/92.44 Found (x3 x20) as proof of (cNUMBER Xn)
% 92.24/92.44 Found (x3 x20) as proof of (cNUMBER Xn)
% 92.24/92.44 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 92.24/92.44 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 92.24/92.44 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 92.24/92.44 Instantiate: Xn00:=Xn:fofType
% 92.24/92.44 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 92.24/92.44 Found (x3 x40) as proof of (cNUMBER Xn)
% 92.24/92.44 Found (x3 x40) as proof of (cNUMBER Xn)
% 92.24/92.44 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x40)) as proof of (cNUMBER Xn)
% 92.24/92.44 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x40)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 97.13/97.35 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 97.13/97.35 Found x40 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 97.13/97.35 Found (x5 x40) as proof of (cNUMBER Xn)
% 97.13/97.35 Found (x5 x40) as proof of (cNUMBER Xn)
% 97.13/97.35 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 97.13/97.35 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 97.13/97.35 Found x30:=(x3 x20):(cNUMBER Xn0)
% 97.13/97.35 Found (x3 x20) as proof of (cNUMBER Xn)
% 97.13/97.35 Found (x3 x20) as proof of (cNUMBER Xn)
% 97.13/97.35 Found (x3 x20) as proof of (cNUMBER Xn)
% 97.13/97.35 Found x70:(cNUMBER Xn0)
% 97.13/97.35 Instantiate: Xn0:=Xn:fofType
% 97.13/97.35 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x70) as proof of (cNUMBER Xn)
% 97.13/97.35 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))
% 97.13/97.35 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)))
% 97.13/97.35 Found x31:(cNUMBER Xn0)
% 97.13/97.35 Instantiate: Xn0:=Xn:fofType
% 97.13/97.35 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x31) as proof of (cNUMBER Xn)
% 97.13/97.35 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))
% 97.13/97.35 Found x30:(cNUMBER Xn0)
% 97.13/97.35 Instantiate: Xn0:=Xn:fofType
% 97.13/97.35 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of (cNUMBER Xn)
% 97.13/97.35 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))
% 97.13/97.35 Found x30:(cNUMBER Xn0)
% 97.13/97.35 Instantiate: Xn0:=Xn:fofType
% 97.13/97.35 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of (cNUMBER Xn)
% 97.13/97.35 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))
% 97.13/97.35 Found x50:(cNUMBER Xn0)
% 97.13/97.35 Instantiate: Xn0:=Xn:fofType
% 97.13/97.35 Found x50 as proof of (cNUMBER Xn)
% 97.13/97.35 Found x30:(cNUMBER Xn0)
% 97.13/97.35 Instantiate: Xn0:=Xn:fofType
% 97.13/97.35 Found x30 as proof of (cNUMBER Xn)
% 97.13/97.35 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 97.13/97.35 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 97.13/97.35 Found (x5 x40) as proof of (cNUMBER Xn)
% 97.13/97.35 Found (x5 x40) as proof of (cNUMBER Xn)
% 97.13/97.35 Found (x5 x40) as proof of (cNUMBER Xn)
% 97.13/97.35 Found x50:=(x5 x40):(cNUMBER Xn0)
% 97.13/97.35 Instantiate: Xn0:=Xn:fofType
% 97.13/97.35 Found (x5 x40) as proof of (cNUMBER Xn)
% 97.13/97.35 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 97.13/97.35 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))
% 97.13/97.35 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 97.13/97.35 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 97.13/97.35 Found (x5 x40) as proof of (cNUMBER Xn)
% 97.13/97.35 Found (x5 x40) as proof of (cNUMBER Xn)
% 97.13/97.35 Found (x5 x40) as proof of (cNUMBER Xn)
% 97.13/97.35 Found x7:(cODD (cS c0))
% 97.13/97.35 Instantiate: Xn0:=(cS c0):fofType
% 97.13/97.35 Found x7 as proof of (cODD Xn0)
% 97.13/97.35 Found (or_intror00 x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 97.13/97.35 Found ((or_intror0 (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 97.13/97.35 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 97.13/97.35 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 97.13/97.35 Found x70:(cNUMBER Xn0)
% 97.13/97.35 Instantiate: Xn0:=Xn:fofType
% 97.13/97.35 Found x70 as proof of (cNUMBER Xn)
% 97.13/97.35 Found x30:=(x3 x20):(cNUMBER Xn0)
% 97.13/97.35 Found (x3 x20) as proof of (cNUMBER Xn0)
% 97.13/97.35 Found (x3 x20) as proof of (cNUMBER Xn0)
% 97.13/97.35 Found x30:=(x3 x21):(cNUMBER Xn0)
% 97.13/97.35 Instantiate: Xn0:=Xn:fofType
% 97.13/97.35 Found (x3 x21) as proof of (cNUMBER Xn)
% 97.13/97.35 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21)) as proof of (cNUMBER Xn)
% 98.14/98.42 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))
% 98.14/98.42 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 98.14/98.42 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 98.14/98.42 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 98.14/98.42 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 98.14/98.42 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)))
% 98.14/98.42 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))))
% 98.14/98.42 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))
% 98.14/98.42 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))
% 98.14/98.42 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))
% 98.14/98.42 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))
% 98.14/98.42 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)
% 98.14/98.42 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)
% 98.14/98.42 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 98.14/98.42 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 98.14/98.42 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 98.14/98.42 Found x30:=(x3 x21):(cNUMBER Xn0)
% 98.14/98.42 Instantiate: Xn0:=Xn:fofType
% 98.14/98.42 Found (x3 x21) as proof of (cNUMBER Xn)
% 98.14/98.42 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21)) as proof of (cNUMBER Xn)
% 98.14/98.42 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))
% 98.14/98.42 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)))
% 99.17/99.42 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 99.17/99.42 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 99.17/99.42 Found (x3 x20) as proof of (cNUMBER Xn)
% 99.17/99.42 Found (x3 x20) as proof of (cNUMBER Xn)
% 99.17/99.42 Found (x3 x20) as proof of (cNUMBER Xn)
% 99.17/99.42 Found x90:(cNUMBER Xn0)
% 99.17/99.42 Instantiate: Xn0:=Xn:fofType
% 99.17/99.42 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x90) as proof of (cNUMBER Xn)
% 99.17/99.42 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))
% 99.17/99.42 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 99.17/99.42 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 99.17/99.42 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 99.17/99.42 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 99.17/99.42 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)))
% 99.17/99.42 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))))
% 99.17/99.42 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))
% 99.17/99.42 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))
% 99.17/99.42 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))
% 99.17/99.42 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))
% 99.17/99.42 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)))
% 99.17/99.42 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))))
% 99.17/99.42 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))
% 99.17/99.42 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))
% 99.17/99.42 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))
% 99.17/99.42 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))
% 99.17/99.43 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)
% 99.17/99.43 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)
% 99.17/99.43 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 99.17/99.43 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 99.17/99.43 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 99.17/99.43 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 99.17/99.43 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)))
% 99.17/99.43 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))))
% 99.17/99.43 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))
% 99.17/99.43 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))
% 99.17/99.43 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))
% 99.17/99.43 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))
% 99.17/99.44 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)
% 99.17/99.44 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)
% 99.17/99.44 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))
% 99.17/99.44 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)))
% 99.17/99.44 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)
% 99.17/99.44 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)
% 99.96/100.19 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)
% 99.96/100.19 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)
% 99.96/100.19 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 99.96/100.19 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 99.96/100.19 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 99.96/100.19 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 99.96/100.19 Found x40:=(x4 x50):((or (cEVEN Xn00)) (cODD Xn00))
% 99.96/100.19 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 99.96/100.19 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 99.96/100.19 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 99.96/100.19 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 99.96/100.19 Instantiate: Xn0:=Xn:fofType
% 99.96/100.19 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 99.96/100.19 Found (x5 x20) as proof of (cNUMBER Xn)
% 99.96/100.19 Found (x5 x20) as proof of (cNUMBER Xn)
% 99.96/100.19 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x20)) as proof of (cNUMBER Xn)
% 99.96/100.19 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))
% 99.96/100.19 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)))
% 99.96/100.19 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 99.96/100.19 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 99.96/100.19 Found (x3 x20) as proof of (cNUMBER Xn)
% 99.96/100.19 Found (x3 x20) as proof of (cNUMBER Xn)
% 99.96/100.19 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 99.96/100.19 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))
% 99.96/100.19 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)))
% 101.65/101.86 Found x300:=(x30 c0):((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 101.65/101.86 Found (x30 c0) as proof of ((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 101.65/101.86 Found (x30 c0) as proof of ((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 101.65/101.86 Found x30:=(x3 x20):(cNUMBER Xn0)
% 101.65/101.86 Found (x3 x20) as proof of (cNUMBER Xn)
% 101.65/101.86 Found (x3 x20) as proof of (cNUMBER Xn)
% 101.65/101.86 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 101.65/101.86 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))
% 101.65/101.86 Found x9:(cODD (cS c0))
% 101.65/101.86 Instantiate: Xn0:=(cS c0):fofType
% 101.65/101.86 Found x9 as proof of (cODD Xn0)
% 101.65/101.86 Found (or_intror00 x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 101.65/101.86 Found ((or_intror0 (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 101.65/101.86 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 101.65/101.86 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 101.65/101.86 Found x50:(cNUMBER Xn0)
% 101.65/101.86 Instantiate: Xn0:=Xn:fofType
% 101.65/101.86 Found x50 as proof of (cNUMBER Xn)
% 101.65/101.86 Found x300:=(x30 (cS Xx)):((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))
% 101.65/101.86 Found (x30 (cS Xx)) as proof of ((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))
% 101.65/101.86 Found (fun (x5:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx))) as proof of ((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))
% 101.65/101.86 Found (fun (Xx:fofType) (x5:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx))) as proof of (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))
% 101.65/101.86 Found (fun (Xx:fofType) (x5:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx))) as proof of (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))
% 101.65/101.86 Found ((conj00 (x30 c0)) (fun (Xx:fofType) (x5:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 101.65/101.86 Found (((conj0 (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))) (x30 c0)) (fun (Xx:fofType) (x5:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 101.65/101.86 Found ((((conj ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))) (x30 c0)) (fun (Xx:fofType) (x5:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 101.65/101.86 Found ((((conj ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))) (x30 c0)) (fun (Xx:fofType) (x5:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 101.65/101.86 Found x30:(cNUMBER Xn0)
% 101.65/101.86 Instantiate: Xn0:=Xn:fofType
% 101.65/101.86 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of (cNUMBER Xn)
% 101.65/101.86 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))
% 101.65/101.86 Found x31:(cNUMBER Xn0)
% 101.65/101.86 Instantiate: Xn0:=Xn:fofType
% 101.65/101.86 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x31) as proof of (cNUMBER Xn)
% 101.65/101.86 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))
% 106.36/106.62 Found x30:(cNUMBER Xn0)
% 106.36/106.62 Instantiate: Xn0:=Xn:fofType
% 106.36/106.62 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of (cNUMBER Xn)
% 106.36/106.62 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))
% 106.36/106.62 Found x70:=(x7 x60):(cNUMBER Xn0)
% 106.36/106.62 Instantiate: Xn0:=Xn:fofType
% 106.36/106.62 Found (x7 x60) as proof of (cNUMBER Xn)
% 106.36/106.62 Found (x7 x60) as proof of (cNUMBER Xn)
% 106.36/106.62 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 106.36/106.62 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 106.36/106.62 Found (x5 x40) as proof of (cNUMBER Xn)
% 106.36/106.62 Found (x5 x40) as proof of (cNUMBER Xn)
% 106.36/106.62 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 106.36/106.62 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x5 x40)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 106.36/106.62 Found x50:=(x5 x40):(cNUMBER Xn0)
% 106.36/106.62 Found (x5 x40) as proof of (cNUMBER Xn0)
% 106.36/106.62 Found (x5 x40) as proof of (cNUMBER Xn0)
% 106.36/106.62 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 106.36/106.62 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 106.36/106.62 Found (x5 x40) as proof of (cNUMBER Xn)
% 106.36/106.62 Found (x5 x40) as proof of (cNUMBER Xn)
% 106.36/106.62 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 106.36/106.62 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x5 x40)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 106.36/106.62 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 106.36/106.62 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 106.36/106.62 Found (x5 x40) as proof of (cNUMBER Xn)
% 106.36/106.62 Found (x5 x40) as proof of (cNUMBER Xn)
% 106.36/106.62 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 106.36/106.62 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x5 x40)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 106.36/106.62 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 106.36/106.62 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 106.36/106.62 Found (x5 x40) as proof of (cNUMBER Xn)
% 106.36/106.62 Found (x5 x40) as proof of (cNUMBER Xn)
% 106.36/106.62 Found (x5 x40) as proof of (cNUMBER Xn)
% 106.36/106.62 Found x50:=(x5 x40):(cNUMBER Xn0)
% 106.36/106.62 Instantiate: Xn0:=Xn:fofType
% 106.36/106.62 Found (x5 x40) as proof of (cNUMBER Xn)
% 106.36/106.62 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 106.36/106.62 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))
% 106.36/106.62 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)))
% 106.36/106.62 Found x40:=(x4 x50):((or (cEVEN Xn0)) (cODD Xn0))
% 106.36/106.62 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 106.36/106.62 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 106.36/106.62 Found x51:(cNUMBER Xn0)
% 106.36/106.62 Instantiate: Xn0:=Xn:fofType
% 106.36/106.62 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x51) as proof of (cNUMBER Xn)
% 106.36/106.62 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))))))=> x51) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 106.36/106.62 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))))))=> 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)))
% 106.36/106.62 Found x70:(cNUMBER Xn0)
% 106.36/106.62 Instantiate: Xn0:=Xn:fofType
% 106.36/106.62 Found x70 as proof of (cNUMBER Xn)
% 106.36/106.62 Found x50:=(x5 x40):(cNUMBER Xn0)
% 106.36/106.62 Instantiate: Xn0:=Xn:fofType
% 106.36/106.62 Found (x5 x40) as proof of (cNUMBER Xn)
% 106.36/106.62 Found (x5 x40) as proof of (cNUMBER Xn)
% 106.36/106.62 Found x300:=(x30 c0):((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 106.36/106.62 Found (x30 c0) as proof of ((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 106.36/106.62 Found (x30 c0) as proof of ((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 110.43/110.65 Found x30:=(x3 x20):(cNUMBER Xn0)
% 110.43/110.65 Found (x3 x20) as proof of (cNUMBER Xn0)
% 110.43/110.65 Found (x3 x20) as proof of (cNUMBER Xn0)
% 110.43/110.65 Found x30:=(x3 x21):(cNUMBER Xn0)
% 110.43/110.65 Instantiate: Xn0:=Xn:fofType
% 110.43/110.65 Found (x3 x21) as proof of (cNUMBER Xn)
% 110.43/110.65 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21)) as proof of (cNUMBER Xn)
% 110.43/110.65 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))
% 110.43/110.65 Found x40:=(x4 x50):((or (cEVEN Xn00)) (cODD Xn00))
% 110.43/110.65 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 110.43/110.65 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 110.43/110.65 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 110.43/110.65 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 110.43/110.65 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 110.43/110.65 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 110.43/110.65 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 110.43/110.65 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 110.43/110.65 Found (x3 x20) as proof of (cNUMBER Xn)
% 110.43/110.65 Found (x3 x20) as proof of (cNUMBER Xn)
% 110.43/110.65 Found (x3 x20) as proof of (cNUMBER Xn)
% 110.43/110.65 Found x90:(cNUMBER Xn0)
% 110.43/110.65 Instantiate: Xn0:=Xn:fofType
% 110.43/110.65 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x90) as proof of (cNUMBER Xn)
% 110.43/110.65 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))
% 110.43/110.65 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)))
% 110.43/110.65 Found x50:=(x5 x40):(cNUMBER Xn0)
% 110.43/110.65 Found (x5 x40) as proof of (cNUMBER Xn)
% 110.43/110.65 Found (x5 x40) as proof of (cNUMBER Xn)
% 110.43/110.65 Found (x5 x40) as proof of (cNUMBER Xn)
% 110.43/110.65 Found x30:=(x3 x20):(cNUMBER Xn0)
% 110.43/110.65 Found (x3 x20) as proof of (cNUMBER Xn0)
% 110.43/110.65 Found (x3 x20) as proof of (cNUMBER Xn0)
% 110.43/110.65 Found x30:=(x3 x21):(cNUMBER Xn0)
% 110.43/110.65 Instantiate: Xn0:=Xn:fofType
% 110.43/110.65 Found (x3 x21) as proof of (cNUMBER Xn)
% 110.43/110.65 Found (x3 x21) as proof of (cNUMBER Xn)
% 110.43/110.65 Found x30:=(x3 x20):(cNUMBER Xn0)
% 110.43/110.65 Found (x3 x20) as proof of (cNUMBER Xn)
% 110.43/110.65 Found (x3 x20) as proof of (cNUMBER Xn)
% 110.43/110.65 Found (x3 x20) as proof of (cNUMBER Xn)
% 110.43/110.65 Found x30:=(x3 x20):(cNUMBER Xn0)
% 110.43/110.65 Found (x3 x20) as proof of (cNUMBER Xn)
% 110.43/110.65 Found (x3 x20) as proof of (cNUMBER Xn)
% 110.43/110.65 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 110.43/110.65 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))
% 110.43/110.65 Found x30:=(x3 x20):(cNUMBER Xn0)
% 110.43/110.65 Found (x3 x20) as proof of (cNUMBER Xn)
% 110.43/110.65 Found (x3 x20) as proof of (cNUMBER Xn)
% 110.43/110.65 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 110.43/110.65 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))
% 110.43/110.65 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)))
% 110.43/110.65 Found x51:(cNUMBER Xn0)
% 110.43/110.65 Instantiate: Xn0:=Xn:fofType
% 110.43/110.65 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x51) as proof of (cNUMBER Xn)
% 110.43/110.65 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))
% 110.43/110.65 Found x50:(cNUMBER Xn0)
% 110.43/110.65 Instantiate: Xn0:=Xn:fofType
% 110.43/110.65 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of (cNUMBER Xn)
% 110.43/110.65 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))
% 110.43/110.65 Found x50:(cNUMBER Xn0)
% 110.43/110.65 Instantiate: Xn0:=Xn:fofType
% 110.43/110.65 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of (cNUMBER Xn)
% 110.43/110.65 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))
% 111.62/111.90 Found x30:=(x3 x20):(cNUMBER Xn0)
% 111.62/111.90 Instantiate: Xn0:=Xn:fofType
% 111.62/111.90 Found (x3 x20) as proof of (cNUMBER Xn)
% 111.62/111.90 Found (x3 x20) as proof of (cNUMBER Xn)
% 111.62/111.90 Found x30:=(x3 x20):(cNUMBER Xn0)
% 111.62/111.90 Instantiate: Xn0:=Xn:fofType
% 111.62/111.90 Found (x3 x20) as proof of (cNUMBER Xn)
% 111.62/111.90 Found (x3 x20) as proof of (cNUMBER Xn)
% 111.62/111.90 Found x50:(cNUMBER Xn0)
% 111.62/111.90 Instantiate: Xn0:=Xn:fofType
% 111.62/111.90 Found x50 as proof of (cNUMBER Xn)
% 111.62/111.90 Found x300:=(x30 (cS Xx)):((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))
% 111.62/111.90 Found (x30 (cS Xx)) as proof of ((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))
% 111.62/111.90 Found (fun (x5:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx))) as proof of ((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))
% 111.62/111.90 Found (fun (Xx:fofType) (x5:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx))) as proof of (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))
% 111.62/111.90 Found (fun (Xx:fofType) (x5:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx))) as proof of (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))
% 111.62/111.90 Found ((conj00 (x30 c0)) (fun (Xx:fofType) (x5:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 111.62/111.90 Found (((conj0 (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))) (x30 c0)) (fun (Xx:fofType) (x5:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 111.62/111.90 Found ((((conj ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))) (x30 c0)) (fun (Xx:fofType) (x5:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 111.62/111.90 Found ((((conj ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))) (x30 c0)) (fun (Xx:fofType) (x5:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 111.62/111.90 Found x30:(cNUMBER Xn0)
% 111.62/111.90 Instantiate: Xn0:=Xn:fofType
% 111.62/111.90 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of (cNUMBER Xn)
% 111.62/111.90 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))
% 111.62/111.90 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)))
% 111.62/111.90 Found x30:(cNUMBER Xn0)
% 111.62/111.90 Instantiate: Xn0:=Xn:fofType
% 111.62/111.90 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of (cNUMBER Xn)
% 111.62/111.90 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))
% 111.62/111.90 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)))
% 113.02/113.25 Found x70:=(x7 x60):(cNUMBER Xn0)
% 113.02/113.25 Instantiate: Xn0:=Xn:fofType
% 113.02/113.25 Found (x7 x60) as proof of (cNUMBER Xn)
% 113.02/113.25 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)) as proof of (cNUMBER Xn)
% 113.02/113.25 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))
% 113.02/113.25 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 113.02/113.25 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 113.02/113.25 Found (x3 x20) as proof of (cNUMBER Xn)
% 113.02/113.25 Found (x3 x20) as proof of (cNUMBER Xn)
% 113.02/113.25 Found (x3 x20) as proof of (cNUMBER Xn)
% 113.02/113.25 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 113.02/113.25 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 113.02/113.25 Found (x5 x40) as proof of (cNUMBER Xn)
% 113.02/113.25 Found (x5 x40) as proof of (cNUMBER Xn)
% 113.02/113.25 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 113.02/113.25 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x5 x40)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 113.02/113.25 Found x300:=(x30 (cS Xx)):((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))
% 113.02/113.25 Found (x30 (cS Xx)) as proof of ((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))
% 113.02/113.25 Found (fun (x6:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx))) as proof of ((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))
% 113.02/113.25 Found (fun (Xx:fofType) (x6:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx))) as proof of (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))
% 113.02/113.25 Found (fun (Xx:fofType) (x6:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx))) as proof of (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))
% 113.02/113.25 Found ((conj00 (x30 c0)) (fun (Xx:fofType) (x6:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 113.02/113.25 Found (((conj0 (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))) (x30 c0)) (fun (Xx:fofType) (x6:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 113.02/113.25 Found ((((conj ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))) (x30 c0)) (fun (Xx:fofType) (x6:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 113.02/113.25 Found ((((conj ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))) (x30 c0)) (fun (Xx:fofType) (x6:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 113.02/113.25 Found x9:(cODD (cS c0))
% 113.02/113.25 Instantiate: Xn0:=(cS c0):fofType
% 113.02/113.25 Found x9 as proof of (cODD Xn0)
% 113.02/113.25 Found (or_intror00 x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 113.02/113.25 Found ((or_intror0 (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 113.02/113.25 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 113.02/113.25 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 113.02/113.25 Found (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9)) as proof of (cNUMBER Xn0)
% 113.02/113.25 Found (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9)) as proof of (cNUMBER Xn0)
% 119.65/119.93 Found x120:=(x12 x110):(cNUMBER Xn0)
% 119.65/119.93 Instantiate: Xn0:=Xn:fofType
% 119.65/119.93 Found (x12 x110) as proof of (cNUMBER Xn)
% 119.65/119.93 Found (x12 x110) as proof of (cNUMBER Xn)
% 119.65/119.93 Found x50:=(x5 x40):(cNUMBER Xn0)
% 119.65/119.93 Instantiate: Xn0:=Xn:fofType
% 119.65/119.93 Found (x5 x40) as proof of (cNUMBER Xn)
% 119.65/119.93 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 119.65/119.93 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x5 x40)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 119.65/119.93 Found x50:=(x5 x40):(cNUMBER Xn0)
% 119.65/119.93 Found (x5 x40) as proof of (cNUMBER Xn0)
% 119.65/119.93 Found (x5 x40) as proof of (cNUMBER Xn0)
% 119.65/119.93 Found x50:=(x5 x41):(cNUMBER Xn0)
% 119.65/119.93 Instantiate: Xn0:=Xn:fofType
% 119.65/119.93 Found (x5 x41) as proof of (cNUMBER Xn)
% 119.65/119.93 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x41)) as proof of (cNUMBER Xn)
% 119.65/119.93 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))
% 119.65/119.93 Found x30:(cNUMBER Xn0)
% 119.65/119.93 Found x30 as proof of (cNUMBER Xn0)
% 119.65/119.93 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 119.65/119.93 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 119.65/119.93 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 119.65/119.93 Found x50:(cNUMBER Xn00)
% 119.65/119.93 Found x50 as proof of (cNUMBER Xn00)
% 119.65/119.93 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 119.65/119.93 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 119.65/119.93 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 119.65/119.93 Found x40:=(x4 x50):((or (cEVEN Xn0)) (cODD Xn0))
% 119.65/119.93 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 119.65/119.93 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 119.65/119.93 Found x50:=(x5 x41):(cNUMBER Xn0)
% 119.65/119.93 Instantiate: Xn0:=Xn:fofType
% 119.65/119.93 Found (x5 x41) as proof of (cNUMBER Xn)
% 119.65/119.93 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x41)) as proof of (cNUMBER Xn)
% 119.65/119.93 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))
% 119.65/119.93 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)))
% 119.65/119.93 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 119.65/119.93 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 119.65/119.93 Found (x3 x20) as proof of (cNUMBER Xn)
% 119.65/119.93 Found (x3 x20) as proof of (cNUMBER Xn)
% 119.65/119.93 Found (x3 x20) as proof of (cNUMBER Xn)
% 119.65/119.93 Found x50:=(x5 x40):(cNUMBER Xn0)
% 119.65/119.93 Found (x5 x40) as proof of (cNUMBER Xn)
% 119.65/119.93 Found (x5 x40) as proof of (cNUMBER Xn)
% 119.65/119.93 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 119.65/119.93 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))
% 119.65/119.93 Found x30:=(x3 x20):(cNUMBER Xn0)
% 119.65/119.93 Found (x3 x20) as proof of (cNUMBER Xn0)
% 119.65/119.93 Found (x3 x20) as proof of (cNUMBER Xn0)
% 119.65/119.93 Found x30:=(x3 x21):(cNUMBER Xn0)
% 119.65/119.93 Instantiate: Xn0:=Xn:fofType
% 119.65/119.93 Found (x3 x21) as proof of (cNUMBER Xn)
% 119.65/119.93 Found (x3 x21) as proof of (cNUMBER Xn)
% 119.65/119.93 Found x30:=(x3 x20):(cNUMBER Xn0)
% 119.65/119.93 Found (x3 x20) as proof of (cNUMBER Xn)
% 119.65/119.93 Found (x3 x20) as proof of (cNUMBER Xn)
% 119.65/119.93 Found (x3 x20) as proof of (cNUMBER Xn)
% 119.65/119.93 Found x30:=(x3 x20):(cNUMBER Xn0)
% 119.65/119.93 Instantiate: Xn0:=Xn:fofType
% 119.65/119.93 Found (x3 x20) as proof of (cNUMBER Xn)
% 119.65/119.93 Found (x3 x20) as proof of (cNUMBER Xn)
% 119.65/119.93 Found x30:=(x3 x20):(cNUMBER Xn0)
% 119.65/119.93 Found (x3 x20) as proof of (cNUMBER Xn)
% 119.65/119.93 Found (x3 x20) as proof of (cNUMBER Xn)
% 119.65/119.93 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 119.65/119.93 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))
% 119.71/119.94 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 119.71/119.94 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 119.71/119.94 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 119.71/119.94 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 119.71/119.94 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)))
% 119.71/119.94 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))))
% 119.71/119.94 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))
% 119.71/119.94 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))
% 119.71/119.94 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))
% 119.71/119.94 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))
% 119.71/119.94 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)))
% 119.71/119.94 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))))
% 119.71/119.94 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))
% 119.71/119.95 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))
% 119.71/119.95 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)) ((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))
% 119.71/119.95 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)) ((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))
% 119.71/119.95 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)
% 119.74/119.96 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)
% 119.74/119.96 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 119.74/119.96 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 119.74/119.96 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 119.74/119.96 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 119.74/119.96 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)))
% 119.74/119.96 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))))
% 119.74/119.96 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))
% 119.74/119.96 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))
% 119.74/119.96 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))
% 119.74/119.96 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))
% 119.74/119.96 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)
% 119.74/119.96 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)
% 119.74/119.96 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))
% 119.74/119.96 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)))
% 119.74/119.96 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)
% 119.74/119.96 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)
% 119.74/119.96 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)
% 121.22/121.49 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) 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)
% 121.22/121.49 Found x30:=(x3 x20):(cNUMBER Xn0)
% 121.22/121.49 Found (x3 x20) as proof of (cNUMBER Xn)
% 121.22/121.49 Found (x3 x20) as proof of (cNUMBER Xn)
% 121.22/121.49 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 121.22/121.49 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))
% 121.22/121.49 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)))
% 121.22/121.49 Found x30:=(x3 x20):(cNUMBER Xn0)
% 121.22/121.49 Instantiate: Xn0:=Xn:fofType
% 121.22/121.49 Found (x3 x20) as proof of (cNUMBER Xn)
% 121.22/121.49 Found (x3 x20) as proof of (cNUMBER Xn)
% 121.22/121.49 Found x90:=(x9 x80):(cNUMBER Xn0)
% 121.22/121.49 Instantiate: Xn0:=Xn:fofType
% 121.22/121.49 Found (x9 x80) as proof of (cNUMBER Xn)
% 121.22/121.49 Found (x9 x80) as proof of (cNUMBER Xn)
% 121.22/121.49 Found x50:(cNUMBER Xn0)
% 121.22/121.49 Instantiate: Xn0:=Xn:fofType
% 121.22/121.49 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of (cNUMBER Xn)
% 121.22/121.49 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))
% 121.22/121.49 Found x50:(cNUMBER Xn0)
% 121.22/121.49 Instantiate: Xn0:=Xn:fofType
% 121.22/121.49 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of (cNUMBER Xn)
% 121.22/121.49 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))
% 121.22/121.49 Found x51:(cNUMBER Xn0)
% 121.22/121.49 Instantiate: Xn0:=Xn:fofType
% 121.22/121.49 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x51) as proof of (cNUMBER Xn)
% 121.22/121.49 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))
% 121.22/121.49 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 121.22/121.49 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 121.22/121.49 Found (x3 x20) as proof of (cNUMBER Xn)
% 121.22/121.49 Found (x3 x20) as proof of (cNUMBER Xn)
% 121.22/121.49 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 121.22/121.49 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))
% 121.22/121.49 Found x70:=(x7 x60):(cNUMBER Xn0)
% 123.33/123.57 Instantiate: Xn0:=Xn:fofType
% 123.33/123.57 Found (x7 x60) as proof of (cNUMBER Xn)
% 123.33/123.57 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)) as proof of (cNUMBER Xn)
% 123.33/123.57 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))
% 123.33/123.57 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)))
% 123.33/123.57 Found x300:=(x30 (cS Xx)):((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))
% 123.33/123.57 Found (x30 (cS Xx)) as proof of ((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))
% 123.33/123.57 Found (fun (x6:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx))) as proof of ((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))
% 123.33/123.57 Found (fun (Xx:fofType) (x6:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx))) as proof of (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))
% 123.33/123.57 Found (fun (Xx:fofType) (x6:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx))) as proof of (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))
% 123.33/123.57 Found ((conj00 (x30 c0)) (fun (Xx:fofType) (x6:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 123.33/123.57 Found (((conj0 (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))) (x30 c0)) (fun (Xx:fofType) (x6:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 123.33/123.57 Found ((((conj ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))) (x30 c0)) (fun (Xx:fofType) (x6:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 123.33/123.57 Found ((((conj ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))) (x30 c0)) (fun (Xx:fofType) (x6:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 123.33/123.57 Found x70:=(x7 x60):(cNUMBER Xn0)
% 123.33/123.57 Found (x7 x60) as proof of (cNUMBER Xn0)
% 123.33/123.57 Found (x7 x60) as proof of (cNUMBER Xn0)
% 123.33/123.57 Found x70:=(x7 x61):(cNUMBER Xn0)
% 123.33/123.57 Instantiate: Xn0:=Xn:fofType
% 123.33/123.57 Found (x7 x61) as proof of (cNUMBER Xn)
% 123.33/123.57 Found (x7 x61) as proof of (cNUMBER Xn)
% 123.33/123.57 Found x70:=(x7 x61):(cNUMBER Xn0)
% 123.33/123.57 Found (x7 x61) as proof of (cNUMBER Xn)
% 123.33/123.57 Found (x7 x61) as proof of (cNUMBER Xn)
% 123.33/123.57 Found (x7 x61) as proof of (cNUMBER Xn)
% 123.33/123.57 Found x30:=(x3 x20):(cNUMBER Xn0)
% 123.33/123.57 Instantiate: Xn0:=Xn:fofType
% 123.33/123.57 Found (x3 x20) as proof of (cNUMBER Xn)
% 123.33/123.57 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 123.33/123.57 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))
% 123.33/123.57 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)))
% 123.33/123.57 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)
% 123.33/123.57 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)
% 124.35/124.61 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)
% 124.35/124.61 Found x120:=(x12 x110):(cNUMBER Xn0)
% 124.35/124.61 Instantiate: Xn0:=Xn:fofType
% 124.35/124.61 Found (x12 x110) as proof of (cNUMBER Xn)
% 124.35/124.61 Found (fun (x12:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x12 x110)) as proof of (cNUMBER Xn)
% 124.35/124.61 Found (fun (x12:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x12 x110)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 124.35/124.61 Found x50:(cNUMBER Xn00)
% 124.35/124.61 Found x50 as proof of (cNUMBER Xn00)
% 124.35/124.61 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 124.35/124.61 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 124.35/124.61 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 124.35/124.61 Found x70:=(x7 x60):(cNUMBER Xn0)
% 124.35/124.61 Instantiate: Xn0:=Xn:fofType
% 124.35/124.61 Found (x7 x60) as proof of (cNUMBER Xn)
% 124.35/124.61 Found (x7 x60) as proof of (cNUMBER Xn)
% 124.35/124.61 Found x70:=(x7 x60):(cNUMBER Xn0)
% 124.35/124.61 Instantiate: Xn0:=Xn:fofType
% 124.35/124.61 Found (x7 x60) as proof of (cNUMBER Xn)
% 124.35/124.61 Found (x7 x60) as proof of (cNUMBER Xn)
% 124.35/124.61 Found x8:(cODD (cS c0))
% 124.35/124.61 Instantiate: Xn0:=(cS c0):fofType
% 124.35/124.61 Found (fun (x8:(cODD (cS c0)))=> x8) as proof of (cODD Xn0)
% 124.35/124.61 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))
% 124.35/124.61 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)))
% 124.35/124.61 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)
% 124.35/124.61 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)
% 124.35/124.61 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)
% 124.35/124.61 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)
% 124.35/124.61 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))
% 124.35/124.61 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))
% 124.35/124.61 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))
% 125.26/125.53 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))
% 125.26/125.53 Found or_introl00:=(or_introl0 (cEVEN Xn0)):((cODD (cS c0))->((or (cODD (cS c0))) (cEVEN Xn0)))
% 125.26/125.53 Found (or_introl0 (cEVEN Xn0)) as proof of ((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0)))
% 125.26/125.53 Found ((or_introl (cODD (cS c0))) (cEVEN Xn0)) as proof of ((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0)))
% 125.26/125.53 Found ((or_introl (cODD (cS c0))) (cEVEN Xn0)) as proof of ((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0)))
% 125.26/125.53 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)))
% 125.26/125.53 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))))
% 125.26/125.53 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))
% 125.26/125.53 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))
% 125.26/125.53 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))
% 125.26/125.53 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))
% 125.26/125.53 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))
% 125.26/125.53 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))
% 128.33/128.58 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))
% 128.33/128.58 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))
% 128.33/128.58 Found x50:=(x5 x40):(cNUMBER Xn0)
% 128.33/128.58 Found (x5 x40) as proof of (cNUMBER Xn0)
% 128.33/128.58 Found (x5 x40) as proof of (cNUMBER Xn0)
% 128.33/128.58 Found x50:=(x5 x41):(cNUMBER Xn0)
% 128.33/128.58 Instantiate: Xn0:=Xn:fofType
% 128.33/128.58 Found (x5 x41) as proof of (cNUMBER Xn)
% 128.33/128.58 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x41)) as proof of (cNUMBER Xn)
% 128.33/128.58 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))
% 128.33/128.58 Found x40:=(x4 x50):((or (cEVEN Xn0)) (cODD Xn0))
% 128.33/128.58 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 128.33/128.58 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 128.33/128.58 Found x300:=(x30 c0):((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 128.33/128.58 Found (x30 c0) as proof of ((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 128.33/128.58 Found (x30 c0) as proof of ((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 128.33/128.58 Found x70:=(x7 x60):(cNUMBER Xn0)
% 128.33/128.58 Found (x7 x60) as proof of (cNUMBER Xn)
% 128.33/128.58 Found (x7 x60) as proof of (cNUMBER Xn)
% 128.33/128.58 Found (x7 x60) as proof of (cNUMBER Xn)
% 128.33/128.58 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 128.33/128.58 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 128.33/128.58 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 128.33/128.58 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 128.33/128.58 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)))
% 128.33/128.58 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))))
% 128.33/128.58 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))
% 128.33/128.58 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))
% 128.33/128.58 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)) ((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))
% 128.33/128.58 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)) ((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))
% 128.33/128.58 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)) ((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)))
% 128.33/128.58 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)) ((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))))
% 128.33/128.58 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)) ((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))
% 128.33/128.58 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))
% 128.33/128.58 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))
% 128.33/128.59 Found (fun (x5:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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))
% 128.33/128.59 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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 (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 128.33/128.59 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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))))))->((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->((or (cEVEN Xn0)) (cODD Xn0))))
% 128.33/128.59 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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))
% 128.33/128.59 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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))
% 128.33/128.60 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))))))->((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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))))))) (((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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))
% 128.33/128.60 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))))))->((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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))))))) (((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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))
% 129.34/129.57 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 129.34/129.57 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 129.34/129.57 Found (x3 x20) as proof of (cNUMBER Xn)
% 129.34/129.57 Found (x3 x20) as proof of (cNUMBER Xn)
% 129.34/129.57 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 129.34/129.57 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))
% 129.34/129.57 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 129.34/129.57 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 129.34/129.57 Found (x3 x20) as proof of (cNUMBER Xn)
% 129.34/129.57 Found (x3 x20) as proof of (cNUMBER Xn)
% 129.34/129.57 Found (x3 x20) as proof of (cNUMBER Xn)
% 129.34/129.57 Found x50:=(x5 x40):(cNUMBER Xn0)
% 129.34/129.57 Found (x5 x40) as proof of (cNUMBER Xn0)
% 129.34/129.57 Found (x5 x40) as proof of (cNUMBER Xn0)
% 129.34/129.57 Found x50:=(x5 x41):(cNUMBER Xn0)
% 129.34/129.57 Instantiate: Xn0:=Xn:fofType
% 129.34/129.57 Found (x5 x41) as proof of (cNUMBER Xn)
% 129.34/129.57 Found (x5 x41) as proof of (cNUMBER Xn)
% 129.34/129.57 Found x50:=(x5 x40):(cNUMBER Xn0)
% 129.34/129.57 Found (x5 x40) as proof of (cNUMBER Xn)
% 129.34/129.57 Found (x5 x40) as proof of (cNUMBER Xn)
% 129.34/129.57 Found (x5 x40) as proof of (cNUMBER Xn)
% 129.34/129.57 Found x50:=(x5 x40):(cNUMBER Xn0)
% 129.34/129.57 Found (x5 x40) as proof of (cNUMBER Xn)
% 129.34/129.57 Found (x5 x40) as proof of (cNUMBER Xn)
% 129.34/129.57 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 129.34/129.57 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))
% 129.34/129.57 Found x30:=(x3 x20):(cNUMBER Xn0)
% 129.34/129.57 Found (x3 x20) as proof of (cNUMBER Xn0)
% 129.34/129.57 Found (x3 x20) as proof of (cNUMBER Xn0)
% 129.34/129.57 Found x30:=(x3 x21):(cNUMBER Xn0)
% 129.34/129.57 Instantiate: Xn0:=Xn:fofType
% 129.34/129.57 Found (x3 x21) as proof of (cNUMBER Xn)
% 129.34/129.57 Found (x3 x21) as proof of (cNUMBER Xn)
% 129.34/129.57 Found x30:=(x3 x20):(cNUMBER Xn0)
% 129.34/129.57 Found (x3 x20) as proof of (cNUMBER Xn)
% 129.34/129.57 Found (x3 x20) as proof of (cNUMBER Xn)
% 129.34/129.57 Found (x3 x20) as proof of (cNUMBER Xn)
% 129.34/129.57 Found x30:=(x3 x20):(cNUMBER Xn0)
% 129.34/129.57 Instantiate: Xn0:=Xn:fofType
% 129.34/129.57 Found (x3 x20) as proof of (cNUMBER Xn)
% 129.34/129.57 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 129.34/129.57 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))
% 129.34/129.57 Found x50:=(x5 x40):(cNUMBER Xn0)
% 129.34/129.57 Found (x5 x40) as proof of (cNUMBER Xn)
% 129.34/129.57 Found (x5 x40) as proof of (cNUMBER Xn)
% 129.34/129.57 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 129.34/129.57 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))
% 129.34/129.57 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)))
% 129.34/129.57 Found x30:=(x3 x20):(cNUMBER Xn0)
% 129.34/129.57 Instantiate: Xn0:=Xn:fofType
% 129.34/129.57 Found (x3 x20) as proof of (cNUMBER Xn)
% 129.34/129.57 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 129.34/129.57 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))
% 133.34/133.63 Found x50:=(x5 x40):(cNUMBER Xn0)
% 133.34/133.63 Instantiate: Xn0:=Xn:fofType
% 133.34/133.63 Found (x5 x40) as proof of (cNUMBER Xn)
% 133.34/133.63 Found (x5 x40) as proof of (cNUMBER Xn)
% 133.34/133.63 Found x30:=(x3 x20):(cNUMBER Xn0)
% 133.34/133.63 Instantiate: Xn0:=Xn:fofType
% 133.34/133.63 Found (x3 x20) as proof of (cNUMBER Xn)
% 133.34/133.63 Found (x3 x20) as proof of (cNUMBER Xn)
% 133.34/133.63 Found x50:=(x5 x40):(cNUMBER Xn0)
% 133.34/133.63 Instantiate: Xn0:=Xn:fofType
% 133.34/133.63 Found (x5 x40) as proof of (cNUMBER Xn)
% 133.34/133.63 Found (x5 x40) as proof of (cNUMBER Xn)
% 133.34/133.63 Found x90:=(x9 x80):(cNUMBER Xn0)
% 133.34/133.63 Instantiate: Xn0:=Xn:fofType
% 133.34/133.63 Found (x9 x80) as proof of (cNUMBER Xn)
% 133.34/133.63 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x9 x80)) as proof of (cNUMBER Xn)
% 133.34/133.63 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))
% 133.34/133.63 Found x30:=(x3 x20):(cNUMBER Xn0)
% 133.34/133.63 Instantiate: Xn0:=Xn:fofType
% 133.34/133.63 Found (x3 x20) as proof of (cNUMBER Xn)
% 133.34/133.63 Found (x3 x20) as proof of (cNUMBER Xn)
% 133.34/133.63 Found x50:(cNUMBER Xn0)
% 133.34/133.63 Instantiate: Xn0:=Xn:fofType
% 133.34/133.63 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of (cNUMBER Xn)
% 133.34/133.63 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))))))=> x50) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 133.34/133.63 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))))))=> 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)))
% 133.34/133.63 Found x50:(cNUMBER Xn0)
% 133.34/133.63 Instantiate: Xn0:=Xn:fofType
% 133.34/133.63 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of (cNUMBER Xn)
% 133.34/133.63 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))))))=> x50) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 133.34/133.63 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))))))=> 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)))
% 133.34/133.63 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 133.34/133.63 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 133.34/133.63 Found (x5 x40) as proof of (cNUMBER Xn)
% 133.34/133.63 Found (x5 x40) as proof of (cNUMBER Xn)
% 133.34/133.63 Found (x5 x40) as proof of (cNUMBER Xn)
% 133.34/133.63 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 133.34/133.63 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 133.34/133.63 Found (x3 x20) as proof of (cNUMBER Xn)
% 133.34/133.63 Found (x3 x20) as proof of (cNUMBER Xn)
% 133.34/133.63 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 133.34/133.63 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))
% 133.34/133.63 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)))
% 133.34/133.63 Found x70:=(x7 x60):(cNUMBER Xn0)
% 133.34/133.63 Found (x7 x60) as proof of (cNUMBER Xn0)
% 133.34/133.63 Found (x7 x60) as proof of (cNUMBER Xn0)
% 133.34/133.63 Found x70:=(x7 x61):(cNUMBER Xn0)
% 133.34/133.63 Instantiate: Xn0:=Xn:fofType
% 133.34/133.63 Found (x7 x61) as proof of (cNUMBER Xn)
% 133.34/133.63 Found (x7 x61) as proof of (cNUMBER Xn)
% 133.34/133.63 Found x70:=(x7 x61):(cNUMBER Xn0)
% 133.34/133.63 Found (x7 x61) as proof of (cNUMBER Xn)
% 133.34/133.63 Found (x7 x61) as proof of (cNUMBER Xn)
% 133.34/133.63 Found (x7 x61) as proof of (cNUMBER Xn)
% 133.34/133.63 Found x9:(cODD (cS c0))
% 133.34/133.63 Instantiate: Xn0:=(cS c0):fofType
% 133.34/133.63 Found x9 as proof of (cODD Xn0)
% 133.34/133.63 Found (or_intror00 x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 133.72/133.98 Found ((or_intror0 (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 133.72/133.98 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 133.72/133.98 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 133.72/133.98 Found (x5 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9)) as proof of (cNUMBER Xn0)
% 133.72/133.98 Found (x5 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9)) as proof of (cNUMBER Xn0)
% 133.72/133.98 Found x30:=(x3 x20):(cNUMBER Xn0)
% 133.72/133.98 Instantiate: Xn0:=Xn:fofType
% 133.72/133.98 Found (x3 x20) as proof of (cNUMBER Xn)
% 133.72/133.98 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 133.72/133.98 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))
% 133.72/133.98 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)))
% 133.72/133.98 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)
% 133.72/133.98 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)
% 133.72/133.98 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)
% 133.72/133.98 Found x61:((or (cEVEN Xn0)) (cODD Xn0))
% 133.72/133.98 Found x61 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 133.72/133.98 Found (x7 x61) as proof of (cNUMBER Xn)
% 133.72/133.98 Found (x7 x61) as proof of (cNUMBER Xn)
% 133.72/133.98 Found (x7 x61) as proof of (cNUMBER Xn)
% 133.72/133.98 Found x300:=(x30 (cS Xx)):((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))
% 133.72/133.98 Found (x30 (cS Xx)) as proof of ((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))
% 133.72/133.98 Found (fun (x6:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx))) as proof of ((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))
% 133.72/133.98 Found (fun (Xx:fofType) (x6:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx))) as proof of (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))
% 133.72/133.98 Found (fun (Xx:fofType) (x6:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx))) as proof of (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))
% 133.72/133.98 Found ((conj00 (x30 c0)) (fun (Xx:fofType) (x6:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 133.72/133.98 Found (((conj0 (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))) (x30 c0)) (fun (Xx:fofType) (x6:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 133.72/133.98 Found ((((conj ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))) (x30 c0)) (fun (Xx:fofType) (x6:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 133.72/133.98 Found ((((conj ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))) (x30 c0)) (fun (Xx:fofType) (x6:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 137.81/138.08 Found x70:=(x7 x60):(cNUMBER Xn0)
% 137.81/138.08 Instantiate: Xn0:=Xn:fofType
% 137.81/138.08 Found (x7 x60) as proof of (cNUMBER Xn)
% 137.81/138.08 Found (x7 x60) as proof of (cNUMBER Xn)
% 137.81/138.08 Found x70:=(x7 x60):(cNUMBER Xn0)
% 137.81/138.08 Instantiate: Xn0:=Xn:fofType
% 137.81/138.08 Found (x7 x60) as proof of (cNUMBER Xn)
% 137.81/138.08 Found (x7 x60) as proof of (cNUMBER Xn)
% 137.81/138.08 Found x30:=(x3 x21):(cNUMBER Xn0)
% 137.81/138.08 Found (x3 x21) as proof of (cNUMBER Xn0)
% 137.81/138.08 Found (x3 x21) as proof of (cNUMBER Xn0)
% 137.81/138.08 Found x30:=(x3 x22):(cNUMBER Xn0)
% 137.81/138.08 Instantiate: Xn0:=Xn:fofType
% 137.81/138.08 Found (x3 x22) as proof of (cNUMBER Xn)
% 137.81/138.08 Found (x3 x22) as proof of (cNUMBER Xn)
% 137.81/138.08 Found x30:=(x3 x22):(cNUMBER Xn0)
% 137.81/138.08 Found (x3 x22) as proof of (cNUMBER Xn)
% 137.81/138.08 Found (x3 x22) as proof of (cNUMBER Xn)
% 137.81/138.08 Found (x3 x22) as proof of (cNUMBER Xn)
% 137.81/138.08 Found x9:(cODD (cS c0))
% 137.81/138.08 Instantiate: Xn0:=(cS c0):fofType
% 137.81/138.08 Found x9 as proof of (cODD Xn0)
% 137.81/138.08 Found (or_intror00 x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 137.81/138.08 Found ((or_intror0 (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 137.81/138.08 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 137.81/138.08 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 137.81/138.08 Found x30:=(x3 x20):(cNUMBER Xn0)
% 137.81/138.08 Instantiate: Xn0:=Xn:fofType
% 137.81/138.08 Found (x3 x20) as proof of (cNUMBER Xn)
% 137.81/138.08 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 137.81/138.08 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))
% 137.81/138.08 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)))
% 137.81/138.08 Found (and_rect50 (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 137.81/138.08 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)
% 137.81/138.08 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)
% 137.81/138.08 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)
% 137.81/138.08 Found x50:(cNUMBER Xn0)
% 137.81/138.08 Instantiate: Xn0:=Xn:fofType
% 137.81/138.08 Found x50 as proof of (cNUMBER Xn)
% 137.81/138.08 Found x70:(cNUMBER Xn00)
% 137.81/138.08 Instantiate: Xn00:=Xn:fofType
% 137.81/138.08 Found x70 as proof of (cNUMBER Xn)
% 137.81/138.08 Found or_comm_i100:=(or_comm_i10 x20):((or (cODD Xn0)) (cEVEN Xn0))
% 137.81/138.08 Found (or_comm_i10 x20) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 137.81/138.08 Found ((or_comm_i1 (cODD Xn0)) x20) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 137.81/138.08 Found (((or_comm_i (cEVEN Xn0)) (cODD Xn0)) x20) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 137.81/138.08 Found (((or_comm_i (cEVEN Xn0)) (cODD Xn0)) x20) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 137.81/138.08 Found x300:=(x30 c0):((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 137.81/138.08 Found (x30 c0) as proof of ((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 137.81/138.08 Found (x30 c0) as proof of ((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 137.81/138.08 Found x50:=(x5 x40):(cNUMBER Xn0)
% 137.81/138.08 Found (x5 x40) as proof of (cNUMBER Xn)
% 137.81/138.08 Found (x5 x40) as proof of (cNUMBER Xn)
% 137.81/138.08 Found (x5 x40) as proof of (cNUMBER Xn)
% 137.81/138.08 Found x22:((or (cEVEN Xn0)) (cODD Xn0))
% 137.81/138.08 Found x22 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 137.81/138.08 Found (x3 x22) as proof of (cNUMBER Xn)
% 137.81/138.08 Found (x3 x22) as proof of (cNUMBER Xn)
% 137.81/138.08 Found (x3 x22) as proof of (cNUMBER Xn)
% 140.22/140.46 Found x70:=(x7 x60):(cNUMBER Xn0)
% 140.22/140.46 Found (x7 x60) as proof of (cNUMBER Xn)
% 140.22/140.46 Found (x7 x60) as proof of (cNUMBER Xn)
% 140.22/140.46 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)) as proof of (cNUMBER Xn)
% 140.22/140.46 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))
% 140.22/140.46 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 140.22/140.46 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 140.22/140.46 Found (x3 x20) as proof of (cNUMBER Xn)
% 140.22/140.46 Found (x3 x20) as proof of (cNUMBER Xn)
% 140.22/140.46 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 140.22/140.46 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))
% 140.22/140.46 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 140.22/140.46 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 140.22/140.46 Found (x3 x20) as proof of (cNUMBER Xn)
% 140.22/140.46 Found (x3 x20) as proof of (cNUMBER Xn)
% 140.22/140.46 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 140.22/140.46 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))
% 140.22/140.46 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)))
% 140.22/140.46 Found x300:=(x30 (cS Xx)):((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))
% 140.22/140.46 Found (x30 (cS Xx)) as proof of ((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))
% 140.22/140.46 Found (fun (x4:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx))) as proof of ((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))
% 140.22/140.46 Found (fun (Xx:fofType) (x4:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx))) as proof of (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))
% 140.22/140.46 Found (fun (Xx:fofType) (x4:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx))) as proof of (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))
% 140.22/140.46 Found ((conj00 (x30 c0)) (fun (Xx:fofType) (x4:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 140.22/140.46 Found (((conj0 (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))) (x30 c0)) (fun (Xx:fofType) (x4:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 140.22/140.46 Found ((((conj ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))) (x30 c0)) (fun (Xx:fofType) (x4:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 140.22/140.46 Found ((((conj ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))) (x30 c0)) (fun (Xx:fofType) (x4:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 140.22/140.46 Found x50:=(x5 x40):(cNUMBER Xn0)
% 140.22/140.46 Found (x5 x40) as proof of (cNUMBER Xn0)
% 140.89/141.20 Found (x5 x40) as proof of (cNUMBER Xn0)
% 140.89/141.20 Found x50:=(x5 x41):(cNUMBER Xn0)
% 140.89/141.20 Instantiate: Xn0:=Xn:fofType
% 140.89/141.20 Found (x5 x41) as proof of (cNUMBER Xn)
% 140.89/141.20 Found (x5 x41) as proof of (cNUMBER Xn)
% 140.89/141.20 Found x50:=(x5 x40):(cNUMBER Xn0)
% 140.89/141.20 Found (x5 x40) as proof of (cNUMBER Xn)
% 140.89/141.20 Found (x5 x40) as proof of (cNUMBER Xn)
% 140.89/141.20 Found (x5 x40) as proof of (cNUMBER Xn)
% 140.89/141.20 Found x50:=(x5 x40):(cNUMBER Xn0)
% 140.89/141.20 Instantiate: Xn0:=Xn:fofType
% 140.89/141.20 Found (x5 x40) as proof of (cNUMBER Xn)
% 140.89/141.20 Found (x5 x40) as proof of (cNUMBER Xn)
% 140.89/141.20 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 140.89/141.20 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 140.89/141.20 Found (x5 x40) as proof of (cNUMBER Xn)
% 140.89/141.20 Found (x5 x40) as proof of (cNUMBER Xn)
% 140.89/141.20 Found (x5 x40) as proof of (cNUMBER Xn)
% 140.89/141.20 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 140.89/141.20 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 140.89/141.20 Found (x3 x20) as proof of (cNUMBER Xn)
% 140.89/141.20 Found (x3 x20) as proof of (cNUMBER Xn)
% 140.89/141.20 Found (x3 x20) as proof of (cNUMBER Xn)
% 140.89/141.20 Found x50:=(x5 x40):(cNUMBER Xn0)
% 140.89/141.20 Found (x5 x40) as proof of (cNUMBER Xn)
% 140.89/141.20 Found (x5 x40) as proof of (cNUMBER Xn)
% 140.89/141.20 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 140.89/141.20 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))
% 140.89/141.20 Found x30:(cNUMBER Xn0)
% 140.89/141.20 Instantiate: Xn0:=Xn:fofType
% 140.89/141.20 Found x30 as proof of (cNUMBER Xn)
% 140.89/141.20 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 140.89/141.20 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 140.89/141.20 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 140.89/141.20 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 140.89/141.20 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)))
% 140.89/141.20 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))))
% 140.89/141.20 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))
% 140.89/141.20 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))
% 140.89/141.20 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))
% 140.89/141.20 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))
% 140.89/141.20 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)))
% 140.89/141.20 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))))
% 140.89/141.20 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))
% 140.89/141.20 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))
% 140.89/141.20 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))
% 140.89/141.20 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))
% 141.18/141.41 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)
% 141.18/141.41 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)
% 141.18/141.41 Found x50:=(x5 x40):(cNUMBER Xn0)
% 141.18/141.41 Found (x5 x40) as proof of (cNUMBER Xn)
% 141.18/141.41 Found (x5 x40) as proof of (cNUMBER Xn)
% 141.18/141.41 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 141.18/141.41 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))))))=> (x5 x40)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 141.18/141.41 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))))))=> (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)))
% 141.18/141.41 Found x50:=(x5 x40):(cNUMBER Xn0)
% 141.18/141.41 Instantiate: Xn0:=Xn:fofType
% 141.18/141.41 Found (x5 x40) as proof of (cNUMBER Xn)
% 141.18/141.41 Found (x5 x40) as proof of (cNUMBER Xn)
% 141.18/141.41 Found x30:=(x3 x20):(cNUMBER Xn0)
% 141.18/141.41 Instantiate: Xn0:=Xn:fofType
% 141.18/141.41 Found (x3 x20) as proof of (cNUMBER Xn)
% 141.18/141.41 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 141.18/141.41 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))
% 141.21/141.46 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 141.21/141.46 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 141.21/141.46 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 141.21/141.46 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 141.21/141.46 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)))
% 141.21/141.46 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))))
% 141.21/141.46 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))
% 141.21/141.46 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))
% 141.21/141.46 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)) ((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))
% 141.21/141.46 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)) ((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))
% 141.21/141.46 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)
% 141.21/141.46 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)
% 141.21/141.46 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))))))=> (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))
% 141.21/141.46 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))))))=> (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)))
% 141.21/141.47 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)
% 141.21/141.47 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)
% 141.21/141.47 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)
% 141.21/141.47 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)
% 145.66/145.93 Found x70:(cNUMBER Xn00)
% 145.66/145.93 Instantiate: Xn00:=Xn:fofType
% 145.66/145.93 Found x70 as proof of (cNUMBER Xn)
% 145.66/145.93 Found x30:=(x3 x20):(cNUMBER Xn0)
% 145.66/145.93 Instantiate: Xn0:=Xn:fofType
% 145.66/145.93 Found (x3 x20) as proof of (cNUMBER Xn)
% 145.66/145.93 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 145.66/145.93 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))
% 145.66/145.93 Found x90:=(x9 x80):(cNUMBER Xn0)
% 145.66/145.93 Instantiate: Xn0:=Xn:fofType
% 145.66/145.93 Found (x9 x80) as proof of (cNUMBER Xn)
% 145.66/145.93 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x9 x80)) as proof of (cNUMBER Xn)
% 145.66/145.93 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))
% 145.66/145.93 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)))
% 145.66/145.93 Found x120:=(x12 x110):(cNUMBER Xn0)
% 145.66/145.93 Found (x12 x110) as proof of (cNUMBER Xn)
% 145.66/145.93 Found (x12 x110) as proof of (cNUMBER Xn)
% 145.66/145.93 Found (x12 x110) as proof of (cNUMBER Xn)
% 145.66/145.93 Found x30:(cNUMBER Xn0)
% 145.66/145.93 Instantiate: Xn0:=Xn:fofType
% 145.66/145.93 Found x30 as proof of (cNUMBER Xn)
% 145.66/145.93 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 145.66/145.93 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 145.66/145.93 Found (x5 x40) as proof of (cNUMBER Xn)
% 145.66/145.93 Found (x5 x40) as proof of (cNUMBER Xn)
% 145.66/145.93 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 145.66/145.93 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))
% 145.66/145.93 Found x61:((or (cEVEN Xn0)) (cODD Xn0))
% 145.66/145.93 Found x61 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 145.66/145.93 Found (x7 x61) as proof of (cNUMBER Xn)
% 145.66/145.93 Found (x7 x61) as proof of (cNUMBER Xn)
% 145.66/145.93 Found (x7 x61) as proof of (cNUMBER Xn)
% 145.66/145.93 Found x30:=(x3 x21):(cNUMBER Xn0)
% 145.66/145.93 Found (x3 x21) as proof of (cNUMBER Xn0)
% 145.66/145.93 Found (x3 x21) as proof of (cNUMBER Xn0)
% 145.66/145.93 Found x30:=(x3 x22):(cNUMBER Xn0)
% 145.66/145.93 Instantiate: Xn0:=Xn:fofType
% 145.66/145.93 Found (x3 x22) as proof of (cNUMBER Xn)
% 145.66/145.93 Found (x3 x22) as proof of (cNUMBER Xn)
% 145.66/145.93 Found x30:=(x3 x22):(cNUMBER Xn0)
% 145.66/145.93 Found (x3 x22) as proof of (cNUMBER Xn)
% 145.66/145.93 Found (x3 x22) as proof of (cNUMBER Xn)
% 145.66/145.93 Found (x3 x22) as proof of (cNUMBER Xn)
% 145.66/145.93 Found x70:=(x7 x60):(cNUMBER Xn0)
% 145.66/145.93 Instantiate: Xn0:=Xn:fofType
% 145.66/145.93 Found (x7 x60) as proof of (cNUMBER Xn)
% 145.66/145.93 Found (fun (x7:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x7 x60)) as proof of (cNUMBER Xn)
% 145.66/145.93 Found (fun (x7:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x7 x60)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 145.66/145.93 Found x70:=(x7 x61):(cNUMBER Xn0)
% 145.66/145.93 Instantiate: Xn0:=Xn:fofType
% 145.66/145.93 Found (x7 x61) as proof of (cNUMBER Xn)
% 145.66/145.93 Found (fun (x7:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x7 x61)) as proof of (cNUMBER Xn)
% 145.66/145.93 Found (fun (x7:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x7 x61)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 145.66/145.93 Found x70:=(x7 x60):(cNUMBER Xn0)
% 145.66/145.93 Instantiate: Xn0:=Xn:fofType
% 145.66/145.93 Found (x7 x60) as proof of (cNUMBER Xn)
% 145.66/145.93 Found (fun (x7:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x7 x60)) as proof of (cNUMBER Xn)
% 145.66/145.93 Found (fun (x7:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x7 x60)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 145.66/145.93 Found x30:=(x3 x20):(cNUMBER Xn0)
% 145.66/145.93 Found (x3 x20) as proof of (cNUMBER Xn)
% 145.66/145.93 Found (x3 x20) as proof of (cNUMBER Xn)
% 145.66/145.93 Found (x3 x20) as proof of (cNUMBER Xn)
% 145.66/145.93 Found x50:(cNUMBER Xn0)
% 145.66/145.93 Instantiate: Xn0:=Xn:fofType
% 145.66/145.93 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x50) as proof of (cNUMBER Xn)
% 145.66/145.93 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x50) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 146.42/146.70 Found x30:=(x3 x20):(cNUMBER Xn0)
% 146.42/146.70 Instantiate: Xn0:=Xn:fofType
% 146.42/146.70 Found (x3 x20) as proof of (cNUMBER Xn)
% 146.42/146.70 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 146.42/146.70 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))
% 146.42/146.70 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)))
% 146.42/146.70 Found (and_rect50 (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 146.42/146.70 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)
% 146.42/146.70 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)
% 146.42/146.70 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)
% 146.42/146.70 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))
% 146.42/146.70 Found x30:=(x3 x20):(cNUMBER Xn0)
% 146.42/146.70 Found (x3 x20) as proof of (cNUMBER Xn)
% 146.42/146.70 Found (x3 x20) as proof of (cNUMBER Xn)
% 146.42/146.70 Found (x3 x20) as proof of (cNUMBER Xn)
% 146.42/146.70 Found x70:=(x7 x60):(cNUMBER Xn0)
% 146.42/146.70 Instantiate: Xn0:=Xn:fofType
% 146.42/146.70 Found (x7 x60) as proof of (cNUMBER Xn)
% 146.42/146.70 Found (x7 x60) as proof of (cNUMBER Xn)
% 146.42/146.70 Found x8:(cODD (cS c0))
% 146.42/146.70 Instantiate: Xn0:=(cS c0):fofType
% 146.42/146.70 Found (fun (x8:(cODD (cS c0)))=> x8) as proof of (cODD Xn0)
% 146.42/146.70 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))
% 146.42/146.70 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)))
% 146.42/146.70 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)
% 146.42/146.70 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)
% 146.42/146.70 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)
% 146.42/146.70 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)
% 146.42/146.70 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))
% 146.47/146.72 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))
% 146.47/146.72 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))
% 146.47/146.72 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))
% 146.47/146.72 Found x70:=(x7 (cS c0)):((cODD (cS c0))->(cODD (cS (cS (cS c0)))))
% 146.47/146.72 Found (x7 (cS c0)) as proof of ((cODD (cS c0))->(cODD Xn0))
% 146.47/146.72 Found (x7 (cS c0)) as proof of ((cODD (cS c0))->(cODD Xn0))
% 146.47/146.72 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))
% 146.47/146.72 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)))
% 146.47/146.72 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)
% 146.47/146.72 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)
% 146.47/146.72 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)
% 146.47/146.72 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)
% 146.47/146.72 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))
% 146.47/146.72 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))
% 146.95/147.23 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))
% 146.95/147.23 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))
% 146.95/147.24 Found x30:(cNUMBER Xn0)
% 146.95/147.24 Instantiate: Xn0:=Xn:fofType
% 146.95/147.24 Found x30 as proof of (cNUMBER Xn)
% 146.95/147.24 Found or_introl00:=(or_introl0 (cEVEN Xn0)):((cODD (cS c0))->((or (cODD (cS c0))) (cEVEN Xn0)))
% 146.95/147.24 Found (or_introl0 (cEVEN Xn0)) as proof of ((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0)))
% 146.95/147.24 Found ((or_introl (cODD (cS c0))) (cEVEN Xn0)) as proof of ((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0)))
% 146.95/147.24 Found ((or_introl (cODD (cS c0))) (cEVEN Xn0)) as proof of ((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0)))
% 146.95/147.24 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)))
% 146.95/147.24 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))))
% 146.95/147.24 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))
% 146.95/147.24 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))
% 146.95/147.24 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) 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))
% 146.95/147.24 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) 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))
% 146.95/147.24 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))
% 146.95/147.24 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))
% 147.48/147.78 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))
% 147.48/147.78 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))
% 147.48/147.78 Found x50:(cNUMBER Xn00)
% 147.48/147.78 Instantiate: Xn00:=Xn:fofType
% 147.48/147.78 Found x50 as proof of (cNUMBER Xn)
% 147.48/147.78 Found or_introl00:=(or_introl0 (cEVEN Xn0)):((cODD (cS c0))->((or (cODD (cS c0))) (cEVEN Xn0)))
% 147.48/147.78 Found (or_introl0 (cEVEN Xn0)) as proof of ((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0)))
% 147.48/147.78 Found ((or_introl (cODD (cS c0))) (cEVEN Xn0)) as proof of ((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0)))
% 147.48/147.78 Found ((or_introl (cODD (cS c0))) (cEVEN Xn0)) as proof of ((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0)))
% 147.48/147.78 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)))
% 147.48/147.78 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))))
% 147.48/147.78 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))
% 147.48/147.78 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))
% 147.48/147.78 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))
% 147.48/147.78 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))
% 147.48/147.78 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))
% 148.16/148.42 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))
% 148.16/148.42 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))
% 148.16/148.42 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))
% 148.16/148.42 Found x30:(cNUMBER Xn0)
% 148.16/148.42 Instantiate: Xn0:=Xn:fofType
% 148.16/148.42 Found (fun (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of (cNUMBER Xn)
% 148.16/148.42 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))
% 148.16/148.42 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)))
% 148.16/148.42 Found x30:(cNUMBER Xn0)
% 148.16/148.42 Instantiate: Xn0:=Xn:fofType
% 148.16/148.42 Found (fun (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of (cNUMBER Xn)
% 148.16/148.42 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))
% 148.16/148.42 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)))
% 148.16/148.42 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))
% 148.16/148.42 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))
% 148.16/148.42 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))
% 148.16/148.42 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))
% 149.82/150.09 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))
% 149.82/150.09 Found x50:=(x5 x40):(cNUMBER Xn0)
% 149.82/150.09 Found (x5 x40) as proof of (cNUMBER Xn)
% 149.82/150.09 Found (x5 x40) as proof of (cNUMBER Xn)
% 149.82/150.09 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 149.82/150.09 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x5 x40)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 149.82/150.09 Found x7:(cODD (cS c0))
% 149.82/150.09 Instantiate: Xn0:=(cS c0):fofType
% 149.82/150.09 Found x7 as proof of (cODD Xn0)
% 149.82/150.09 Found (or_intror00 x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 149.82/150.09 Found ((or_intror0 (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 149.82/150.09 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 149.82/150.09 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 149.82/150.09 Found (x9 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7)) as proof of (cNUMBER Xn0)
% 149.82/150.09 Found (x9 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7)) as proof of (cNUMBER Xn0)
% 149.82/150.09 Found x22:((or (cEVEN Xn0)) (cODD Xn0))
% 149.82/150.09 Found x22 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 149.82/150.09 Found (x3 x22) as proof of (cNUMBER Xn)
% 149.82/150.09 Found (x3 x22) as proof of (cNUMBER Xn)
% 149.82/150.09 Found (x3 x22) as proof of (cNUMBER Xn)
% 149.82/150.09 Found x90:=(x9 x80):(cNUMBER Xn0)
% 149.82/150.09 Found (x9 x80) as proof of (cNUMBER Xn)
% 149.82/150.09 Found (x9 x80) as proof of (cNUMBER Xn)
% 149.82/150.09 Found (x9 x80) as proof of (cNUMBER Xn)
% 149.82/150.09 Found x30:=(x3 x20):(cNUMBER Xn0)
% 149.82/150.09 Instantiate: Xn0:=Xn:fofType
% 149.82/150.09 Found (x3 x20) as proof of (cNUMBER Xn)
% 149.82/150.09 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 149.82/150.09 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))
% 149.82/150.09 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)))
% 149.82/150.09 Found (and_rect50 (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 149.82/150.09 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)
% 149.82/150.09 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))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 149.82/150.09 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))))))=> (x3 x20)))) as proof of (cNUMBER Xn)
% 149.82/150.09 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))))))=> (x3 x20)))) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 152.46/152.75 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)))
% 152.46/152.75 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 152.46/152.75 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 152.46/152.75 Found (x5 x40) as proof of (cNUMBER Xn)
% 152.46/152.75 Found (x5 x40) as proof of (cNUMBER Xn)
% 152.46/152.75 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 152.46/152.75 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))
% 152.46/152.75 Found x70:=(x7 x60):(cNUMBER Xn0)
% 152.46/152.75 Found (x7 x60) as proof of (cNUMBER Xn)
% 152.46/152.75 Found (x7 x60) as proof of (cNUMBER Xn)
% 152.46/152.75 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)) as proof of (cNUMBER Xn)
% 152.46/152.75 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))
% 152.46/152.75 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)))
% 152.46/152.75 Found x300:=(x30 c0):((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 152.46/152.75 Found (x30 c0) as proof of ((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 152.46/152.75 Found (x30 c0) as proof of ((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 152.46/152.75 Found x30:(cNUMBER Xn0)
% 152.46/152.75 Instantiate: Xn0:=Xn:fofType
% 152.46/152.75 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30) as proof of (cNUMBER Xn)
% 152.46/152.75 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 152.46/152.75 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 152.46/152.75 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 152.46/152.75 Found (x5 x40) as proof of (cNUMBER Xn)
% 152.46/152.75 Found (x5 x40) as proof of (cNUMBER Xn)
% 152.46/152.75 Found (x5 x40) as proof of (cNUMBER Xn)
% 152.46/152.75 Found x50:=(x5 x40):(cNUMBER Xn0)
% 152.46/152.75 Found (x5 x40) as proof of (cNUMBER Xn0)
% 152.46/152.75 Found (x5 x40) as proof of (cNUMBER Xn0)
% 152.46/152.75 Found x50:=(x5 x41):(cNUMBER Xn0)
% 152.46/152.75 Instantiate: Xn0:=Xn:fofType
% 152.46/152.75 Found (x5 x41) as proof of (cNUMBER Xn)
% 152.46/152.75 Found (x5 x41) as proof of (cNUMBER Xn)
% 152.46/152.75 Found x50:=(x5 x40):(cNUMBER Xn0)
% 152.46/152.75 Found (x5 x40) as proof of (cNUMBER Xn)
% 152.46/152.75 Found (x5 x40) as proof of (cNUMBER Xn)
% 152.46/152.75 Found (x5 x40) as proof of (cNUMBER Xn)
% 152.46/152.75 Found x50:=(x5 x40):(cNUMBER Xn0)
% 152.46/152.75 Instantiate: Xn0:=Xn:fofType
% 152.46/152.75 Found (x5 x40) as proof of (cNUMBER Xn)
% 152.46/152.75 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 152.46/152.75 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))
% 152.46/152.75 Found x50:=(x5 x40):(cNUMBER Xn0)
% 152.46/152.75 Instantiate: Xn0:=Xn:fofType
% 152.46/152.75 Found (x5 x40) as proof of (cNUMBER Xn)
% 152.46/152.75 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 152.46/152.75 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))
% 152.46/152.75 Found x300:=(x30 c0):((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 152.46/152.75 Found (x30 c0) as proof of ((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 152.46/152.75 Found (x30 c0) as proof of ((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 152.46/152.75 Found x300:=(x30 c0):((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 152.46/152.75 Found (x30 c0) as proof of ((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 152.46/152.75 Found (x30 c0) as proof of ((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 155.32/155.62 Found x50:=(x5 x40):(cNUMBER Xn0)
% 155.32/155.62 Instantiate: Xn0:=Xn:fofType
% 155.32/155.62 Found (x5 x40) as proof of (cNUMBER Xn)
% 155.32/155.62 Found (x5 x40) as proof of (cNUMBER Xn)
% 155.32/155.62 Found x60:((or (cEVEN Xn0)) (cODD Xn0))
% 155.32/155.62 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 155.32/155.62 Found (x7 x60) as proof of (cNUMBER Xn)
% 155.32/155.62 Found (x7 x60) as proof of (cNUMBER Xn)
% 155.32/155.62 Found (x7 x60) as proof of (cNUMBER Xn)
% 155.32/155.62 Found x30:=(x3 x20):(cNUMBER Xn0)
% 155.32/155.62 Instantiate: Xn0:=Xn:fofType
% 155.32/155.62 Found (x3 x20) as proof of (cNUMBER Xn)
% 155.32/155.62 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 155.32/155.62 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 x20)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 155.32/155.62 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 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)))
% 155.32/155.62 Found x30:=(x3 x20):(cNUMBER Xn0)
% 155.32/155.62 Instantiate: Xn0:=Xn:fofType
% 155.32/155.62 Found (x3 x20) as proof of (cNUMBER Xn)
% 155.32/155.62 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 155.32/155.62 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 x20)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 155.32/155.62 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 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)))
% 155.32/155.62 Found x120:=(x12 x110):(cNUMBER Xn0)
% 155.32/155.62 Found (x12 x110) as proof of (cNUMBER Xn)
% 155.32/155.62 Found (x12 x110) as proof of (cNUMBER Xn)
% 155.32/155.62 Found (fun (x12:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x12 x110)) as proof of (cNUMBER Xn)
% 155.32/155.62 Found (fun (x12:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x12 x110)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 155.32/155.62 Found x50:=(x5 x40):(cNUMBER Xn0)
% 155.32/155.62 Instantiate: Xn0:=Xn:fofType
% 155.32/155.62 Found (x5 x40) as proof of (cNUMBER Xn)
% 155.32/155.62 Found (x5 x40) as proof of (cNUMBER Xn)
% 155.32/155.62 Found x9:(cODD (cS c0))
% 155.32/155.62 Instantiate: Xn0:=(cS c0):fofType
% 155.32/155.62 Found x9 as proof of (cODD Xn0)
% 155.32/155.62 Found (or_intror00 x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 155.32/155.62 Found ((or_intror0 (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 155.32/155.62 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 155.32/155.62 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 155.32/155.62 Found x11:(cEVEN c0)
% 155.32/155.62 Instantiate: Xn0:=c0:fofType
% 155.32/155.62 Found x11 as proof of (cEVEN Xn0)
% 155.32/155.62 Found (or_introl00 x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 155.32/155.62 Found ((or_introl0 (cODD Xn0)) x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 155.32/155.62 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 155.32/155.62 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 155.32/155.62 Found x30:(cNUMBER Xn0)
% 155.32/155.62 Instantiate: Xn0:=Xn:fofType
% 155.32/155.62 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of (cNUMBER Xn)
% 155.32/155.62 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))
% 155.32/155.62 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 155.32/155.62 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 155.32/155.62 Found (x5 x40) as proof of (cNUMBER Xn)
% 155.32/155.62 Found (x5 x40) as proof of (cNUMBER Xn)
% 155.32/155.62 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 155.32/155.62 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))
% 157.96/158.28 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)))
% 157.96/158.28 Found x9:(cODD (cS c0))
% 157.96/158.28 Instantiate: Xn0:=(cS c0):fofType
% 157.96/158.28 Found x9 as proof of (cODD Xn0)
% 157.96/158.28 Found (or_intror00 x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 157.96/158.28 Found ((or_intror0 (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 157.96/158.28 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 157.96/158.28 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 157.96/158.28 Found (x7 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9)) as proof of (cNUMBER Xn0)
% 157.96/158.28 Found (x7 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9)) as proof of (cNUMBER Xn0)
% 157.96/158.28 Found x30:=(x3 x20):(cNUMBER Xn0)
% 157.96/158.28 Found (x3 x20) as proof of (cNUMBER Xn)
% 157.96/158.28 Found (x3 x20) as proof of (cNUMBER Xn)
% 157.96/158.28 Found (x3 x20) as proof of (cNUMBER Xn)
% 157.96/158.28 Found x70:=(x7 x60):(cNUMBER Xn0)
% 157.96/158.28 Instantiate: Xn0:=Xn:fofType
% 157.96/158.28 Found (x7 x60) as proof of (cNUMBER Xn)
% 157.96/158.28 Found (fun (x7:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x7 x60)) as proof of (cNUMBER Xn)
% 157.96/158.28 Found (fun (x7:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x7 x60)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 157.96/158.28 Found x30:=(x3 x20):(cNUMBER Xn0)
% 157.96/158.28 Found (x3 x20) as proof of (cNUMBER Xn)
% 157.96/158.28 Found (x3 x20) as proof of (cNUMBER Xn)
% 157.96/158.28 Found (x3 x20) as proof of (cNUMBER Xn)
% 157.96/158.28 Found x30:(cNUMBER Xn0)
% 157.96/158.28 Instantiate: Xn0:=Xn:fofType
% 157.96/158.28 Found (fun (x7:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> x30) as proof of (cNUMBER Xn)
% 157.96/158.28 Found (fun (x7:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> x30) as proof of ((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn))
% 157.96/158.28 Found x50:(cNUMBER Xn00)
% 157.96/158.28 Instantiate: Xn00:=Xn:fofType
% 157.96/158.28 Found (fun (x7:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> x50) as proof of (cNUMBER Xn)
% 157.96/158.28 Found (fun (x7:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> x50) as proof of ((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn))
% 157.96/158.28 Found x9:(cODD (cS c0))
% 157.96/158.28 Instantiate: Xn0:=(cS c0):fofType
% 157.96/158.28 Found x9 as proof of (cODD Xn0)
% 157.96/158.28 Found (or_intror00 x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 157.96/158.28 Found ((or_intror0 (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 157.96/158.28 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 157.96/158.28 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 157.96/158.28 Found x50:=(x5 x40):(cNUMBER Xn0)
% 157.96/158.28 Instantiate: Xn0:=Xn:fofType
% 157.96/158.28 Found (x5 x40) as proof of (cNUMBER Xn)
% 157.96/158.28 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 157.96/158.28 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))
% 160.40/160.68 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)))
% 160.40/160.68 Found (and_rect50 (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 160.40/160.68 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)
% 160.40/160.68 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)
% 160.40/160.68 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)
% 160.40/160.68 Found x50:(cNUMBER Xn0)
% 160.40/160.68 Instantiate: Xn0:=Xn:fofType
% 160.40/160.68 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x50) as proof of (cNUMBER Xn)
% 160.40/160.68 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))
% 160.40/160.68 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)))
% 160.40/160.68 Found x30:=(x3 x21):(cNUMBER Xn0)
% 160.40/160.68 Instantiate: Xn0:=Xn:fofType
% 160.40/160.68 Found (x3 x21) as proof of (cNUMBER Xn)
% 160.40/160.68 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21)) as proof of (cNUMBER Xn)
% 160.40/160.68 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))
% 160.40/160.68 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)))
% 160.40/160.68 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)
% 160.40/160.68 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)
% 160.40/160.68 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)
% 160.40/160.68 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)
% 160.99/161.27 Found x30:(cNUMBER Xn0)
% 160.99/161.27 Instantiate: Xn0:=Xn:fofType
% 160.99/161.27 Found (fun (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of (cNUMBER Xn)
% 160.99/161.27 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))
% 160.99/161.27 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)))
% 160.99/161.27 Found x30:(cNUMBER Xn0)
% 160.99/161.27 Instantiate: Xn0:=Xn:fofType
% 160.99/161.27 Found (fun (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of (cNUMBER Xn)
% 160.99/161.27 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))
% 160.99/161.27 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)))
% 160.99/161.27 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))
% 160.99/161.27 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))
% 160.99/161.27 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))
% 160.99/161.27 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))
% 160.99/161.27 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))
% 160.99/161.27 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)))
% 165.16/165.41 Found x90:=(x9 x80):(cNUMBER Xn0)
% 165.16/165.41 Found (x9 x80) as proof of (cNUMBER Xn)
% 165.16/165.41 Found (x9 x80) as proof of (cNUMBER Xn)
% 165.16/165.41 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x9 x80)) as proof of (cNUMBER Xn)
% 165.16/165.41 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))
% 165.16/165.41 Found x70:=(x7 x60):(cNUMBER Xn0)
% 165.16/165.41 Found (x7 x60) as proof of (cNUMBER Xn)
% 165.16/165.41 Found (x7 x60) as proof of (cNUMBER Xn)
% 165.16/165.41 Found (x7 x60) as proof of (cNUMBER Xn)
% 165.16/165.41 Found x70:=(x7 x60):(cNUMBER Xn0)
% 165.16/165.41 Found (x7 x60) as proof of (cNUMBER Xn)
% 165.16/165.41 Found (x7 x60) as proof of (cNUMBER Xn)
% 165.16/165.41 Found (x7 x60) as proof of (cNUMBER Xn)
% 165.16/165.41 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 165.16/165.41 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 165.16/165.41 Found (x5 x40) as proof of (cNUMBER Xn)
% 165.16/165.41 Found (x5 x40) as proof of (cNUMBER Xn)
% 165.16/165.41 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 165.16/165.41 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))
% 165.16/165.41 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 165.16/165.41 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 165.16/165.41 Found (x5 x40) as proof of (cNUMBER Xn)
% 165.16/165.41 Found (x5 x40) as proof of (cNUMBER Xn)
% 165.16/165.41 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 165.16/165.41 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))))))=> (x5 x40)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 165.16/165.41 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))))))=> (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)))
% 165.16/165.41 Found x30:=(x3 x20):(cNUMBER Xn0)
% 165.16/165.41 Instantiate: Xn0:=Xn:fofType
% 165.16/165.41 Found (x3 x20) as proof of (cNUMBER Xn)
% 165.16/165.41 Found (fun (x4:(cODD Xn0))=> (x3 x20)) as proof of (cNUMBER Xn)
% 165.16/165.41 Found (fun (x4:(cODD Xn0))=> (x3 x20)) as proof of ((cODD Xn0)->(cNUMBER Xn))
% 165.16/165.41 Found x30:=(x3 x20):(cNUMBER Xn0)
% 165.16/165.41 Instantiate: Xn0:=Xn:fofType
% 165.16/165.41 Found (x3 x20) as proof of (cNUMBER Xn)
% 165.16/165.41 Found (fun (x4:(cEVEN Xn0))=> (x3 x20)) as proof of (cNUMBER Xn)
% 165.16/165.41 Found (fun (x4:(cEVEN Xn0))=> (x3 x20)) as proof of ((cEVEN Xn0)->(cNUMBER Xn))
% 165.16/165.41 Found ((or_ind00 (fun (x4:(cEVEN Xn0))=> (x3 x20))) (fun (x4:(cODD Xn0))=> (x3 x20))) as proof of (cNUMBER Xn)
% 165.16/165.41 Found (((or_ind0 (cNUMBER Xn)) (fun (x4:(cEVEN Xn0))=> (x3 x20))) (fun (x4:(cODD Xn0))=> (x3 x20))) as proof of (cNUMBER Xn)
% 165.16/165.41 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)
% 165.16/165.41 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)
% 165.16/165.41 Found x30:(cNUMBER Xn0)
% 165.16/165.41 Instantiate: Xn0:=Xn:fofType
% 165.16/165.41 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30) as proof of (cNUMBER Xn)
% 165.16/165.41 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))
% 165.16/165.41 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)))
% 167.20/167.47 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 167.20/167.47 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 167.20/167.47 Found (x5 x40) as proof of (cNUMBER Xn)
% 167.20/167.47 Found (x5 x40) as proof of (cNUMBER Xn)
% 167.20/167.47 Found (x5 x40) as proof of (cNUMBER Xn)
% 167.20/167.47 Found x50:=(x5 x40):(cNUMBER Xn0)
% 167.20/167.47 Instantiate: Xn0:=Xn:fofType
% 167.20/167.47 Found (x5 x40) as proof of (cNUMBER Xn)
% 167.20/167.47 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 167.20/167.47 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))
% 167.20/167.47 Found x50:=(x5 x40):(cNUMBER Xn0)
% 167.20/167.47 Instantiate: Xn0:=Xn:fofType
% 167.20/167.47 Found (x5 x40) as proof of (cNUMBER Xn)
% 167.20/167.47 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 167.20/167.47 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))
% 167.20/167.47 Found x300:=(x30 c0):((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 167.20/167.47 Found (x30 c0) as proof of ((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 167.20/167.47 Found (x30 c0) as proof of ((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 167.20/167.47 Found x60:((or (cEVEN Xn0)) (cODD Xn0))
% 167.20/167.47 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 167.20/167.47 Found (x7 x60) as proof of (cNUMBER Xn)
% 167.20/167.47 Found (x7 x60) as proof of (cNUMBER Xn)
% 167.20/167.47 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)) as proof of (cNUMBER Xn)
% 167.20/167.47 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))
% 167.20/167.47 Found x30:=(x3 x21):(cNUMBER Xn0)
% 167.20/167.47 Instantiate: Xn0:=Xn:fofType
% 167.20/167.47 Found (x3 x21) as proof of (cNUMBER Xn)
% 167.20/167.47 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21)) as proof of (cNUMBER Xn)
% 167.20/167.47 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))))))=> (x3 x21)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 167.20/167.47 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))))))=> (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)))
% 167.20/167.47 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)
% 167.20/167.47 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)
% 167.20/167.47 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)
% 167.20/167.47 Found (fun (x5:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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)
% 168.63/168.88 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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 (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn))
% 168.63/168.88 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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))))))->((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn)))
% 168.63/168.88 Found x300:=(x30 c0):((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 168.63/168.88 Found (x30 c0) as proof of ((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 168.63/168.88 Found (x30 c0) as proof of ((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 168.63/168.88 Found x300:=(x30 (cS Xx)):((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))
% 168.63/168.88 Found (x30 (cS Xx)) as proof of ((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))
% 168.63/168.88 Found (fun (x5:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx))) as proof of ((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))
% 168.63/168.88 Found (fun (Xx:fofType) (x5:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx))) as proof of (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))
% 168.63/168.88 Found (fun (Xx:fofType) (x5:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx))) as proof of (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))
% 169.80/170.06 Found ((conj00 (x30 c0)) (fun (Xx:fofType) (x5:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 169.80/170.06 Found (((conj0 (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))) (x30 c0)) (fun (Xx:fofType) (x5:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 169.80/170.06 Found ((((conj ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))) (x30 c0)) (fun (Xx:fofType) (x5:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 169.80/170.06 Found ((((conj ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))) (x30 c0)) (fun (Xx:fofType) (x5:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 169.80/170.06 Found x50:(cNUMBER Xn0)
% 169.80/170.06 Instantiate: Xn0:=Xn:fofType
% 169.80/170.06 Found x50 as proof of (cNUMBER Xn)
% 169.80/170.06 Found x30:(cNUMBER Xn0)
% 169.80/170.06 Instantiate: Xn0:=Xn:fofType
% 169.80/170.06 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of (cNUMBER Xn)
% 169.80/170.06 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))
% 169.80/170.06 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)))
% 169.80/170.06 Found x30:(cNUMBER Xn0)
% 169.80/170.06 Instantiate: Xn0:=Xn:fofType
% 169.80/170.06 Found x30 as proof of (cNUMBER Xn)
% 169.80/170.06 Found x8:(cODD (cS c0))
% 169.80/170.06 Instantiate: Xn0:=(cS c0):fofType
% 169.80/170.06 Found x8 as proof of (cODD Xn0)
% 169.80/170.06 Found (or_intror00 x8) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 169.80/170.06 Found ((or_intror0 (cODD Xn0)) x8) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 169.80/170.06 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x8) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 169.80/170.06 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x8) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 169.80/170.06 Found (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x8)) as proof of (cNUMBER Xn0)
% 169.80/170.06 Found (fun (x8:(cODD (cS c0)))=> (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x8))) as proof of (cNUMBER Xn0)
% 169.80/170.06 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))
% 169.80/170.06 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)))
% 169.80/170.06 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)
% 169.80/170.06 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)
% 169.80/170.06 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)
% 171.43/171.68 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)
% 171.43/171.68 Found x110:((or (cEVEN Xn0)) (cODD Xn0))
% 171.43/171.68 Found x110 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 171.43/171.68 Found (x12 x110) as proof of (cNUMBER Xn)
% 171.43/171.68 Found (x12 x110) as proof of (cNUMBER Xn)
% 171.43/171.68 Found (x12 x110) as proof of (cNUMBER Xn)
% 171.43/171.68 Found x30:=(x3 x20):(cNUMBER Xn0)
% 171.43/171.68 Found (x3 x20) as proof of (cNUMBER Xn)
% 171.43/171.68 Found (x3 x20) as proof of (cNUMBER Xn)
% 171.43/171.68 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 171.43/171.68 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))
% 171.43/171.68 Found x30:=(x3 x20):(cNUMBER Xn0)
% 171.43/171.68 Found (x3 x20) as proof of (cNUMBER Xn)
% 171.43/171.68 Found (x3 x20) as proof of (cNUMBER Xn)
% 171.43/171.68 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 171.43/171.68 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))
% 171.43/171.68 Found x300:=(x30 c0):((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 171.43/171.68 Found (x30 c0) as proof of ((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 171.43/171.68 Found (x30 c0) as proof of ((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 171.43/171.68 Found x30:(cNUMBER Xn0)
% 171.43/171.68 Instantiate: Xn0:=Xn:fofType
% 171.43/171.68 Found (fun (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of (cNUMBER Xn)
% 171.43/171.68 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))
% 171.43/171.68 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)))
% 171.43/171.68 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))))
% 171.43/171.68 Found x30:(cNUMBER Xn0)
% 171.43/171.68 Instantiate: Xn0:=Xn:fofType
% 171.43/171.68 Found (fun (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of (cNUMBER Xn)
% 171.43/171.68 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))
% 171.43/171.68 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)))
% 171.43/171.69 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))))
% 171.43/171.69 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)))
% 171.43/171.69 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)))
% 171.43/171.69 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)))
% 171.43/171.69 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)))
% 171.43/171.69 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)))
% 172.60/172.90 Found x50:=(x5 x40):(cNUMBER Xn0)
% 172.60/172.90 Found (x5 x40) as proof of (cNUMBER Xn)
% 172.60/172.90 Found (x5 x40) as proof of (cNUMBER Xn)
% 172.60/172.90 Found (x5 x40) as proof of (cNUMBER Xn)
% 172.60/172.90 Found x50:=(x5 x40):(cNUMBER Xn0)
% 172.60/172.90 Found (x5 x40) as proof of (cNUMBER Xn)
% 172.60/172.90 Found (x5 x40) as proof of (cNUMBER Xn)
% 172.60/172.90 Found (x5 x40) as proof of (cNUMBER Xn)
% 172.60/172.90 Found x30:=(x3 x20):(cNUMBER Xn0)
% 172.60/172.90 Found (x3 x20) as proof of (cNUMBER Xn)
% 172.60/172.90 Found (x3 x20) as proof of (cNUMBER Xn)
% 172.60/172.90 Found (x3 x20) as proof of (cNUMBER Xn)
% 172.60/172.90 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 172.60/172.90 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 172.60/172.90 Found (x5 x40) as proof of (cNUMBER Xn)
% 172.60/172.90 Found (x5 x40) as proof of (cNUMBER Xn)
% 172.60/172.90 Found (x5 x40) as proof of (cNUMBER Xn)
% 172.60/172.90 Found x50:=(x5 x40):(cNUMBER Xn0)
% 172.60/172.90 Instantiate: Xn0:=Xn:fofType
% 172.60/172.90 Found (x5 x40) as proof of (cNUMBER Xn)
% 172.60/172.90 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 172.60/172.90 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))
% 172.60/172.90 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)))
% 172.60/172.90 Found (and_rect50 (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 172.60/172.90 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)
% 172.60/172.90 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 x40))) as proof of (cNUMBER Xn)
% 172.60/172.90 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 x40)))) as proof of (cNUMBER Xn)
% 172.60/172.90 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 x40)))) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 172.60/172.90 Found x30:=(x3 x20):(cNUMBER Xn0)
% 172.60/172.90 Found (x3 x20) as proof of (cNUMBER Xn)
% 172.60/172.90 Found (x3 x20) as proof of (cNUMBER Xn)
% 172.60/172.90 Found (x3 x20) as proof of (cNUMBER Xn)
% 172.60/172.90 Found x30:(cNUMBER Xn0)
% 172.60/172.90 Instantiate: Xn0:=Xn:fofType
% 172.60/172.90 Found (fun (x7:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> x30) as proof of (cNUMBER Xn)
% 172.60/172.90 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> x30) as proof of ((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn))
% 172.68/172.96 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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))))))->((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn)))
% 172.68/172.96 Found x50:(cNUMBER Xn00)
% 172.68/172.96 Instantiate: Xn00:=Xn:fofType
% 172.68/172.96 Found (fun (x7:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> x50) as proof of (cNUMBER Xn)
% 172.68/172.96 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> x50) as proof of ((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn))
% 172.68/172.96 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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))))))->((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn)))
% 172.68/172.96 Found x70:=(x7 (cS c0)):((cODD (cS c0))->(cODD (cS (cS (cS c0)))))
% 172.68/172.96 Found (x7 (cS c0)) as proof of ((cODD (cS c0))->(cODD Xn0))
% 172.68/172.96 Found (x7 (cS c0)) as proof of ((cODD (cS c0))->(cODD Xn0))
% 172.68/172.96 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))
% 172.68/172.96 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)))
% 172.68/172.96 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)
% 172.68/172.96 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)
% 172.68/172.96 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)
% 172.72/173.02 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)
% 172.72/173.02 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))
% 172.72/173.02 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))
% 172.72/173.02 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))
% 172.72/173.02 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))
% 172.72/173.02 Found x30:=(x3 x21):(cNUMBER Xn0)
% 172.72/173.02 Instantiate: Xn0:=Xn:fofType
% 172.72/173.02 Found (x3 x21) as proof of (cNUMBER Xn)
% 172.72/173.02 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21)) as proof of (cNUMBER Xn)
% 172.72/173.02 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))
% 172.72/173.02 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)))
% 172.72/173.02 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)
% 172.72/173.02 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)
% 172.72/173.02 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)
% 173.24/173.52 Found (fun (x5:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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)
% 173.24/173.52 Found (fun (x5:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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 (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn))
% 173.24/173.52 Found or_introl00:=(or_introl0 (cEVEN Xn0)):((cODD (cS c0))->((or (cODD (cS c0))) (cEVEN Xn0)))
% 173.24/173.52 Found (or_introl0 (cEVEN Xn0)) as proof of ((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0)))
% 173.24/173.52 Found ((or_introl (cODD (cS c0))) (cEVEN Xn0)) as proof of ((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0)))
% 173.24/173.52 Found ((or_introl (cODD (cS c0))) (cEVEN Xn0)) as proof of ((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0)))
% 173.24/173.52 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)))
% 173.24/173.52 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))))
% 173.24/173.52 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))
% 173.24/173.52 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))
% 173.24/173.52 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))
% 174.58/174.87 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))
% 174.58/174.87 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))
% 174.58/174.87 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))
% 174.58/174.87 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))
% 174.58/174.87 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))
% 174.58/174.87 Found x70:(cNUMBER Xn0)
% 174.58/174.87 Instantiate: Xn0:=Xn:fofType
% 174.58/174.87 Found x70 as proof of (cNUMBER Xn)
% 174.58/174.87 Found x70:=(x7 x60):(cNUMBER Xn00)
% 174.58/174.87 Instantiate: Xn00:=Xn:fofType
% 174.58/174.87 Found (x7 x60) as proof of (cNUMBER Xn)
% 174.58/174.87 Found (x7 x60) as proof of (cNUMBER Xn)
% 174.58/174.87 Found x50:=(x5 x40):(cNUMBER Xn0)
% 174.58/174.87 Instantiate: Xn0:=Xn:fofType
% 174.58/174.87 Found (x5 x40) as proof of (cNUMBER Xn)
% 174.58/174.87 Found (x5 x40) as proof of (cNUMBER Xn)
% 174.58/174.87 Found x30:=(x3 x21):(cNUMBER Xn0)
% 174.58/174.87 Instantiate: Xn0:=Xn:fofType
% 174.58/174.87 Found (x3 x21) as proof of (cNUMBER Xn)
% 174.58/174.87 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21)) as proof of (cNUMBER Xn)
% 174.58/174.87 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))
% 174.58/174.87 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)))
% 174.58/174.87 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)
% 174.58/174.87 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)
% 174.68/174.98 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)
% 174.68/174.98 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)
% 174.68/174.98 Found x50:(cNUMBER Xn0)
% 174.68/174.98 Instantiate: Xn0:=Xn:fofType
% 174.68/174.98 Found (fun (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of (cNUMBER Xn)
% 174.68/174.98 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))
% 174.68/174.98 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)))
% 174.68/174.98 Found x50:(cNUMBER Xn0)
% 174.68/174.98 Instantiate: Xn0:=Xn:fofType
% 174.68/174.98 Found (fun (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of (cNUMBER Xn)
% 174.68/174.98 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))
% 174.68/174.98 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)))
% 174.68/174.98 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))
% 174.68/174.98 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))
% 174.68/174.98 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))
% 174.68/174.98 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))
% 177.30/177.57 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))
% 177.30/177.57 Found x50:=(x5 x40):(cNUMBER Xn0)
% 177.30/177.57 Instantiate: Xn0:=Xn:fofType
% 177.30/177.57 Found (x5 x40) as proof of (cNUMBER Xn)
% 177.30/177.57 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 177.30/177.57 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))
% 177.30/177.57 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)))
% 177.30/177.57 Found (and_rect50 (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 177.30/177.57 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)
% 177.30/177.57 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)
% 177.30/177.57 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)
% 177.30/177.57 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))
% 177.30/177.57 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)))
% 177.30/177.57 Found x90:=(x9 x80):(cNUMBER Xn0)
% 177.30/177.57 Found (x9 x80) as proof of (cNUMBER Xn)
% 177.30/177.57 Found (x9 x80) as proof of (cNUMBER Xn)
% 177.30/177.57 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x9 x80)) as proof of (cNUMBER Xn)
% 177.30/177.57 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))
% 177.30/177.57 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)))
% 177.30/177.57 Found x70:=(x7 x60):(cNUMBER Xn0)
% 177.30/177.57 Found (x7 x60) as proof of (cNUMBER Xn)
% 177.30/177.57 Found (x7 x60) as proof of (cNUMBER Xn)
% 177.30/177.57 Found (x7 x60) as proof of (cNUMBER Xn)
% 177.30/177.57 Found x70:=(x7 x60):(cNUMBER Xn0)
% 177.30/177.57 Found (x7 x60) as proof of (cNUMBER Xn)
% 177.30/177.57 Found (x7 x60) as proof of (cNUMBER Xn)
% 178.67/178.97 Found (x7 x60) as proof of (cNUMBER Xn)
% 178.67/178.97 Found x30:=(x3 x21):(cNUMBER Xn0)
% 178.67/178.97 Instantiate: Xn0:=Xn:fofType
% 178.67/178.97 Found (x3 x21) as proof of (cNUMBER Xn)
% 178.67/178.97 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21)) as proof of (cNUMBER Xn)
% 178.67/178.97 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))
% 178.67/178.97 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)))
% 178.67/178.97 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)
% 178.67/178.97 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)
% 178.67/178.97 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)
% 178.67/178.97 Found (fun (x5:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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)
% 178.67/178.97 Found (fun (x5:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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 (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn))
% 178.67/178.97 Found x9:(cODD (cS c0))
% 178.67/178.97 Instantiate: Xn0:=(cS c0):fofType
% 178.67/178.97 Found x9 as proof of (cODD Xn0)
% 178.67/178.97 Found (or_intror00 x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 178.98/179.27 Found ((or_intror0 (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 178.98/179.27 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 178.98/179.27 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 178.98/179.27 Found x11:(cEVEN c0)
% 178.98/179.27 Instantiate: Xn0:=c0:fofType
% 178.98/179.27 Found x11 as proof of (cEVEN Xn0)
% 178.98/179.27 Found (or_introl00 x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 178.98/179.27 Found ((or_introl0 (cODD Xn0)) x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 178.98/179.27 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 178.98/179.27 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 178.98/179.27 Found x30:=(x3 x21):(cNUMBER Xn0)
% 178.98/179.27 Instantiate: Xn0:=Xn:fofType
% 178.98/179.27 Found (x3 x21) as proof of (cNUMBER Xn)
% 178.98/179.27 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21)) as proof of (cNUMBER Xn)
% 178.98/179.27 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))
% 178.98/179.27 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)))
% 178.98/179.27 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)
% 178.98/179.27 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)
% 178.98/179.27 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)
% 178.98/179.27 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)
% 178.98/179.27 Found x30:=(x3 x20):(cNUMBER Xn0)
% 178.98/179.27 Instantiate: Xn0:=Xn:fofType
% 178.98/179.27 Found (x3 x20) as proof of (cNUMBER Xn)
% 178.98/179.27 Found (fun (x4:(cEVEN Xn0))=> (x3 x20)) as proof of (cNUMBER Xn)
% 178.98/179.27 Found (fun (x4:(cEVEN Xn0))=> (x3 x20)) as proof of ((cEVEN Xn0)->(cNUMBER Xn))
% 178.98/179.27 Found x30:=(x3 x20):(cNUMBER Xn0)
% 178.98/179.27 Instantiate: Xn0:=Xn:fofType
% 178.98/179.27 Found (x3 x20) as proof of (cNUMBER Xn)
% 178.98/179.27 Found (fun (x4:(cODD Xn0))=> (x3 x20)) as proof of (cNUMBER Xn)
% 178.98/179.27 Found (fun (x4:(cODD Xn0))=> (x3 x20)) as proof of ((cODD Xn0)->(cNUMBER Xn))
% 178.98/179.27 Found ((or_ind00 (fun (x4:(cEVEN Xn0))=> (x3 x20))) (fun (x4:(cODD Xn0))=> (x3 x20))) as proof of (cNUMBER Xn)
% 178.98/179.27 Found (((or_ind0 (cNUMBER Xn)) (fun (x4:(cEVEN Xn0))=> (x3 x20))) (fun (x4:(cODD Xn0))=> (x3 x20))) as proof of (cNUMBER Xn)
% 178.98/179.27 Found ((((fun (P:Prop) (x4:((cEVEN Xn0)->P)) (x5:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x4) x5) x20)) (cNUMBER Xn)) (fun (x4:(cEVEN Xn0))=> (x3 x20))) (fun (x4:(cODD Xn0))=> (x3 x20))) as proof of (cNUMBER Xn)
% 183.09/183.38 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)
% 183.09/183.38 Found x80:((or (cEVEN Xn0)) (cODD Xn0))
% 183.09/183.38 Found x80 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 183.09/183.38 Found (x9 x80) as proof of (cNUMBER Xn)
% 183.09/183.38 Found (x9 x80) as proof of (cNUMBER Xn)
% 183.09/183.38 Found (x9 x80) as proof of (cNUMBER Xn)
% 183.09/183.38 Found x30:=(x3 x20):(cNUMBER Xn0)
% 183.09/183.38 Instantiate: Xn0:=Xn:fofType
% 183.09/183.38 Found (x3 x20) as proof of (cNUMBER Xn)
% 183.09/183.38 Found (x3 x20) as proof of (cNUMBER Xn)
% 183.09/183.38 Found x70:=(x7 x60):(cNUMBER Xn00)
% 183.09/183.38 Instantiate: Xn00:=Xn:fofType
% 183.09/183.38 Found (x7 x60) as proof of (cNUMBER Xn)
% 183.09/183.38 Found (x7 x60) as proof of (cNUMBER Xn)
% 183.09/183.38 Found x50:=(x5 x40):(cNUMBER Xn0)
% 183.09/183.38 Instantiate: Xn0:=Xn:fofType
% 183.09/183.38 Found (x5 x40) as proof of (cNUMBER Xn)
% 183.09/183.38 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 183.09/183.38 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))
% 183.09/183.38 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)))
% 183.09/183.38 Found x50:=(x5 x40):(cNUMBER Xn0)
% 183.09/183.38 Instantiate: Xn0:=Xn:fofType
% 183.09/183.38 Found (x5 x40) as proof of (cNUMBER Xn)
% 183.09/183.38 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 183.09/183.38 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))
% 183.09/183.38 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)))
% 183.09/183.38 Found x60:((or (cEVEN Xn0)) (cODD Xn0))
% 183.09/183.38 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 183.09/183.38 Found (x7 x60) as proof of (cNUMBER Xn)
% 183.09/183.38 Found (x7 x60) as proof of (cNUMBER Xn)
% 183.09/183.38 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)) as proof of (cNUMBER Xn)
% 183.09/183.38 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))
% 183.09/183.38 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)))
% 183.09/183.38 Found x11:(cEVEN c0)
% 183.09/183.38 Instantiate: Xn0:=c0:fofType
% 183.09/183.38 Found x11 as proof of (cEVEN Xn0)
% 183.09/183.38 Found (or_introl00 x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 183.09/183.38 Found ((or_introl0 (cODD Xn0)) x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 183.09/183.38 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 183.09/183.38 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 183.09/183.38 Found x9:(cODD (cS c0))
% 183.09/183.38 Instantiate: Xn0:=(cS c0):fofType
% 183.09/183.38 Found x9 as proof of (cODD Xn0)
% 183.09/183.38 Found (or_intror00 x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 183.09/183.38 Found ((or_intror0 (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 183.09/183.38 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 186.15/186.43 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 186.15/186.43 Found x50:(cNUMBER Xn0)
% 186.15/186.43 Instantiate: Xn0:=Xn:fofType
% 186.15/186.43 Found x50 as proof of (cNUMBER Xn)
% 186.15/186.43 Found x50:(cNUMBER Xn0)
% 186.15/186.43 Instantiate: Xn0:=Xn:fofType
% 186.15/186.43 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of (cNUMBER Xn)
% 186.15/186.43 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))
% 186.15/186.43 Found x300:=(x30 c0):((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 186.15/186.43 Found (x30 c0) as proof of ((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 186.15/186.43 Found (x30 c0) as proof of ((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 186.15/186.43 Found x30:(cNUMBER Xn0)
% 186.15/186.43 Instantiate: Xn0:=Xn:fofType
% 186.15/186.43 Found x30 as proof of (cNUMBER Xn)
% 186.15/186.43 Found x300:=(x30 (cS Xx)):((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))
% 186.15/186.43 Found (x30 (cS Xx)) as proof of ((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))
% 186.15/186.43 Found (fun (x6:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx))) as proof of ((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))
% 186.15/186.43 Found (fun (Xx:fofType) (x6:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx))) as proof of (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))
% 186.15/186.43 Found (fun (Xx:fofType) (x6:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx))) as proof of (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))
% 186.15/186.43 Found ((conj00 (x30 c0)) (fun (Xx:fofType) (x6:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 186.15/186.43 Found (((conj0 (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))) (x30 c0)) (fun (Xx:fofType) (x6:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 186.15/186.43 Found ((((conj ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))) (x30 c0)) (fun (Xx:fofType) (x6:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 186.15/186.43 Found ((((conj ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))) (x30 c0)) (fun (Xx:fofType) (x6:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 186.15/186.43 Found x30:=(x3 x20):(cNUMBER Xn0)
% 186.15/186.43 Found (x3 x20) as proof of (cNUMBER Xn0)
% 186.15/186.43 Found (x3 x20) as proof of (cNUMBER Xn0)
% 186.15/186.43 Found x9:(cODD (cS c0))
% 186.15/186.43 Instantiate: Xn0:=(cS c0):fofType
% 186.15/186.43 Found x9 as proof of (cODD Xn0)
% 186.15/186.43 Found (or_intror00 x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 186.15/186.43 Found ((or_intror0 (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 186.15/186.43 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 186.15/186.43 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 186.15/186.43 Found x110:((or (cEVEN Xn0)) (cODD Xn0))
% 186.15/186.43 Found x110 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 186.15/186.43 Found (x12 x110) as proof of (cNUMBER Xn)
% 186.15/186.43 Found (x12 x110) as proof of (cNUMBER Xn)
% 186.15/186.43 Found (fun (x12:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x12 x110)) as proof of (cNUMBER Xn)
% 186.15/186.43 Found (fun (x12:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x12 x110)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 186.15/186.43 Found x70:=(x7 x60):(cNUMBER Xn0)
% 186.15/186.43 Instantiate: Xn0:=Xn:fofType
% 186.15/186.43 Found (x7 x60) as proof of (cNUMBER Xn)
% 186.15/186.43 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)) as proof of (cNUMBER Xn)
% 187.09/187.37 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))
% 187.09/187.37 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)))
% 187.09/187.37 Found (and_rect50 (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60))) as proof of (cNUMBER Xn)
% 187.09/187.37 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)
% 187.09/187.37 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)
% 187.09/187.37 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)
% 187.09/187.37 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 187.09/187.37 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 187.09/187.37 Found (x3 x20) as proof of (cNUMBER Xn)
% 187.09/187.37 Found (x3 x20) as proof of (cNUMBER Xn)
% 187.09/187.37 Found (x3 x20) as proof of (cNUMBER Xn)
% 187.09/187.37 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 187.09/187.37 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 187.09/187.37 Found (x3 x20) as proof of (cNUMBER Xn)
% 187.09/187.37 Found (x3 x20) as proof of (cNUMBER Xn)
% 187.09/187.37 Found (x3 x20) as proof of (cNUMBER Xn)
% 187.09/187.37 Found x50:=(x5 x40):(cNUMBER Xn0)
% 187.09/187.37 Found (x5 x40) as proof of (cNUMBER Xn)
% 187.09/187.37 Found (x5 x40) as proof of (cNUMBER Xn)
% 187.09/187.37 Found (x5 x40) as proof of (cNUMBER Xn)
% 187.09/187.37 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 187.09/187.37 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 187.09/187.37 Found (x5 x40) as proof of (cNUMBER Xn)
% 187.09/187.37 Found (x5 x40) as proof of (cNUMBER Xn)
% 187.09/187.37 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 187.09/187.37 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x5 x40)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 187.09/187.37 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 187.09/187.37 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 187.09/187.37 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 187.09/187.37 Found x31:(cNUMBER Xn0)
% 187.09/187.37 Instantiate: Xn0:=Xn:fofType
% 187.09/187.37 Found (fun (x9:(cODD (cS c0)))=> x31) as proof of (cNUMBER Xn)
% 187.09/187.37 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))
% 187.09/187.37 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)))
% 187.09/187.37 Found x30:=(x3 x20):(cNUMBER Xn0)
% 187.09/187.37 Found (x3 x20) as proof of (cNUMBER Xn)
% 187.09/187.37 Found (x3 x20) as proof of (cNUMBER Xn)
% 187.09/187.37 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 187.09/187.37 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))
% 187.09/187.37 Found x300:=(x30 c0):((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 187.09/187.37 Found (x30 c0) as proof of ((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 187.09/187.37 Found (x30 c0) as proof of ((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 187.09/187.37 Found x50:=(x5 x40):(cNUMBER Xn0)
% 187.09/187.37 Instantiate: Xn0:=Xn:fofType
% 187.09/187.37 Found (x5 x40) as proof of (cNUMBER Xn)
% 187.09/187.37 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 187.09/187.37 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 190.49/190.80 Found x50:=(x5 x40):(cNUMBER Xn0)
% 190.49/190.80 Found (x5 x40) as proof of (cNUMBER Xn)
% 190.49/190.80 Found (x5 x40) as proof of (cNUMBER Xn)
% 190.49/190.80 Found (x5 x40) as proof of (cNUMBER Xn)
% 190.49/190.80 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 190.49/190.80 Instantiate: Xn00:=Xn:fofType
% 190.49/190.80 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 190.49/190.80 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 190.49/190.80 Instantiate: Xn0:=Xn:fofType
% 190.49/190.80 Found x40 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 190.49/190.80 Found x70:=(x7 x60):(cNUMBER Xn00)
% 190.49/190.80 Instantiate: Xn00:=Xn:fofType
% 190.49/190.80 Found (x7 x60) as proof of (cNUMBER Xn)
% 190.49/190.80 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x7 x60)) as proof of (cNUMBER Xn)
% 190.49/190.80 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x7 x60)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 190.49/190.80 Found x30:=(x3 x20):(cNUMBER Xn0)
% 190.49/190.80 Found (x3 x20) as proof of (cNUMBER Xn)
% 190.49/190.80 Found (x3 x20) as proof of (cNUMBER Xn)
% 190.49/190.80 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 190.49/190.80 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))
% 190.49/190.80 Found x6:(cNUMBER (cS Xx))
% 190.49/190.80 Found x6 as proof of (cNUMBER (cS Xx))
% 190.49/190.80 Found x70:(cNUMBER Xn0)
% 190.49/190.80 Instantiate: Xn0:=Xn:fofType
% 190.49/190.80 Found x70 as proof of (cNUMBER Xn)
% 190.49/190.80 Found x30:=(x3 x20):(cNUMBER Xn0)
% 190.49/190.80 Instantiate: Xn0:=Xn:fofType
% 190.49/190.80 Found (x3 x20) as proof of (cNUMBER Xn)
% 190.49/190.80 Found (x3 x20) as proof of (cNUMBER Xn)
% 190.49/190.80 Found x50:=(x5 x40):(cNUMBER Xn00)
% 190.49/190.80 Instantiate: Xn00:=Xn:fofType
% 190.49/190.80 Found (x5 x40) as proof of (cNUMBER Xn)
% 190.49/190.80 Found (x5 x40) as proof of (cNUMBER Xn)
% 190.49/190.80 Found x300:=(x30 c0):((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 190.49/190.80 Found (x30 c0) as proof of ((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 190.49/190.80 Found (x30 c0) as proof of ((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 190.49/190.80 Found x50:(cNUMBER Xn0)
% 190.49/190.80 Instantiate: Xn0:=Xn:fofType
% 190.49/190.80 Found (fun (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of (cNUMBER Xn)
% 190.49/190.80 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))
% 190.49/190.80 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)))
% 190.49/190.80 Found x50:(cNUMBER Xn0)
% 190.49/190.80 Instantiate: Xn0:=Xn:fofType
% 190.49/190.80 Found (fun (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of (cNUMBER Xn)
% 190.49/190.80 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))
% 190.49/190.80 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)))
% 190.49/190.80 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))
% 190.49/190.80 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))
% 190.49/190.80 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))
% 190.49/190.80 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))
% 190.89/191.16 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))
% 190.89/191.16 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)))
% 190.89/191.16 Found x50:=(x5 x41):(cNUMBER Xn0)
% 190.89/191.16 Instantiate: Xn0:=Xn:fofType
% 190.89/191.16 Found (x5 x41) as proof of (cNUMBER Xn)
% 190.89/191.16 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x41)) as proof of (cNUMBER Xn)
% 190.89/191.16 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))
% 190.89/191.16 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)))
% 190.89/191.16 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)
% 190.89/191.16 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)
% 190.89/191.16 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)
% 190.89/191.16 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)
% 199.17/199.48 Found x70:=(x7 x60):(cNUMBER Xn0)
% 199.17/199.48 Found (x7 x60) as proof of (cNUMBER Xn)
% 199.17/199.48 Found (x7 x60) as proof of (cNUMBER Xn)
% 199.17/199.48 Found (fun (x7:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x7 x60)) as proof of (cNUMBER Xn)
% 199.17/199.48 Found (fun (x7:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x7 x60)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 199.17/199.48 Found x70:=(x7 x61):(cNUMBER Xn0)
% 199.17/199.48 Found (x7 x61) as proof of (cNUMBER Xn)
% 199.17/199.48 Found (x7 x61) as proof of (cNUMBER Xn)
% 199.17/199.48 Found (fun (x7:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x7 x61)) as proof of (cNUMBER Xn)
% 199.17/199.48 Found (fun (x7:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x7 x61)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 199.17/199.48 Found x70:=(x7 x60):(cNUMBER Xn0)
% 199.17/199.48 Found (x7 x60) as proof of (cNUMBER Xn)
% 199.17/199.48 Found (x7 x60) as proof of (cNUMBER Xn)
% 199.17/199.48 Found (fun (x7:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x7 x60)) as proof of (cNUMBER Xn)
% 199.17/199.48 Found (fun (x7:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x7 x60)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 199.17/199.48 Found x70:=(x7 x60):(cNUMBER Xn0)
% 199.17/199.48 Found (x7 x60) as proof of (cNUMBER Xn)
% 199.17/199.48 Found (x7 x60) as proof of (cNUMBER Xn)
% 199.17/199.48 Found (x7 x60) as proof of (cNUMBER Xn)
% 199.17/199.48 Found x30:=(x3 x20):(cNUMBER Xn0)
% 199.17/199.48 Instantiate: Xn0:=Xn:fofType
% 199.17/199.48 Found (x3 x20) as proof of (cNUMBER Xn)
% 199.17/199.48 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 199.17/199.48 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 199.17/199.48 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 199.17/199.48 Instantiate: Xn00:=Xn:fofType
% 199.17/199.48 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 199.17/199.48 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 199.17/199.48 Instantiate: Xn0:=Xn:fofType
% 199.17/199.48 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 199.17/199.48 Found x70:=(x7 x60):(cNUMBER Xn00)
% 199.17/199.48 Instantiate: Xn00:=Xn:fofType
% 199.17/199.48 Found (x7 x60) as proof of (cNUMBER Xn)
% 199.17/199.48 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x7 x60)) as proof of (cNUMBER Xn)
% 199.17/199.48 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x7 x60)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 199.17/199.48 Found x80:((or (cEVEN Xn0)) (cODD Xn0))
% 199.17/199.48 Found x80 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 199.17/199.48 Found (x9 x80) as proof of (cNUMBER Xn)
% 199.17/199.48 Found (x9 x80) as proof of (cNUMBER Xn)
% 199.17/199.48 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x9 x80)) as proof of (cNUMBER Xn)
% 199.17/199.48 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))
% 199.17/199.48 Found x500:=(x50 c0):((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 199.17/199.48 Found (x50 c0) as proof of ((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 199.17/199.48 Found (x50 c0) as proof of ((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 199.17/199.48 Found x50:(cNUMBER Xn0)
% 199.17/199.48 Instantiate: Xn0:=Xn:fofType
% 199.17/199.48 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of (cNUMBER Xn)
% 199.17/199.48 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))
% 199.17/199.48 Found x50:(cNUMBER Xn0)
% 199.17/199.48 Instantiate: Xn0:=Xn:fofType
% 199.17/199.48 Found x50 as proof of (cNUMBER Xn)
% 199.17/199.48 Found x30:=(x3 x20):(cNUMBER Xn0)
% 199.17/199.48 Instantiate: Xn0:=Xn:fofType
% 199.17/199.48 Found (x3 x20) as proof of (cNUMBER Xn)
% 199.17/199.48 Found (x3 x20) as proof of (cNUMBER Xn)
% 199.17/199.48 Found x31:(cNUMBER Xn0)
% 199.17/199.48 Instantiate: Xn0:=Xn:fofType
% 199.17/199.48 Found (fun (x9:(cODD (cS c0)))=> x31) as proof of (cNUMBER Xn)
% 199.17/199.48 Found (fun (x9:(cODD (cS c0)))=> x31) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 199.17/199.48 Found x50:(cNUMBER Xn0)
% 199.17/199.48 Instantiate: Xn0:=Xn:fofType
% 199.17/199.48 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of (cNUMBER Xn)
% 200.58/200.92 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))
% 200.58/200.92 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)))
% 200.58/200.92 Found x30:(cNUMBER Xn0)
% 200.58/200.92 Instantiate: Xn0:=Xn:fofType
% 200.58/200.92 Found (fun (x9:(cODD (cS c0)))=> x30) as proof of (cNUMBER Xn)
% 200.58/200.92 Found (fun (x9:(cODD (cS c0)))=> x30) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 200.58/200.92 Found x30:(cNUMBER Xn0)
% 200.58/200.92 Instantiate: Xn0:=Xn:fofType
% 200.58/200.92 Found (fun (x9:(cODD (cS c0)))=> x30) as proof of (cNUMBER Xn)
% 200.58/200.92 Found (fun (x9:(cODD (cS c0)))=> x30) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 200.58/200.92 Found x50:(cNUMBER Xn0)
% 200.58/200.92 Instantiate: Xn0:=Xn:fofType
% 200.58/200.92 Found x50 as proof of (cNUMBER Xn)
% 200.58/200.92 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 200.58/200.92 Instantiate: Xn00:=Xn:fofType
% 200.58/200.92 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 200.58/200.92 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 200.58/200.92 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 200.58/200.92 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 200.58/200.92 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 200.58/200.92 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)))
% 200.58/200.92 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))))
% 200.58/200.92 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))
% 200.58/200.92 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))
% 200.58/200.92 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))
% 200.58/200.92 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))
% 200.58/200.92 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)))
% 200.58/200.92 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))))
% 200.58/200.92 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))
% 200.58/200.92 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))
% 200.58/200.92 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))
% 200.58/200.92 Found (fun (x5:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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))
% 200.58/200.93 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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 (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 200.58/200.93 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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))))))->((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->((or (cEVEN Xn0)) (cODD Xn0))))
% 200.58/200.93 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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))
% 200.58/200.93 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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))
% 200.58/200.93 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))))))->((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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))))))) (((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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))
% 200.67/200.95 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))))))->((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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))))))) (((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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))
% 200.67/200.95 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))))))->((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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))))))) (((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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)
% 200.67/200.95 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))))))->((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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))))))) (((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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)
% 200.67/200.99 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 200.67/200.99 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 200.67/200.99 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 200.67/200.99 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 200.67/200.99 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)))
% 200.67/200.99 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))))
% 200.67/200.99 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))
% 200.67/200.99 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))
% 200.67/200.99 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))
% 200.67/200.99 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))
% 200.67/200.99 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)))
% 200.67/200.99 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))))
% 200.71/200.99 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))
% 200.71/200.99 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))
% 200.71/200.99 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))
% 200.71/200.99 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))
% 200.71/200.99 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)
% 200.71/201.00 Found (fun (x5:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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)
% 200.71/201.00 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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 (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn0))
% 200.71/201.00 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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))))))->((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn0)))
% 200.71/201.00 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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)
% 200.71/201.00 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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)
% 200.71/201.00 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))))))->((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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))))))) (((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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)
% 200.71/201.00 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))))))->((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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))))))) (((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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)
% 201.59/201.91 Found x300:=(x30 (cS Xx)):((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))
% 201.59/201.91 Found (x30 (cS Xx)) as proof of ((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))
% 201.59/201.91 Found (fun (x4:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx))) as proof of ((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))
% 201.59/201.91 Found (fun (Xx:fofType) (x4:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx))) as proof of (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))
% 201.59/201.91 Found (fun (Xx:fofType) (x4:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx))) as proof of (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))
% 201.59/201.91 Found ((conj00 (x30 c0)) (fun (Xx:fofType) (x4:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 201.59/201.91 Found (((conj0 (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))) (x30 c0)) (fun (Xx:fofType) (x4:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 201.59/201.91 Found ((((conj ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))) (x30 c0)) (fun (Xx:fofType) (x4:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 201.59/201.91 Found ((((conj ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))) (x30 c0)) (fun (Xx:fofType) (x4:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 201.59/201.91 Found x8:(cODD (cS c0))
% 201.59/201.91 Instantiate: Xn0:=(cS c0):fofType
% 201.59/201.91 Found x8 as proof of (cODD Xn0)
% 201.59/201.91 Found (or_intror00 x8) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 201.59/201.91 Found ((or_intror0 (cODD Xn0)) x8) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 201.59/201.91 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x8) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 201.59/201.91 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x8) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 201.59/201.91 Found (x5 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x8)) as proof of (cNUMBER Xn0)
% 201.59/201.91 Found (fun (x8:(cODD (cS c0)))=> (x5 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x8))) as proof of (cNUMBER Xn0)
% 201.68/201.97 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))
% 201.68/201.97 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)))
% 201.68/201.97 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)
% 201.68/201.97 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)
% 201.68/201.97 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)
% 201.68/201.97 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)
% 201.68/201.97 Found x9:(cODD (cS c0))
% 201.68/201.97 Instantiate: Xn0:=(cS c0):fofType
% 201.68/201.97 Found x9 as proof of (cODD Xn0)
% 201.68/201.97 Found (or_intror00 x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 201.68/201.97 Found ((or_intror0 (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 201.68/201.97 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 201.68/201.97 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 201.68/201.97 Found (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9)) as proof of (cNUMBER Xn0)
% 201.68/201.97 Found (fun (x9:(cODD (cS c0)))=> (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9))) as proof of (cNUMBER Xn0)
% 201.68/201.97 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))
% 201.68/201.97 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)))
% 201.68/201.97 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)
% 201.68/201.97 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)
% 201.68/201.97 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 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)
% 201.68/201.97 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 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)
% 203.24/203.56 Found x70:=(x7 x60):(cNUMBER Xn0)
% 203.24/203.56 Instantiate: Xn0:=Xn:fofType
% 203.24/203.56 Found (x7 x60) as proof of (cNUMBER Xn)
% 203.24/203.56 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)) as proof of (cNUMBER Xn)
% 203.24/203.56 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))
% 203.24/203.56 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)))
% 203.24/203.56 Found (and_rect50 (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60))) as proof of (cNUMBER Xn)
% 203.24/203.56 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)
% 203.24/203.56 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)
% 203.24/203.56 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)
% 203.24/203.56 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))
% 203.24/203.56 Found x30:(cNUMBER Xn0)
% 203.24/203.56 Instantiate: Xn0:=Xn:fofType
% 203.24/203.56 Found x30 as proof of (cNUMBER Xn)
% 203.24/203.56 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 203.24/203.56 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 203.24/203.56 Found (x3 x20) as proof of (cNUMBER Xn)
% 203.24/203.56 Found (x3 x20) as proof of (cNUMBER Xn)
% 203.24/203.56 Found (x3 x20) as proof of (cNUMBER Xn)
% 203.24/203.56 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 203.24/203.56 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 203.24/203.56 Found (x3 x20) as proof of (cNUMBER Xn)
% 203.24/203.56 Found (x3 x20) as proof of (cNUMBER Xn)
% 203.24/203.56 Found (x3 x20) as proof of (cNUMBER Xn)
% 203.24/203.56 Found x50:=(x5 (cS c0)):((cODD (cS c0))->(cODD (cS (cS (cS c0)))))
% 203.24/203.56 Found (x5 (cS c0)) as proof of ((cODD (cS c0))->(cODD Xn0))
% 203.24/203.56 Found (x5 (cS c0)) as proof of ((cODD (cS c0))->(cODD Xn0))
% 203.24/203.56 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))
% 203.24/203.56 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)))
% 203.24/203.56 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)
% 203.24/203.56 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)
% 203.24/203.56 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)
% 203.41/203.70 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) 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)
% 203.41/203.70 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))
% 203.41/203.70 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))
% 203.41/203.70 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))
% 203.41/203.70 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))
% 203.41/203.70 Found x50:(cNUMBER Xn0)
% 203.41/203.70 Instantiate: Xn0:=Xn:fofType
% 203.41/203.70 Found (fun (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of (cNUMBER Xn)
% 203.41/203.70 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))
% 203.41/203.70 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)))
% 203.41/203.70 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))))
% 203.41/203.70 Found x50:(cNUMBER Xn0)
% 203.41/203.70 Instantiate: Xn0:=Xn:fofType
% 203.41/203.70 Found (fun (x8:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of (cNUMBER Xn)
% 203.41/203.70 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))
% 203.41/203.70 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)))
% 203.41/203.71 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))))
% 203.41/203.71 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)))
% 203.41/203.71 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)))
% 203.41/203.71 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)))
% 203.41/203.71 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)))
% 203.41/203.71 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)))
% 203.91/204.23 Found x50:=(x5 x40):(cNUMBER Xn0)
% 203.91/204.23 Found (x5 x40) as proof of (cNUMBER Xn)
% 203.91/204.23 Found (x5 x40) as proof of (cNUMBER Xn)
% 203.91/204.23 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 203.91/204.23 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))
% 203.91/204.23 Found x50:=(x5 x40):(cNUMBER Xn0)
% 203.91/204.23 Found (x5 x40) as proof of (cNUMBER Xn)
% 203.91/204.23 Found (x5 x40) as proof of (cNUMBER Xn)
% 203.91/204.23 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 203.91/204.23 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))
% 203.91/204.23 Found or_introl00:=(or_introl0 (cEVEN Xn0)):((cODD (cS c0))->((or (cODD (cS c0))) (cEVEN Xn0)))
% 203.91/204.23 Found (or_introl0 (cEVEN Xn0)) as proof of ((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0)))
% 203.91/204.23 Found ((or_introl (cODD (cS c0))) (cEVEN Xn0)) as proof of ((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0)))
% 203.91/204.23 Found ((or_introl (cODD (cS c0))) (cEVEN Xn0)) as proof of ((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0)))
% 203.91/204.23 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)))
% 203.91/204.23 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))))
% 203.91/204.23 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))
% 203.91/204.23 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))
% 203.91/204.23 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)) ((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))
% 203.91/204.23 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)) ((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))
% 203.91/204.23 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))
% 204.01/204.30 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))
% 204.01/204.30 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))
% 204.01/204.30 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))
% 204.01/204.30 Found x50:=(x5 x40):(cNUMBER Xn0)
% 204.01/204.30 Instantiate: Xn0:=Xn:fofType
% 204.01/204.30 Found (x5 x40) as proof of (cNUMBER Xn)
% 204.01/204.30 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 204.01/204.30 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))
% 204.01/204.30 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)))
% 204.01/204.30 Found x300:=(x30 (cS Xx)):((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))
% 204.01/204.30 Found (x30 (cS Xx)) as proof of ((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))
% 204.01/204.30 Found (fun (x6:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx))) as proof of ((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))
% 204.01/204.30 Found (fun (Xx:fofType) (x6:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx))) as proof of (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))
% 204.01/204.30 Found (fun (Xx:fofType) (x6:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx))) as proof of (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))
% 204.01/204.30 Found ((conj00 (x30 c0)) (fun (Xx:fofType) (x6:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 204.01/204.30 Found (((conj0 (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))) (x30 c0)) (fun (Xx:fofType) (x6:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 204.01/204.30 Found ((((conj ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))) (x30 c0)) (fun (Xx:fofType) (x6:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 205.68/206.01 Found ((((conj ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))) (x30 c0)) (fun (Xx:fofType) (x6:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 205.68/206.01 Found x30:=(x3 x20):(cNUMBER Xn0)
% 205.68/206.01 Instantiate: Xn0:=Xn:fofType
% 205.68/206.01 Found (x3 x20) as proof of (cNUMBER Xn)
% 205.68/206.01 Found (fun (x7:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 205.68/206.01 Found (fun (x7:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x3 x20)) as proof of ((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn))
% 205.68/206.01 Found x50:=(x5 x40):(cNUMBER Xn00)
% 205.68/206.01 Instantiate: Xn00:=Xn:fofType
% 205.68/206.01 Found (x5 x40) as proof of (cNUMBER Xn)
% 205.68/206.01 Found (fun (x7:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 205.68/206.01 Found (fun (x7:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x5 x40)) as proof of ((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn))
% 205.68/206.01 Found x50:=(x5 x40):(cNUMBER Xn0)
% 205.68/206.01 Found (x5 x40) as proof of (cNUMBER Xn)
% 205.68/206.01 Found (x5 x40) as proof of (cNUMBER Xn)
% 205.68/206.01 Found (x5 x40) as proof of (cNUMBER Xn)
% 205.68/206.01 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 205.68/206.01 Instantiate: Xn0:=Xn:fofType
% 205.68/206.01 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 205.68/206.01 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 205.68/206.01 Instantiate: Xn00:=Xn:fofType
% 205.68/206.01 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 205.68/206.01 Found x30:=(x3 x20):(cNUMBER Xn0)
% 205.68/206.01 Found (x3 x20) as proof of (cNUMBER Xn)
% 205.68/206.01 Found (x3 x20) as proof of (cNUMBER Xn)
% 205.68/206.01 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 205.68/206.01 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))
% 205.68/206.01 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)))
% 205.68/206.01 Found x300:=(x30 c0):((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 205.68/206.01 Found (x30 c0) as proof of ((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 205.68/206.01 Found (x30 c0) as proof of ((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 205.68/206.01 Found x30:=(x3 x20):(cNUMBER Xn0)
% 205.68/206.01 Found (x3 x20) as proof of (cNUMBER Xn)
% 205.68/206.01 Found (x3 x20) as proof of (cNUMBER Xn)
% 205.68/206.01 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 205.68/206.01 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))
% 205.99/206.35 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)))
% 205.99/206.35 Found x50:=(x5 x40):(cNUMBER Xn0)
% 205.99/206.35 Found (x5 x40) as proof of (cNUMBER Xn)
% 205.99/206.35 Found (x5 x40) as proof of (cNUMBER Xn)
% 205.99/206.35 Found (x5 x40) as proof of (cNUMBER Xn)
% 205.99/206.35 Found x60:=(x6 (cS c0)):((cODD (cS c0))->(cODD (cS (cS (cS c0)))))
% 205.99/206.35 Found (x6 (cS c0)) as proof of ((cODD (cS c0))->(cODD Xn0))
% 205.99/206.35 Found (x6 (cS c0)) as proof of ((cODD (cS c0))->(cODD Xn0))
% 205.99/206.35 Found (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x6 (cS c0))) as proof of ((cODD (cS c0))->(cODD Xn0))
% 205.99/206.35 Found (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x6 (cS c0))) as proof of (((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->(cODD Xn0)))
% 205.99/206.35 Found (and_rect40 (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x6 (cS c0)))) as proof of (cODD Xn0)
% 205.99/206.35 Found ((and_rect4 (cODD Xn0)) (fun (x7:((and (cEVEN c0)) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> (x6 (cS c0)))) as proof of (cODD Xn0)
% 205.99/206.35 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)))))))=> (x6 (cS c0)))) as proof of (cODD Xn0)
% 205.99/206.35 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)))))))=> (x6 (cS c0))))) as proof of (cODD Xn0)
% 205.99/206.35 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)))))))=> (x6 (cS c0))))) as proof of ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->(cODD Xn0))
% 205.99/206.35 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)))))))=> (x6 (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)))
% 205.99/206.35 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)))))))=> (x6 (cS c0)))))) as proof of (cODD Xn0)
% 206.07/206.36 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)))))))=> (x6 (cS c0)))))) as proof of (cODD Xn0)
% 206.07/206.36 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)))))))=> (x6 (cS c0)))))) as proof of (cODD Xn0)
% 206.07/206.36 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)))))))=> (x6 (cS c0)))))) as proof of (cODD Xn0)
% 206.07/206.36 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)))))))=> (x6 (cS c0))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 206.07/206.36 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)))))))=> (x6 (cS c0))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 207.86/208.20 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)))))))=> (x6 (cS c0))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 207.86/208.20 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)))))))=> (x6 (cS c0))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 207.86/208.20 Found x300:=(x30 c0):((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 207.86/208.20 Found (x30 c0) as proof of ((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 207.86/208.20 Found (x30 c0) as proof of ((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 207.86/208.20 Found x70:(cNUMBER Xn0)
% 207.86/208.20 Instantiate: Xn0:=Xn:fofType
% 207.86/208.20 Found x70 as proof of (cNUMBER Xn)
% 207.86/208.20 Found or_introl00:=(or_introl0 (cEVEN Xn0)):((cODD (cS c0))->((or (cODD (cS c0))) (cEVEN Xn0)))
% 207.86/208.20 Found (or_introl0 (cEVEN Xn0)) as proof of ((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0)))
% 207.86/208.20 Found ((or_introl (cODD (cS c0))) (cEVEN Xn0)) as proof of ((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0)))
% 207.86/208.20 Found ((or_introl (cODD (cS c0))) (cEVEN Xn0)) as proof of ((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0)))
% 207.86/208.20 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)))
% 207.86/208.20 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))))
% 207.86/208.21 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))
% 207.86/208.21 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))
% 207.86/208.21 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))
% 207.86/208.21 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))
% 207.86/208.21 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)))
% 207.86/208.21 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))))
% 207.86/208.21 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))
% 207.86/208.21 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))
% 207.86/208.21 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))
% 207.86/208.21 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))
% 207.86/208.21 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))
% 207.86/208.21 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))
% 207.98/208.31 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))
% 207.98/208.31 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))
% 207.98/208.31 Found x70:=(x7 x60):(cNUMBER Xn0)
% 207.98/208.31 Instantiate: Xn0:=Xn:fofType
% 207.98/208.31 Found (x7 x60) as proof of (cNUMBER Xn)
% 207.98/208.31 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)) as proof of (cNUMBER Xn)
% 207.98/208.31 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))
% 207.98/208.31 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)))
% 207.98/208.31 Found (and_rect50 (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60))) as proof of (cNUMBER Xn)
% 207.98/208.31 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)
% 207.98/208.31 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)
% 208.09/208.43 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)
% 208.09/208.43 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))
% 208.09/208.43 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)))
% 208.09/208.43 Found x50:=(x5 x41):(cNUMBER Xn0)
% 208.09/208.43 Instantiate: Xn0:=Xn:fofType
% 208.09/208.43 Found (x5 x41) as proof of (cNUMBER Xn)
% 208.09/208.43 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x41)) as proof of (cNUMBER Xn)
% 208.09/208.43 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))
% 208.09/208.43 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)))
% 208.09/208.43 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)
% 208.09/208.43 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)
% 208.09/208.43 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)
% 208.09/208.43 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)
% 211.09/211.42 Found x300:=(x30 (cS Xx)):((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))
% 211.09/211.42 Found (x30 (cS Xx)) as proof of ((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))
% 211.09/211.42 Found (fun (x7:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx))) as proof of ((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))
% 211.09/211.42 Found (fun (Xx:fofType) (x7:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx))) as proof of (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))
% 211.09/211.42 Found (fun (Xx:fofType) (x7:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx))) as proof of (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))
% 211.09/211.42 Found ((conj00 (x30 c0)) (fun (Xx:fofType) (x7:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 211.09/211.42 Found (((conj0 (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))) (x30 c0)) (fun (Xx:fofType) (x7:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 211.09/211.42 Found ((((conj ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))) (x30 c0)) (fun (Xx:fofType) (x7:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 211.09/211.42 Found ((((conj ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))) (x30 c0)) (fun (Xx:fofType) (x7:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 211.09/211.42 Found x300:=(x30 c0):((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 211.09/211.42 Found (x30 c0) as proof of ((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 211.09/211.42 Found (x30 c0) as proof of ((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 211.09/211.42 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 211.09/211.42 Instantiate: Xn00:=Xn:fofType
% 211.09/211.42 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 211.09/211.42 Found x30:=(x3 x20):(cNUMBER Xn0)
% 211.09/211.42 Found (x3 x20) as proof of (cNUMBER Xn0)
% 211.09/211.42 Found (x3 x20) as proof of (cNUMBER Xn0)
% 211.09/211.42 Found x30:=(x3 x21):(cNUMBER Xn0)
% 211.09/211.42 Instantiate: Xn0:=Xn:fofType
% 211.09/211.42 Found (x3 x21) as proof of (cNUMBER Xn)
% 211.09/211.42 Found (fun (x9:(cODD (cS c0)))=> (x3 x21)) as proof of (cNUMBER Xn)
% 211.09/211.42 Found (fun (x9:(cODD (cS c0)))=> (x3 x21)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 211.09/211.42 Found x60:((or (cEVEN Xn0)) (cODD Xn0))
% 211.09/211.42 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 211.09/211.42 Found (x7 x60) as proof of (cNUMBER Xn)
% 211.09/211.42 Found (x7 x60) as proof of (cNUMBER Xn)
% 211.09/211.42 Found (x7 x60) as proof of (cNUMBER Xn)
% 211.09/211.42 Found x70:=(x7 x60):(cNUMBER Xn0)
% 211.09/211.42 Found (x7 x60) as proof of (cNUMBER Xn)
% 211.09/211.42 Found (x7 x60) as proof of (cNUMBER Xn)
% 211.09/211.42 Found (fun (x7:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x7 x60)) as proof of (cNUMBER Xn)
% 211.09/211.42 Found (fun (x7:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x7 x60)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 211.09/211.42 Found x60:((or (cEVEN Xn0)) (cODD Xn0))
% 211.09/211.42 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 211.09/211.42 Found (x7 x60) as proof of (cNUMBER Xn)
% 211.09/211.42 Found (x7 x60) as proof of (cNUMBER Xn)
% 211.09/211.42 Found (x7 x60) as proof of (cNUMBER Xn)
% 211.09/211.42 Found x70:=(x7 x60):(cNUMBER Xn00)
% 211.09/211.42 Found (x7 x60) as proof of (cNUMBER Xn)
% 211.09/211.42 Found (x7 x60) as proof of (cNUMBER Xn)
% 211.09/211.42 Found (x7 x60) as proof of (cNUMBER Xn)
% 211.09/211.42 Found x50:=(x5 x40):(cNUMBER Xn0)
% 211.09/211.42 Found (x5 x40) as proof of (cNUMBER Xn)
% 211.09/211.42 Found (x5 x40) as proof of (cNUMBER Xn)
% 214.93/215.25 Found (x5 x40) as proof of (cNUMBER Xn)
% 214.93/215.25 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 214.93/215.25 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 214.93/215.25 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 214.93/215.25 Found x9:(cODD (cS c0))
% 214.93/215.25 Instantiate: Xn0:=(cS c0):fofType
% 214.93/215.25 Found x9 as proof of (cODD Xn0)
% 214.93/215.25 Found (or_intror00 x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 214.93/215.25 Found ((or_intror0 (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 214.93/215.25 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 214.93/215.25 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 214.93/215.25 Found x11:(cEVEN c0)
% 214.93/215.25 Instantiate: Xn0:=c0:fofType
% 214.93/215.25 Found x11 as proof of (cEVEN Xn0)
% 214.93/215.25 Found (or_introl00 x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 214.93/215.25 Found ((or_introl0 (cODD Xn0)) x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 214.93/215.25 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 214.93/215.25 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 214.93/215.25 Found x30:=(x3 x20):(cNUMBER Xn0)
% 214.93/215.25 Instantiate: Xn0:=Xn:fofType
% 214.93/215.25 Found (x3 x20) as proof of (cNUMBER Xn)
% 214.93/215.25 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 214.93/215.25 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))
% 214.93/215.25 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)))
% 214.93/215.25 Found x9:(cODD (cS c0))
% 214.93/215.25 Instantiate: Xn0:=(cS c0):fofType
% 214.93/215.25 Found x9 as proof of (cODD Xn0)
% 214.93/215.25 Found (or_intror00 x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 214.93/215.25 Found ((or_intror0 (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 214.93/215.25 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 214.93/215.25 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 214.93/215.25 Found (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9)) as proof of (cNUMBER Xn0)
% 214.93/215.25 Found (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9)) as proof of (cNUMBER Xn0)
% 214.93/215.25 Found x80:((or (cEVEN Xn0)) (cODD Xn0))
% 214.93/215.25 Found x80 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 214.93/215.25 Found (x9 x80) as proof of (cNUMBER Xn)
% 214.93/215.25 Found (x9 x80) as proof of (cNUMBER Xn)
% 214.93/215.25 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x9 x80)) as proof of (cNUMBER Xn)
% 214.93/215.25 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))
% 214.93/215.25 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)))
% 214.93/215.25 Found x9:(cODD (cS c0))
% 214.93/215.25 Instantiate: Xn0:=(cS c0):fofType
% 214.93/215.25 Found x9 as proof of (cODD Xn0)
% 214.93/215.25 Found (or_intror00 x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 214.93/215.25 Found ((or_intror0 (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 214.93/215.25 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 214.93/215.25 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 214.93/215.25 Found x11:(cEVEN c0)
% 214.93/215.25 Instantiate: Xn0:=c0:fofType
% 214.93/215.25 Found x11 as proof of (cEVEN Xn0)
% 214.93/215.25 Found (or_introl00 x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 214.93/215.25 Found ((or_introl0 (cODD Xn0)) x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 214.93/215.25 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 214.93/215.25 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 214.93/215.25 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 214.93/215.25 Instantiate: Xn00:=Xn:fofType
% 214.93/215.25 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x60) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 214.93/215.25 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)))
% 215.17/215.52 Found x30:=(x3 x20):(cNUMBER Xn0)
% 215.17/215.52 Instantiate: Xn0:=Xn:fofType
% 215.17/215.52 Found (x3 x20) as proof of (cNUMBER Xn)
% 215.17/215.52 Found (fun (x5:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 215.17/215.52 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x3 x20)) as proof of ((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn))
% 215.17/215.52 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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))))))->((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn)))
% 215.17/215.52 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 215.17/215.52 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 215.17/215.52 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))))))->((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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))))))) (((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 216.35/216.70 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))))))->((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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))))))) (((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x3 x20)))) as proof of (cNUMBER Xn)
% 216.35/216.70 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))))))->((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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))))))) (((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x3 x20)))) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 216.35/216.70 Found x30:=(x3 x21):(cNUMBER Xn0)
% 216.35/216.70 Instantiate: Xn0:=Xn:fofType
% 216.35/216.70 Found (x3 x21) as proof of (cNUMBER Xn)
% 216.35/216.70 Found (fun (x9:(cODD (cS c0)))=> (x3 x21)) as proof of (cNUMBER Xn)
% 216.35/216.70 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))
% 216.35/216.70 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)))
% 216.35/216.70 Found x50:(cNUMBER Xn0)
% 216.35/216.70 Instantiate: Xn0:=Xn:fofType
% 216.35/216.70 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of (cNUMBER Xn)
% 216.35/216.70 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))
% 216.35/216.70 Found x30:=(x3 x20):(cNUMBER Xn0)
% 216.35/216.70 Instantiate: Xn0:=Xn:fofType
% 216.35/216.70 Found (x3 x20) as proof of (cNUMBER Xn)
% 216.35/216.70 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 216.35/216.70 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 219.86/220.18 Found x50:(cNUMBER Xn0)
% 219.86/220.18 Instantiate: Xn0:=Xn:fofType
% 219.86/220.18 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of (cNUMBER Xn)
% 219.86/220.18 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))
% 219.86/220.18 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)))
% 219.86/220.18 Found x7:(cODD (cS c0))
% 219.86/220.18 Instantiate: Xn0:=(cS c0):fofType
% 219.86/220.18 Found x7 as proof of (cODD Xn0)
% 219.86/220.18 Found (or_intror00 x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 219.86/220.18 Found ((or_intror0 (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 219.86/220.18 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 219.86/220.18 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 219.86/220.18 Found x90:=(x9 x80):(cNUMBER Xn0)
% 219.86/220.18 Instantiate: Xn0:=Xn:fofType
% 219.86/220.18 Found (x9 x80) as proof of (cNUMBER Xn)
% 219.86/220.18 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x9 x80)) as proof of (cNUMBER Xn)
% 219.86/220.18 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))
% 219.86/220.18 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)))
% 219.86/220.18 Found (and_rect50 (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x9 x80))) as proof of (cNUMBER Xn)
% 219.86/220.18 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)
% 219.86/220.18 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)
% 219.86/220.18 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)
% 219.86/220.18 Found x50:(cNUMBER Xn0)
% 219.86/220.18 Instantiate: Xn0:=Xn:fofType
% 219.86/220.18 Found x50 as proof of (cNUMBER Xn)
% 219.86/220.18 Found x50:=(x5 x40):(cNUMBER Xn0)
% 219.86/220.18 Found (x5 x40) as proof of (cNUMBER Xn0)
% 219.86/220.18 Found (x5 x40) as proof of (cNUMBER Xn0)
% 219.86/220.18 Found x31:(cNUMBER Xn0)
% 219.86/220.18 Instantiate: Xn0:=Xn:fofType
% 219.86/220.18 Found (fun (x9:(cODD (cS c0)))=> x31) as proof of (cNUMBER Xn)
% 219.86/220.18 Found (fun (x9:(cODD (cS c0)))=> x31) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 219.86/220.18 Found x30:(cNUMBER Xn0)
% 219.86/220.18 Instantiate: Xn0:=Xn:fofType
% 219.86/220.18 Found (fun (x9:(cODD (cS c0)))=> x30) as proof of (cNUMBER Xn)
% 219.86/220.18 Found (fun (x9:(cODD (cS c0)))=> x30) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 219.86/220.18 Found x30:(cNUMBER Xn0)
% 219.86/220.18 Instantiate: Xn0:=Xn:fofType
% 219.86/220.18 Found (fun (x9:(cODD (cS c0)))=> x30) as proof of (cNUMBER Xn)
% 219.86/220.18 Found (fun (x9:(cODD (cS c0)))=> x30) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 219.86/220.18 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 219.86/220.18 Instantiate: Xn0:=Xn:fofType
% 219.86/220.18 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 219.86/220.18 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 219.86/220.18 Instantiate: Xn00:=Xn:fofType
% 219.86/220.18 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 219.86/220.18 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 222.05/222.39 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 222.05/222.39 Found (x3 x20) as proof of (cNUMBER Xn)
% 222.05/222.39 Found (x3 x20) as proof of (cNUMBER Xn)
% 222.05/222.39 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 222.05/222.39 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))
% 222.05/222.39 Found x70:=(x7 x60):(cNUMBER Xn00)
% 222.05/222.39 Found (x7 x60) as proof of (cNUMBER Xn)
% 222.05/222.39 Found (x7 x60) as proof of (cNUMBER Xn)
% 222.05/222.39 Found (x7 x60) as proof of (cNUMBER Xn)
% 222.05/222.39 Found x30:=(x3 x20):(cNUMBER Xn0)
% 222.05/222.39 Found (x3 x20) as proof of (cNUMBER Xn)
% 222.05/222.39 Found (x3 x20) as proof of (cNUMBER Xn)
% 222.05/222.39 Found (x3 x20) as proof of (cNUMBER Xn)
% 222.05/222.39 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 222.05/222.39 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 222.05/222.39 Found (x3 x20) as proof of (cNUMBER Xn)
% 222.05/222.39 Found (x3 x20) as proof of (cNUMBER Xn)
% 222.05/222.39 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 222.05/222.39 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))
% 222.05/222.39 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 222.05/222.39 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 222.05/222.39 Found (x5 x40) as proof of (cNUMBER Xn)
% 222.05/222.39 Found (x5 x40) as proof of (cNUMBER Xn)
% 222.05/222.39 Found (x5 x40) as proof of (cNUMBER Xn)
% 222.05/222.39 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 222.05/222.39 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 222.05/222.39 Found (x3 x20) as proof of (cNUMBER Xn)
% 222.05/222.39 Found (x3 x20) as proof of (cNUMBER Xn)
% 222.05/222.39 Found (x3 x20) as proof of (cNUMBER Xn)
% 222.05/222.39 Found x40:=(x4 x50):((or (cEVEN Xn0)) (cODD Xn0))
% 222.05/222.39 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 222.05/222.39 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 222.05/222.39 Found x51:(cNUMBER Xn0)
% 222.05/222.39 Instantiate: Xn0:=Xn:fofType
% 222.05/222.39 Found (fun (x9:(cODD (cS c0)))=> x51) as proof of (cNUMBER Xn)
% 222.05/222.39 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))
% 222.05/222.39 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)))
% 222.05/222.39 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 222.05/222.39 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 222.05/222.39 Found (x5 x40) as proof of (cNUMBER Xn)
% 222.05/222.39 Found (x5 x40) as proof of (cNUMBER Xn)
% 222.05/222.39 Found (x5 x40) as proof of (cNUMBER Xn)
% 222.05/222.39 Found x50:=(x5 x40):(cNUMBER Xn0)
% 222.05/222.39 Found (x5 x40) as proof of (cNUMBER Xn)
% 222.05/222.39 Found (x5 x40) as proof of (cNUMBER Xn)
% 222.05/222.39 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 222.05/222.39 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))
% 222.05/222.39 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 222.05/222.39 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 222.05/222.39 Found (x3 x20) as proof of (cNUMBER Xn)
% 222.05/222.39 Found (x3 x20) as proof of (cNUMBER Xn)
% 222.05/222.39 Found (x3 x20) as proof of (cNUMBER Xn)
% 222.05/222.39 Found x50:=(x5 x40):(cNUMBER Xn00)
% 222.05/222.39 Instantiate: Xn00:=Xn:fofType
% 222.05/222.39 Found (x5 x40) as proof of (cNUMBER Xn)
% 222.05/222.39 Found (fun (x7:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 222.05/222.39 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x5 x40)) as proof of ((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn))
% 226.00/226.34 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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))))))->((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn)))
% 226.00/226.34 Found x30:=(x3 x20):(cNUMBER Xn0)
% 226.00/226.34 Instantiate: Xn0:=Xn:fofType
% 226.00/226.34 Found (x3 x20) as proof of (cNUMBER Xn)
% 226.00/226.34 Found (fun (x7:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 226.00/226.34 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x3 x20)) as proof of ((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn))
% 226.00/226.34 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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))))))->((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn)))
% 226.00/226.34 Found x50:=(x5 x40):(cNUMBER Xn0)
% 226.00/226.34 Found (x5 x40) as proof of (cNUMBER Xn)
% 226.00/226.34 Found (x5 x40) as proof of (cNUMBER Xn)
% 226.00/226.34 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 226.00/226.34 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))
% 226.00/226.34 Found x90:(cNUMBER Xn0)
% 226.00/226.34 Instantiate: Xn0:=Xn:fofType
% 226.00/226.34 Found x90 as proof of (cNUMBER Xn)
% 226.00/226.34 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 226.00/226.34 Instantiate: Xn00:=Xn:fofType
% 226.00/226.34 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x60) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 226.00/226.34 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)))
% 226.00/226.34 Found x300:=(x30 c0):((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 226.00/226.34 Found (x30 c0) as proof of ((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 226.00/226.34 Found (x30 c0) as proof of ((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 226.00/226.34 Found x300:=(x30 (cS Xx)):((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))
% 226.00/226.34 Found (x30 (cS Xx)) as proof of ((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))
% 226.00/226.34 Found (fun (x5:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx))) as proof of ((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))
% 228.27/228.61 Found (fun (Xx:fofType) (x5:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx))) as proof of (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))
% 228.27/228.61 Found (fun (Xx:fofType) (x5:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx))) as proof of (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))
% 228.27/228.61 Found ((conj00 (x30 c0)) (fun (Xx:fofType) (x5:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 228.27/228.61 Found (((conj0 (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))) (x30 c0)) (fun (Xx:fofType) (x5:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 228.27/228.61 Found ((((conj ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))) (x30 c0)) (fun (Xx:fofType) (x5:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 228.27/228.61 Found ((((conj ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))) (x30 c0)) (fun (Xx:fofType) (x5:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 228.27/228.61 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 228.27/228.61 Instantiate: Xn00:=Xn:fofType
% 228.27/228.61 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 228.27/228.61 Found x9:(cODD (cS c0))
% 228.27/228.61 Instantiate: Xn0:=(cS c0):fofType
% 228.27/228.61 Found x9 as proof of (cODD Xn0)
% 228.27/228.61 Found (or_introl00 x9) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 228.27/228.61 Found ((or_introl0 (cEVEN Xn0)) x9) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 228.27/228.61 Found (((or_introl (cODD Xn0)) (cEVEN Xn0)) x9) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 228.27/228.61 Found (((or_introl (cODD Xn0)) (cEVEN Xn0)) x9) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 228.27/228.61 Found (or_comm_i00 (((or_introl (cODD Xn0)) (cEVEN Xn0)) x9)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 228.27/228.61 Found ((or_comm_i0 (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x9)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 228.27/228.61 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x9)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 228.27/228.61 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x9)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 228.27/228.61 Found x300:=(x30 c0):((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 228.27/228.61 Found (x30 c0) as proof of ((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 228.27/228.61 Found (x30 c0) as proof of ((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 228.27/228.61 Found x50:=(x5 x40):(cNUMBER Xn0)
% 228.27/228.61 Found (x5 x40) as proof of (cNUMBER Xn)
% 228.27/228.61 Found (x5 x40) as proof of (cNUMBER Xn)
% 228.27/228.61 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 228.27/228.61 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 228.27/228.61 Found x60:((or (cEVEN Xn0)) (cODD Xn0))
% 228.27/228.61 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 228.27/228.61 Found (x7 x60) as proof of (cNUMBER Xn)
% 228.27/228.61 Found (x7 x60) as proof of (cNUMBER Xn)
% 228.27/228.61 Found (x7 x60) as proof of (cNUMBER Xn)
% 228.27/228.61 Found x300:=(x30 (cS Xx)):((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))
% 228.27/228.61 Found (x30 (cS Xx)) as proof of ((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))
% 228.27/228.61 Found (fun (x7:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx))) as proof of ((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))
% 235.92/236.28 Found (fun (Xx:fofType) (x7:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx))) as proof of (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))
% 235.92/236.28 Found (fun (Xx:fofType) (x7:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx))) as proof of (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))
% 235.92/236.28 Found ((conj00 (x30 c0)) (fun (Xx:fofType) (x7:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 235.92/236.28 Found (((conj0 (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))) (x30 c0)) (fun (Xx:fofType) (x7:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 235.92/236.28 Found ((((conj ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))) (x30 c0)) (fun (Xx:fofType) (x7:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 235.92/236.28 Found ((((conj ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))) (x30 c0)) (fun (Xx:fofType) (x7:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 235.92/236.28 Found x60:((or (cEVEN Xn0)) (cODD Xn0))
% 235.92/236.28 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 235.92/236.28 Found (x7 x60) as proof of (cNUMBER Xn)
% 235.92/236.28 Found (x7 x60) as proof of (cNUMBER Xn)
% 235.92/236.28 Found (x7 x60) as proof of (cNUMBER Xn)
% 235.92/236.28 Found x70:=(x7 x60):(cNUMBER Xn00)
% 235.92/236.28 Found (x7 x60) as proof of (cNUMBER Xn)
% 235.92/236.28 Found (x7 x60) as proof of (cNUMBER Xn)
% 235.92/236.28 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x7 x60)) as proof of (cNUMBER Xn)
% 235.92/236.28 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x7 x60)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 235.92/236.28 Found x50:(cNUMBER Xn0)
% 235.92/236.28 Instantiate: Xn0:=Xn:fofType
% 235.92/236.28 Found x50 as proof of (cNUMBER Xn)
% 235.92/236.28 Found x30:=(x3 x20):(cNUMBER Xn0)
% 235.92/236.28 Found (x3 x20) as proof of (cNUMBER Xn0)
% 235.92/236.28 Found (x3 x20) as proof of (cNUMBER Xn0)
% 235.92/236.28 Found x30:=(x3 x21):(cNUMBER Xn0)
% 235.92/236.28 Instantiate: Xn0:=Xn:fofType
% 235.92/236.28 Found (x3 x21) as proof of (cNUMBER Xn)
% 235.92/236.28 Found (fun (x9:(cODD (cS c0)))=> (x3 x21)) as proof of (cNUMBER Xn)
% 235.92/236.28 Found (fun (x9:(cODD (cS c0)))=> (x3 x21)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 235.92/236.28 Found x30:=(x3 x20):(cNUMBER Xn0)
% 235.92/236.28 Found (x3 x20) as proof of (cNUMBER Xn)
% 235.92/236.28 Found (x3 x20) as proof of (cNUMBER Xn)
% 235.92/236.28 Found (x3 x20) as proof of (cNUMBER Xn)
% 235.92/236.28 Found x50:=(x5 x40):(cNUMBER Xn00)
% 235.92/236.28 Found (x5 x40) as proof of (cNUMBER Xn)
% 235.92/236.28 Found (x5 x40) as proof of (cNUMBER Xn)
% 235.92/236.28 Found (x5 x40) as proof of (cNUMBER Xn)
% 235.92/236.28 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 235.92/236.28 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 235.92/236.28 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 235.92/236.28 Found x300:=(x30 c0):((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 235.92/236.28 Found (x30 c0) as proof of ((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 235.92/236.28 Found (x30 c0) as proof of ((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 235.92/236.28 Found x300:=(x30 (cS Xx)):((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))
% 235.92/236.28 Found (x30 (cS Xx)) as proof of ((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))
% 235.92/236.28 Found (fun (x8:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx))) as proof of ((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))
% 235.92/236.28 Found (fun (Xx:fofType) (x8:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx))) as proof of (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))
% 236.96/237.34 Found (fun (Xx:fofType) (x8:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx))) as proof of (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))
% 236.96/237.34 Found ((conj00 (x30 c0)) (fun (Xx:fofType) (x8:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 236.96/237.34 Found (((conj0 (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))) (x30 c0)) (fun (Xx:fofType) (x8:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 236.96/237.34 Found ((((conj ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))) (x30 c0)) (fun (Xx:fofType) (x8:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 236.96/237.34 Found ((((conj ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))) (x30 c0)) (fun (Xx:fofType) (x8:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 236.96/237.34 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 236.96/237.34 Instantiate: Xn00:=Xn:fofType
% 236.96/237.34 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 236.96/237.34 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 236.96/237.34 Instantiate: Xn0:=Xn:fofType
% 236.96/237.34 Found (fun (x7:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> x20) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 236.96/237.34 Found (fun (x7:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> x20) as proof of ((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->((or (cEVEN Xn00)) (cODD Xn00)))
% 236.96/237.34 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 236.96/237.34 Instantiate: Xn00:=Xn:fofType
% 236.96/237.34 Found (fun (x7:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> x40) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 236.96/237.34 Found (fun (x7:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> x40) as proof of ((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 236.96/237.34 Found x70:(cNUMBER Xn0)
% 236.96/237.34 Instantiate: Xn0:=Xn:fofType
% 236.96/237.34 Found x70 as proof of (cNUMBER Xn)
% 236.96/237.34 Found x30:=(x3 x20):(cNUMBER Xn0)
% 236.96/237.34 Instantiate: Xn0:=Xn:fofType
% 236.96/237.34 Found (x3 x20) as proof of (cNUMBER Xn)
% 236.96/237.34 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 236.96/237.34 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))
% 238.06/238.39 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)))
% 238.06/238.39 Found x50:=(x5 x40):(cNUMBER Xn0)
% 238.06/238.39 Instantiate: Xn0:=Xn:fofType
% 238.06/238.39 Found (x5 x40) as proof of (cNUMBER Xn)
% 238.06/238.39 Found (x5 x40) as proof of (cNUMBER Xn)
% 238.06/238.39 Found x90:=(x9 x80):(cNUMBER Xn0)
% 238.06/238.39 Instantiate: Xn0:=Xn:fofType
% 238.06/238.39 Found (x9 x80) as proof of (cNUMBER Xn)
% 238.06/238.39 Found (fun (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x9 x80)) as proof of (cNUMBER Xn)
% 238.06/238.39 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))
% 238.06/238.39 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)))
% 238.06/238.39 Found (and_rect50 (fun (x11:(cEVEN c0)) (x12:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x9 x80))) as proof of (cNUMBER Xn)
% 238.06/238.39 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)
% 238.06/238.39 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)
% 238.06/238.39 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)
% 238.06/238.39 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))
% 238.06/238.39 Found x51:(cNUMBER Xn0)
% 238.06/238.39 Instantiate: Xn0:=Xn:fofType
% 238.06/238.39 Found (fun (x9:(cODD (cS c0)))=> x51) as proof of (cNUMBER Xn)
% 238.06/238.39 Found (fun (x9:(cODD (cS c0)))=> x51) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 238.06/238.39 Found x50:(cNUMBER Xn0)
% 238.06/238.39 Instantiate: Xn0:=Xn:fofType
% 238.06/238.39 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of (cNUMBER Xn)
% 238.06/238.39 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))
% 238.06/238.39 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)))
% 238.06/238.39 Found x50:(cNUMBER Xn0)
% 238.06/238.39 Instantiate: Xn0:=Xn:fofType
% 238.06/238.39 Found (fun (x9:(cODD (cS c0)))=> x50) as proof of (cNUMBER Xn)
% 238.06/238.39 Found (fun (x9:(cODD (cS c0)))=> x50) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 240.73/241.08 Found x50:(cNUMBER Xn0)
% 240.73/241.08 Instantiate: Xn0:=Xn:fofType
% 240.73/241.08 Found (fun (x9:(cODD (cS c0)))=> x50) as proof of (cNUMBER Xn)
% 240.73/241.08 Found (fun (x9:(cODD (cS c0)))=> x50) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 240.73/241.08 Found x30:=(x3 x20):(cNUMBER Xn0)
% 240.73/241.08 Found (x3 x20) as proof of (cNUMBER Xn)
% 240.73/241.08 Found (x3 x20) as proof of (cNUMBER Xn)
% 240.73/241.08 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 240.73/241.08 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 240.73/241.08 Found x70:=(x7 x60):(cNUMBER Xn00)
% 240.73/241.08 Found (x7 x60) as proof of (cNUMBER Xn)
% 240.73/241.08 Found (x7 x60) as proof of (cNUMBER Xn)
% 240.73/241.08 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x7 x60)) as proof of (cNUMBER Xn)
% 240.73/241.08 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x7 x60)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 240.73/241.08 Found x50:(cNUMBER Xn0)
% 240.73/241.08 Instantiate: Xn0:=Xn:fofType
% 240.73/241.08 Found x50 as proof of (cNUMBER Xn)
% 240.73/241.08 Found x9:(cODD (cS c0))
% 240.73/241.08 Instantiate: Xn0:=(cS c0):fofType
% 240.73/241.08 Found x9 as proof of (cODD Xn0)
% 240.73/241.08 Found (or_intror00 x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 240.73/241.08 Found ((or_intror0 (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 240.73/241.08 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 240.73/241.08 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 240.73/241.08 Found (x5 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9)) as proof of (cNUMBER Xn0)
% 240.73/241.08 Found (fun (x9:(cODD (cS c0)))=> (x5 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9))) as proof of (cNUMBER Xn0)
% 240.73/241.08 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))
% 240.73/241.08 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)))
% 240.73/241.08 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)
% 240.73/241.08 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)
% 240.73/241.08 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)
% 240.73/241.08 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)
% 240.73/241.08 Found x30:(cNUMBER Xn0)
% 240.73/241.08 Instantiate: Xn0:=Xn:fofType
% 240.73/241.08 Found (fun (x9:(cODD (cS c0)))=> x30) as proof of (cNUMBER Xn)
% 240.73/241.08 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))
% 240.73/241.08 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)))
% 240.73/241.08 Found x30:(cNUMBER Xn0)
% 240.73/241.08 Instantiate: Xn0:=Xn:fofType
% 240.73/241.08 Found (fun (x9:(cODD (cS c0)))=> x30) as proof of (cNUMBER Xn)
% 243.32/243.67 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))
% 243.32/243.67 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)))
% 243.32/243.67 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 243.32/243.67 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 243.32/243.67 Found (x5 x40) as proof of (cNUMBER Xn)
% 243.32/243.67 Found (x5 x40) as proof of (cNUMBER Xn)
% 243.32/243.67 Found (x5 x40) as proof of (cNUMBER Xn)
% 243.32/243.67 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 243.32/243.67 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 243.32/243.67 Found (x5 x40) as proof of (cNUMBER Xn)
% 243.32/243.67 Found (x5 x40) as proof of (cNUMBER Xn)
% 243.32/243.67 Found (x5 x40) as proof of (cNUMBER Xn)
% 243.32/243.67 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 243.32/243.67 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 243.32/243.67 Found (x3 x20) as proof of (cNUMBER Xn)
% 243.32/243.67 Found (x3 x20) as proof of (cNUMBER Xn)
% 243.32/243.67 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 243.32/243.67 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))
% 243.32/243.67 Found x30:=(x3 x20):(cNUMBER Xn0)
% 243.32/243.67 Found (x3 x20) as proof of (cNUMBER Xn0)
% 243.32/243.67 Found (x3 x20) as proof of (cNUMBER Xn0)
% 243.32/243.67 Found x30:=(x3 x21):(cNUMBER Xn0)
% 243.32/243.67 Instantiate: Xn0:=Xn:fofType
% 243.32/243.67 Found (x3 x21) as proof of (cNUMBER Xn)
% 243.32/243.67 Found (x3 x21) as proof of (cNUMBER Xn)
% 243.32/243.67 Found x30:=(x3 x20):(cNUMBER Xn0)
% 243.32/243.67 Found (x3 x20) as proof of (cNUMBER Xn)
% 243.32/243.67 Found (x3 x20) as proof of (cNUMBER Xn)
% 243.32/243.67 Found (x3 x20) as proof of (cNUMBER Xn)
% 243.32/243.67 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 243.32/243.67 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 243.32/243.67 Found (x3 x20) as proof of (cNUMBER Xn)
% 243.32/243.67 Found (x3 x20) as proof of (cNUMBER Xn)
% 243.32/243.67 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 243.32/243.67 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))
% 243.32/243.67 Found x30:=(x3 x20):(cNUMBER Xn0)
% 243.32/243.67 Instantiate: Xn0:=Xn:fofType
% 243.32/243.67 Found (x3 x20) as proof of (cNUMBER Xn)
% 243.32/243.67 Found (x3 x20) as proof of (cNUMBER Xn)
% 243.32/243.67 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 243.32/243.67 Instantiate: Xn00:=Xn:fofType
% 243.32/243.67 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x60) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 243.32/243.67 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)))
% 243.32/243.67 Found x30:=(x3 x20):(cNUMBER Xn0)
% 243.32/243.67 Instantiate: Xn0:=Xn:fofType
% 243.32/243.67 Found (x3 x20) as proof of (cNUMBER Xn)
% 243.32/243.67 Found (x3 x20) as proof of (cNUMBER Xn)
% 243.32/243.67 Found x90:(cNUMBER Xn0)
% 243.32/243.67 Instantiate: Xn0:=Xn:fofType
% 243.32/243.67 Found x90 as proof of (cNUMBER Xn)
% 243.32/243.67 Found x50:=(x5 x40):(cNUMBER Xn0)
% 243.32/243.67 Found (x5 x40) as proof of (cNUMBER Xn)
% 243.32/243.67 Found (x5 x40) as proof of (cNUMBER Xn)
% 243.32/243.67 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 243.32/243.67 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))
% 243.32/243.67 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)))
% 243.32/243.67 Found x50:=(x5 x40):(cNUMBER Xn0)
% 243.32/243.67 Found (x5 x40) as proof of (cNUMBER Xn)
% 243.32/243.67 Found (x5 x40) as proof of (cNUMBER Xn)
% 243.32/243.67 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 243.32/243.67 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))
% 246.23/246.56 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)))
% 246.23/246.56 Found x70:=(x7 x60):(cNUMBER Xn0)
% 246.23/246.56 Instantiate: Xn0:=Xn:fofType
% 246.23/246.56 Found (x7 x60) as proof of (cNUMBER Xn)
% 246.23/246.56 Found (x7 x60) as proof of (cNUMBER Xn)
% 246.23/246.56 Found x60:=(x6 x70):((or (cEVEN Xn00)) (cODD Xn00))
% 246.23/246.56 Instantiate: Xn00:=Xn:fofType
% 246.23/246.56 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 246.23/246.56 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 246.23/246.56 Found x40:=(x4 x50):((or (cEVEN Xn0)) (cODD Xn0))
% 246.23/246.56 Instantiate: Xn0:=Xn:fofType
% 246.23/246.56 Found (x4 x50) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 246.23/246.56 Found (x4 x50) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 246.23/246.56 Found x30:=(x3 x20):(cNUMBER Xn0)
% 246.23/246.56 Found (x3 x20) as proof of (cNUMBER Xn)
% 246.23/246.56 Found (x3 x20) as proof of (cNUMBER Xn)
% 246.23/246.56 Found (fun (x9:(cODD (cS c0)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 246.23/246.56 Found (fun (x9:(cODD (cS c0)))=> (x3 x20)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 246.23/246.56 Found x300:=(x30 (cS Xx)):((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))
% 246.23/246.56 Found (x30 (cS Xx)) as proof of ((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))
% 246.23/246.56 Found (fun (x5:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx))) as proof of ((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))
% 246.23/246.56 Found (fun (Xx:fofType) (x5:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx))) as proof of (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))
% 246.23/246.56 Found (fun (Xx:fofType) (x5:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx))) as proof of (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))
% 246.23/246.56 Found ((conj00 (x30 c0)) (fun (Xx:fofType) (x5:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 246.23/246.56 Found (((conj0 (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))) (x30 c0)) (fun (Xx:fofType) (x5:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 246.23/246.56 Found ((((conj ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))) (x30 c0)) (fun (Xx:fofType) (x5:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 246.23/246.56 Found ((((conj ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))) (x30 c0)) (fun (Xx:fofType) (x5:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 246.23/246.56 Found x30:=(x3 x21):(cNUMBER Xn0)
% 246.23/246.56 Found (x3 x21) as proof of (cNUMBER Xn0)
% 246.23/246.56 Found (x3 x21) as proof of (cNUMBER Xn0)
% 246.23/246.56 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 246.23/246.56 Instantiate: Xn0:=Xn:fofType
% 246.23/246.56 Found x40 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 246.23/246.56 Found (x7 x40) as proof of (cNUMBER Xn)
% 246.23/246.56 Found (x7 x40) as proof of (cNUMBER Xn)
% 246.23/246.56 Found (x7 x40) as proof of (cNUMBER Xn)
% 246.23/246.56 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 246.23/246.56 Instantiate: Xn00:=Xn:fofType
% 247.82/248.18 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 247.82/248.18 Found (x5 x60) as proof of (cNUMBER Xn)
% 247.82/248.18 Found (x5 x60) as proof of (cNUMBER Xn)
% 247.82/248.18 Found (x5 x60) as proof of (cNUMBER Xn)
% 247.82/248.18 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 247.82/248.18 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 247.82/248.18 Found (x5 x40) as proof of (cNUMBER Xn)
% 247.82/248.18 Found (x5 x40) as proof of (cNUMBER Xn)
% 247.82/248.18 Found (x5 x40) as proof of (cNUMBER Xn)
% 247.82/248.18 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 247.82/248.18 Found x60 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 247.82/248.18 Found (x7 x60) as proof of (cNUMBER Xn)
% 247.82/248.18 Found (x7 x60) as proof of (cNUMBER Xn)
% 247.82/248.18 Found (x7 x60) as proof of (cNUMBER Xn)
% 247.82/248.18 Found x30:=(x3 x20):(cNUMBER Xn0)
% 247.82/248.18 Found (x3 x20) as proof of (cNUMBER Xn)
% 247.82/248.18 Found (x3 x20) as proof of (cNUMBER Xn)
% 247.82/248.18 Found (fun (x7:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 247.82/248.18 Found (fun (x7:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x3 x20)) as proof of ((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn))
% 247.82/248.18 Found x50:=(x5 x40):(cNUMBER Xn0)
% 247.82/248.18 Found (x5 x40) as proof of (cNUMBER Xn)
% 247.82/248.18 Found (x5 x40) as proof of (cNUMBER Xn)
% 247.82/248.18 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 247.82/248.18 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))
% 247.82/248.18 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)))
% 247.82/248.18 Found x50:=(x5 x40):(cNUMBER Xn00)
% 247.82/248.18 Found (x5 x40) as proof of (cNUMBER Xn)
% 247.82/248.18 Found (x5 x40) as proof of (cNUMBER Xn)
% 247.82/248.18 Found (fun (x7:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 247.82/248.18 Found (fun (x7:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x5 x40)) as proof of ((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn))
% 247.82/248.18 Found x60:((or (cEVEN Xn0)) (cODD Xn0))
% 247.82/248.18 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 247.82/248.18 Found (x7 x60) as proof of (cNUMBER Xn)
% 247.82/248.18 Found (x7 x60) as proof of (cNUMBER Xn)
% 247.82/248.18 Found (fun (x7:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x7 x60)) as proof of (cNUMBER Xn)
% 247.82/248.18 Found (fun (x7:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x7 x60)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 247.82/248.18 Found x300:=(x30 c0):((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 247.82/248.18 Found (x30 c0) as proof of ((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 247.82/248.18 Found (x30 c0) as proof of ((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 247.82/248.18 Found x9:(cODD (cS c0))
% 247.82/248.18 Instantiate: Xn0:=(cS c0):fofType
% 247.82/248.18 Found x9 as proof of (cODD Xn0)
% 247.82/248.18 Found (or_intror00 x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 247.82/248.18 Found ((or_intror0 (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 247.82/248.18 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 247.82/248.18 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 248.53/248.87 Found (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9)) as proof of (cNUMBER Xn0)
% 248.53/248.87 Found (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9)) as proof of (cNUMBER Xn0)
% 248.53/248.87 Found x20:=(x2 x31):((or (cEVEN Xn0)) (cODD Xn0))
% 248.53/248.87 Found (x2 x31) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 248.53/248.87 Found (x2 x31) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 248.53/248.87 Found x32:(cNUMBER Xn0)
% 248.53/248.87 Instantiate: Xn0:=Xn:fofType
% 248.53/248.87 Found (fun (x5:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> x32) as proof of (cNUMBER Xn)
% 248.53/248.87 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> x32) as proof of ((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn))
% 248.53/248.87 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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))))))->((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn)))
% 248.53/248.87 Found x50:=(x5 x40):(cNUMBER Xn0)
% 248.53/248.87 Found (x5 x40) as proof of (cNUMBER Xn0)
% 248.53/248.87 Found (x5 x40) as proof of (cNUMBER Xn0)
% 248.53/248.87 Found x50:=(x5 x41):(cNUMBER Xn0)
% 248.53/248.87 Instantiate: Xn0:=Xn:fofType
% 248.53/248.87 Found (x5 x41) as proof of (cNUMBER Xn)
% 248.53/248.87 Found (fun (x9:(cODD (cS c0)))=> (x5 x41)) as proof of (cNUMBER Xn)
% 248.53/248.87 Found (fun (x9:(cODD (cS c0)))=> (x5 x41)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 248.53/248.87 Found x60:((or (cEVEN Xn0)) (cODD Xn0))
% 248.53/248.87 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 248.53/248.87 Found (x7 x60) as proof of (cNUMBER Xn)
% 248.53/248.87 Found (x7 x60) as proof of (cNUMBER Xn)
% 248.53/248.87 Found (fun (x7:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x7 x60)) as proof of (cNUMBER Xn)
% 248.53/248.87 Found (fun (x7:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x7 x60)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 248.53/248.87 Found x61:((or (cEVEN Xn0)) (cODD Xn0))
% 248.53/248.87 Found x61 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 248.53/248.87 Found (x7 x61) as proof of (cNUMBER Xn)
% 248.53/248.87 Found (x7 x61) as proof of (cNUMBER Xn)
% 248.53/248.87 Found (fun (x7:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x7 x61)) as proof of (cNUMBER Xn)
% 248.53/248.87 Found (fun (x7:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x7 x61)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 248.53/248.87 Found x60:((or (cEVEN Xn0)) (cODD Xn0))
% 248.53/248.87 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 248.53/248.87 Found (x7 x60) as proof of (cNUMBER Xn)
% 248.53/248.87 Found (x7 x60) as proof of (cNUMBER Xn)
% 248.53/248.87 Found (x7 x60) as proof of (cNUMBER Xn)
% 248.53/248.87 Found x70:=(x7 (cS c0)):((cODD (cS c0))->(cODD (cS (cS (cS c0)))))
% 248.53/248.87 Found (x7 (cS c0)) as proof of ((cODD (cS c0))->(cODD Xn0))
% 248.53/248.87 Found (x7 (cS c0)) as proof of ((cODD (cS c0))->(cODD Xn0))
% 248.53/248.87 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))
% 248.53/248.87 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)))
% 248.53/248.88 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)
% 248.53/248.88 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)
% 248.53/248.88 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)
% 248.53/248.88 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)
% 248.53/248.88 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))
% 248.53/248.88 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)))
% 248.53/248.88 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)
% 248.53/248.88 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)
% 248.53/248.88 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)))))))=> (x7 (cS c0)))))) as proof of (cODD Xn0)
% 248.53/248.89 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)) (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)
% 248.53/248.89 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)))))))=> (x7 (cS c0))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 248.53/248.89 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)))))))=> (x7 (cS c0))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 248.53/248.89 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)))))))=> (x7 (cS c0))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 251.04/251.39 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)))))))=> (x7 (cS c0))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 251.04/251.39 Found x30:=(x3 x21):(cNUMBER Xn0)
% 251.04/251.39 Found (x3 x21) as proof of (cNUMBER Xn0)
% 251.04/251.39 Found (x3 x21) as proof of (cNUMBER Xn0)
% 251.04/251.39 Found x30:=(x3 x22):(cNUMBER Xn0)
% 251.04/251.39 Instantiate: Xn0:=Xn:fofType
% 251.04/251.39 Found (x3 x22) as proof of (cNUMBER Xn)
% 251.04/251.39 Found (x3 x22) as proof of (cNUMBER Xn)
% 251.04/251.39 Found x30:=(x3 x22):(cNUMBER Xn0)
% 251.04/251.39 Found (x3 x22) as proof of (cNUMBER Xn)
% 251.04/251.39 Found (x3 x22) as proof of (cNUMBER Xn)
% 251.04/251.39 Found (x3 x22) as proof of (cNUMBER Xn)
% 251.04/251.39 Found x50:(cNUMBER Xn0)
% 251.04/251.39 Instantiate: Xn0:=Xn:fofType
% 251.04/251.39 Found x50 as proof of (cNUMBER Xn)
% 251.04/251.39 Found x9:(cODD (cS c0))
% 251.04/251.39 Instantiate: Xn0:=(cS c0):fofType
% 251.04/251.39 Found x9 as proof of (cODD Xn0)
% 251.04/251.39 Found (or_intror00 x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 251.04/251.39 Found ((or_intror0 (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 251.04/251.39 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 251.04/251.39 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 251.04/251.39 Found x11:(cEVEN c0)
% 251.04/251.39 Instantiate: Xn0:=c0:fofType
% 251.04/251.39 Found x11 as proof of (cEVEN Xn0)
% 251.04/251.39 Found (or_introl00 x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 251.04/251.39 Found ((or_introl0 (cODD Xn0)) x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 251.04/251.39 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 251.04/251.39 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 251.04/251.39 Found x50:(cNUMBER Xn0)
% 251.04/251.39 Instantiate: Xn0:=Xn:fofType
% 251.04/251.39 Found x50 as proof of (cNUMBER Xn)
% 251.04/251.39 Found or_introl00:=(or_introl0 (cEVEN Xn0)):((cODD (cS c0))->((or (cODD (cS c0))) (cEVEN Xn0)))
% 251.04/251.39 Found (or_introl0 (cEVEN Xn0)) as proof of ((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0)))
% 251.04/251.39 Found ((or_introl (cODD (cS c0))) (cEVEN Xn0)) as proof of ((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0)))
% 251.04/251.39 Found ((or_introl (cODD (cS c0))) (cEVEN Xn0)) as proof of ((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0)))
% 251.04/251.39 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)))
% 251.04/251.39 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))))
% 251.08/251.40 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))
% 251.08/251.40 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))
% 251.08/251.40 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))
% 251.08/251.40 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))
% 251.08/251.40 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)))
% 251.08/251.40 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))))
% 251.08/251.40 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))
% 251.08/251.40 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))
% 251.08/251.41 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))
% 251.08/251.41 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))
% 251.08/251.41 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))
% 251.08/251.41 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))
% 252.60/252.95 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))
% 252.60/252.95 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))
% 252.60/252.95 Found x40:=(x4 x50):((or (cEVEN Xn0)) (cODD Xn0))
% 252.60/252.95 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 252.60/252.95 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 252.60/252.95 Found x7:(cODD (cS c0))
% 252.60/252.95 Instantiate: Xn0:=(cS c0):fofType
% 252.60/252.95 Found x7 as proof of (cODD Xn0)
% 252.60/252.95 Found (or_intror00 x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 252.60/252.95 Found ((or_intror0 (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 252.60/252.95 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 252.60/252.95 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 252.60/252.95 Found x11:(cEVEN c0)
% 252.60/252.95 Instantiate: Xn0:=c0:fofType
% 252.60/252.95 Found x11 as proof of (cEVEN Xn0)
% 252.60/252.95 Found (or_introl00 x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 252.60/252.95 Found ((or_introl0 (cODD Xn0)) x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 252.60/252.95 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 252.60/252.95 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 252.60/252.95 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 252.60/252.95 Instantiate: Xn00:=Xn:fofType
% 252.60/252.95 Found (fun (x7:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> x40) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 256.33/256.65 Found (fun (x7:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> x40) as proof of ((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 256.33/256.65 Found x9:(cODD (cS c0))
% 256.33/256.65 Instantiate: Xn0:=(cS c0):fofType
% 256.33/256.65 Found x9 as proof of (cODD Xn0)
% 256.33/256.65 Found (or_intror00 x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 256.33/256.65 Found ((or_intror0 (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 256.33/256.65 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 256.33/256.65 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 256.33/256.65 Found (x5 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9)) as proof of (cNUMBER Xn0)
% 256.33/256.65 Found (x5 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9)) as proof of (cNUMBER Xn0)
% 256.33/256.65 Found x300:=(x30 c0):((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 256.33/256.65 Found (x30 c0) as proof of ((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 256.33/256.65 Found (x30 c0) as proof of ((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 256.33/256.65 Found x300:=(x30 c0):((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 256.33/256.65 Found (x30 c0) as proof of ((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 256.33/256.65 Found (x30 c0) as proof of ((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 256.33/256.65 Found x60:=(x6 x70):((or (cEVEN Xn00)) (cODD Xn00))
% 256.33/256.65 Instantiate: Xn00:=Xn:fofType
% 256.33/256.65 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 256.33/256.65 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 256.33/256.65 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 256.33/256.65 Instantiate: Xn0:=Xn:fofType
% 256.33/256.65 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 256.33/256.65 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 256.33/256.65 Found x50:=(x5 x41):(cNUMBER Xn0)
% 256.33/256.65 Instantiate: Xn0:=Xn:fofType
% 256.33/256.65 Found (x5 x41) as proof of (cNUMBER Xn)
% 256.33/256.65 Found (fun (x9:(cODD (cS c0)))=> (x5 x41)) as proof of (cNUMBER Xn)
% 256.33/256.65 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))
% 256.33/256.65 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)))
% 256.33/256.65 Found x300:=(x30 (cS Xx)):((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))
% 256.33/256.65 Found (x30 (cS Xx)) as proof of ((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))
% 256.33/256.65 Found (fun (x6:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx))) as proof of ((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))
% 256.33/256.65 Found (fun (Xx:fofType) (x6:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx))) as proof of (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))
% 256.33/256.65 Found (fun (Xx:fofType) (x6:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx))) as proof of (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))
% 256.33/256.65 Found ((conj00 (x30 c0)) (fun (Xx:fofType) (x6:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 256.33/256.65 Found (((conj0 (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))) (x30 c0)) (fun (Xx:fofType) (x6:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 256.33/256.65 Found ((((conj ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))) (x30 c0)) (fun (Xx:fofType) (x6:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 257.12/257.50 Found ((((conj ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))) (x30 c0)) (fun (Xx:fofType) (x6:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 257.12/257.50 Found x50:(cNUMBER Xn0)
% 257.12/257.50 Instantiate: Xn0:=Xn:fofType
% 257.12/257.50 Found x50 as proof of (cNUMBER Xn)
% 257.12/257.50 Found x70:(cNUMBER Xn0)
% 257.12/257.50 Instantiate: Xn0:=Xn:fofType
% 257.12/257.50 Found x70 as proof of (cNUMBER Xn)
% 257.12/257.50 Found x50:=(x5 x40):(cNUMBER Xn0)
% 257.12/257.50 Instantiate: Xn0:=Xn:fofType
% 257.12/257.50 Found (x5 x40) as proof of (cNUMBER Xn)
% 257.12/257.50 Found (x5 x40) as proof of (cNUMBER Xn)
% 257.12/257.50 Found x50:=(x5 x40):(cNUMBER Xn0)
% 257.12/257.50 Instantiate: Xn0:=Xn:fofType
% 257.12/257.50 Found (x5 x40) as proof of (cNUMBER Xn)
% 257.12/257.50 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 257.12/257.50 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))
% 257.12/257.50 Found x70:=(x7 x60):(cNUMBER Xn0)
% 257.12/257.50 Found (x7 x60) as proof of (cNUMBER Xn0)
% 257.12/257.50 Found (x7 x60) as proof of (cNUMBER Xn0)
% 257.12/257.50 Found x300:=(x30 (cS Xx)):((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))
% 257.12/257.50 Found (x30 (cS Xx)) as proof of ((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))
% 257.12/257.50 Found (fun (x8:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx))) as proof of ((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))
% 257.12/257.50 Found (fun (Xx:fofType) (x8:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx))) as proof of (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))
% 257.12/257.50 Found (fun (Xx:fofType) (x8:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx))) as proof of (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))
% 257.12/257.50 Found ((conj00 (x30 c0)) (fun (Xx:fofType) (x8:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 257.12/257.50 Found (((conj0 (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))) (x30 c0)) (fun (Xx:fofType) (x8:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 257.12/257.50 Found ((((conj ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))) (x30 c0)) (fun (Xx:fofType) (x8:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 257.12/257.50 Found ((((conj ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))) (x30 c0)) (fun (Xx:fofType) (x8:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 257.12/257.50 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 257.12/257.50 Instantiate: Xn00:=Xn:fofType
% 257.12/257.50 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 257.12/257.50 Found (x3 x60) as proof of (cNUMBER Xn)
% 257.12/257.50 Found (x3 x60) as proof of (cNUMBER Xn)
% 257.12/257.50 Found (x3 x60) as proof of (cNUMBER Xn)
% 257.12/257.50 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 257.12/257.53 Instantiate: Xn0:=Xn:fofType
% 257.12/257.53 Found (fun (x7:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> x20) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 257.12/257.53 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> x20) as proof of ((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->((or (cEVEN Xn00)) (cODD Xn00)))
% 257.12/257.53 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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))))))->((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->((or (cEVEN Xn00)) (cODD Xn00))))
% 257.12/257.53 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 257.12/257.53 Found x60 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 257.12/257.53 Found (x7 x60) as proof of (cNUMBER Xn)
% 257.12/257.53 Found (x7 x60) as proof of (cNUMBER Xn)
% 257.12/257.53 Found (x7 x60) as proof of (cNUMBER Xn)
% 257.12/257.53 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 257.12/257.53 Instantiate: Xn00:=Xn:fofType
% 257.12/257.53 Found (fun (x7:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> x40) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 257.12/257.53 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> x40) as proof of ((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 257.12/257.53 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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))))))->((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->((or (cEVEN Xn0)) (cODD Xn0))))
% 257.12/257.53 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 261.72/262.06 Instantiate: Xn0:=Xn:fofType
% 261.72/262.06 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 261.72/262.06 Found (x7 x20) as proof of (cNUMBER Xn)
% 261.72/262.06 Found (x7 x20) as proof of (cNUMBER Xn)
% 261.72/262.06 Found (x7 x20) as proof of (cNUMBER Xn)
% 261.72/262.06 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 261.72/262.06 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 261.72/262.06 Found (x3 x20) as proof of (cNUMBER Xn)
% 261.72/262.06 Found (x3 x20) as proof of (cNUMBER Xn)
% 261.72/262.06 Found (x3 x20) as proof of (cNUMBER Xn)
% 261.72/262.06 Found x32:(cNUMBER Xn0)
% 261.72/262.06 Instantiate: Xn0:=Xn:fofType
% 261.72/262.06 Found (fun (x5:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> x32) as proof of (cNUMBER Xn)
% 261.72/262.06 Found (fun (x5:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> x32) as proof of ((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn))
% 261.72/262.06 Found x30:=(x3 x20):(cNUMBER Xn0)
% 261.72/262.06 Found (x3 x20) as proof of (cNUMBER Xn)
% 261.72/262.06 Found (x3 x20) as proof of (cNUMBER Xn)
% 261.72/262.06 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 261.72/262.06 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))
% 261.72/262.06 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)))
% 261.72/262.06 Found x300:=(x30 c0):((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 261.72/262.06 Found (x30 c0) as proof of ((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 261.72/262.06 Found (x30 c0) as proof of ((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 261.72/262.06 Found x50:(cNUMBER Xn0)
% 261.72/262.06 Instantiate: Xn0:=Xn:fofType
% 261.72/262.06 Found (fun (x9:(cODD (cS c0)))=> x50) as proof of (cNUMBER Xn)
% 261.72/262.06 Found (fun (x9:(cODD (cS c0)))=> x50) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 261.72/262.06 Found x50:(cNUMBER Xn0)
% 261.72/262.06 Instantiate: Xn0:=Xn:fofType
% 261.72/262.06 Found (fun (x9:(cODD (cS c0)))=> x50) as proof of (cNUMBER Xn)
% 261.72/262.06 Found (fun (x9:(cODD (cS c0)))=> x50) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 261.72/262.06 Found x51:(cNUMBER Xn0)
% 261.72/262.06 Instantiate: Xn0:=Xn:fofType
% 261.72/262.06 Found (fun (x9:(cODD (cS c0)))=> x51) as proof of (cNUMBER Xn)
% 261.72/262.06 Found (fun (x9:(cODD (cS c0)))=> x51) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 261.72/262.06 Found x60:=(x6 x70):((or (cEVEN Xn0)) (cODD Xn0))
% 261.72/262.06 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 261.72/262.06 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 261.72/262.06 Found x71:(cNUMBER Xn0)
% 261.72/262.06 Instantiate: Xn0:=Xn:fofType
% 261.72/262.06 Found (fun (x9:(cODD (cS c0)))=> x71) as proof of (cNUMBER Xn)
% 261.72/262.06 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))
% 261.72/262.06 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)))
% 261.72/262.06 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 261.72/262.06 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 261.72/262.06 Found (x5 x40) as proof of (cNUMBER Xn)
% 261.72/262.06 Found (x5 x40) as proof of (cNUMBER Xn)
% 261.72/262.06 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 261.72/262.06 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))
% 261.72/262.06 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 261.72/262.06 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 261.72/262.06 Found (x5 x40) as proof of (cNUMBER Xn)
% 261.72/262.06 Found (x5 x40) as proof of (cNUMBER Xn)
% 261.72/262.06 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 264.92/265.28 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))
% 264.92/265.28 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 264.92/265.28 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 264.92/265.28 Found (x5 x40) as proof of (cNUMBER Xn)
% 264.92/265.28 Found (x5 x40) as proof of (cNUMBER Xn)
% 264.92/265.28 Found (x5 x40) as proof of (cNUMBER Xn)
% 264.92/265.28 Found x60:=(x6 x70):((or (cEVEN Xn00)) (cODD Xn00))
% 264.92/265.28 Instantiate: Xn00:=Xn:fofType
% 264.92/265.28 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 264.92/265.28 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 264.92/265.28 Found x30:=(x3 x20):(cNUMBER Xn0)
% 264.92/265.28 Found (x3 x20) as proof of (cNUMBER Xn0)
% 264.92/265.28 Found (x3 x20) as proof of (cNUMBER Xn0)
% 264.92/265.28 Found x30:=(x3 x21):(cNUMBER Xn0)
% 264.92/265.28 Instantiate: Xn0:=Xn:fofType
% 264.92/265.28 Found (x3 x21) as proof of (cNUMBER Xn)
% 264.92/265.28 Found (x3 x21) as proof of (cNUMBER Xn)
% 264.92/265.28 Found x30:=(x3 x20):(cNUMBER Xn0)
% 264.92/265.28 Found (x3 x20) as proof of (cNUMBER Xn)
% 264.92/265.28 Found (x3 x20) as proof of (cNUMBER Xn)
% 264.92/265.28 Found (x3 x20) as proof of (cNUMBER Xn)
% 264.92/265.28 Found x30:=(x3 x20):(cNUMBER Xn0)
% 264.92/265.28 Instantiate: Xn0:=Xn:fofType
% 264.92/265.28 Found (x3 x20) as proof of (cNUMBER Xn)
% 264.92/265.28 Found (x3 x20) as proof of (cNUMBER Xn)
% 264.92/265.28 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 264.92/265.28 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 264.92/265.28 Found (x3 x20) as proof of (cNUMBER Xn)
% 264.92/265.28 Found (x3 x20) as proof of (cNUMBER Xn)
% 264.92/265.28 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 264.92/265.28 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))
% 264.92/265.28 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)))
% 264.92/265.28 Found x30:=(x3 x20):(cNUMBER Xn0)
% 264.92/265.28 Instantiate: Xn0:=Xn:fofType
% 264.92/265.28 Found (x3 x20) as proof of (cNUMBER Xn)
% 264.92/265.28 Found (x3 x20) as proof of (cNUMBER Xn)
% 264.92/265.28 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 264.92/265.28 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 264.92/265.28 Found (x3 x20) as proof of (cNUMBER Xn)
% 264.92/265.28 Found (x3 x20) as proof of (cNUMBER Xn)
% 264.92/265.28 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 264.92/265.28 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))
% 264.92/265.28 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)))
% 264.92/265.28 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 264.92/265.28 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 264.92/265.28 Found (x5 x40) as proof of (cNUMBER Xn)
% 264.92/265.28 Found (x5 x40) as proof of (cNUMBER Xn)
% 264.92/265.28 Found (x5 x40) as proof of (cNUMBER Xn)
% 264.92/265.28 Found or_comm_i100:=(or_comm_i10 x20):((or (cODD Xn0)) (cEVEN Xn0))
% 264.92/265.28 Found (or_comm_i10 x20) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 264.92/265.28 Found ((or_comm_i1 (cODD Xn0)) x20) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 264.92/265.28 Found (((or_comm_i (cEVEN Xn0)) (cODD Xn0)) x20) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 264.92/265.28 Found (((or_comm_i (cEVEN Xn0)) (cODD Xn0)) x20) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 264.92/265.28 Found x70:=(x7 x60):(cNUMBER Xn0)
% 264.92/265.28 Instantiate: Xn0:=Xn:fofType
% 264.92/265.28 Found (x7 x60) as proof of (cNUMBER Xn)
% 264.92/265.28 Found (fun (x7:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x7 x60)) as proof of (cNUMBER Xn)
% 264.92/265.28 Found (fun (x7:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x7 x60)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 267.88/268.21 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 267.88/268.21 Instantiate: Xn0:=Xn:fofType
% 267.88/268.21 Found x40 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 267.88/268.21 Found (x7 x40) as proof of (cNUMBER Xn)
% 267.88/268.21 Found (x7 x40) as proof of (cNUMBER Xn)
% 267.88/268.21 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x7 x40)) as proof of (cNUMBER Xn)
% 267.88/268.21 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x7 x40)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 267.88/268.21 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 267.88/268.21 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 267.88/268.21 Found (x5 x40) as proof of (cNUMBER Xn)
% 267.88/268.21 Found (x5 x40) as proof of (cNUMBER Xn)
% 267.88/268.21 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 267.88/268.21 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 267.88/268.21 Found x90:(cNUMBER Xn0)
% 267.88/268.21 Instantiate: Xn0:=Xn:fofType
% 267.88/268.21 Found x90 as proof of (cNUMBER Xn)
% 267.88/268.21 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 267.88/268.21 Instantiate: Xn00:=Xn:fofType
% 267.88/268.21 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 267.88/268.21 Found (x5 x60) as proof of (cNUMBER Xn)
% 267.88/268.21 Found (x5 x60) as proof of (cNUMBER Xn)
% 267.88/268.21 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x60)) as proof of (cNUMBER Xn)
% 267.88/268.21 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x60)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 267.88/268.21 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 267.88/268.21 Found x60 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 267.88/268.21 Found (x7 x60) as proof of (cNUMBER Xn)
% 267.88/268.21 Found (x7 x60) as proof of (cNUMBER Xn)
% 267.88/268.21 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x7 x60)) as proof of (cNUMBER Xn)
% 267.88/268.21 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x7 x60)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 267.88/268.21 Found x30:=(x3 x20):(cNUMBER Xn0)
% 267.88/268.21 Found (x3 x20) as proof of (cNUMBER Xn)
% 267.88/268.21 Found (x3 x20) as proof of (cNUMBER Xn)
% 267.88/268.21 Found (x3 x20) as proof of (cNUMBER Xn)
% 267.88/268.21 Found x70:=(x7 x60):(cNUMBER Xn0)
% 267.88/268.21 Instantiate: Xn0:=Xn:fofType
% 267.88/268.21 Found (x7 x60) as proof of (cNUMBER Xn)
% 267.88/268.21 Found (x7 x60) as proof of (cNUMBER Xn)
% 267.88/268.21 Found x40:=(x4 x50):((or (cEVEN Xn00)) (cODD Xn00))
% 267.88/268.21 Instantiate: Xn00:=Xn:fofType
% 267.88/268.21 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 267.88/268.21 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 267.88/268.21 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 267.88/268.21 Instantiate: Xn0:=Xn:fofType
% 267.88/268.21 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 267.88/268.21 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 267.88/268.21 Found x9:(cODD (cS c0))
% 267.88/268.21 Instantiate: Xn0:=(cS c0):fofType
% 267.88/268.21 Found x9 as proof of (cODD Xn0)
% 267.88/268.21 Found (or_introl00 x9) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 267.88/268.21 Found ((or_introl0 (cEVEN Xn0)) x9) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 267.88/268.21 Found (((or_introl (cODD Xn0)) (cEVEN Xn0)) x9) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 267.88/268.21 Found (((or_introl (cODD Xn0)) (cEVEN Xn0)) x9) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 267.88/268.21 Found (or_comm_i00 (((or_introl (cODD Xn0)) (cEVEN Xn0)) x9)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 267.88/268.21 Found ((or_comm_i0 (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x9)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 267.88/268.21 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x9)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 267.88/268.21 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x9)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 267.88/268.21 Found x500:=(x50 (cS Xx)):((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))
% 267.88/268.21 Found (x50 (cS Xx)) as proof of ((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))
% 267.88/268.21 Found (fun (x6:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x50 (cS Xx))) as proof of ((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))
% 267.88/268.21 Found (fun (Xx:fofType) (x6:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x50 (cS Xx))) as proof of (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))
% 267.88/268.21 Found (fun (Xx:fofType) (x6:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x50 (cS Xx))) as proof of (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))
% 269.85/270.20 Found ((conj00 (x50 c0)) (fun (Xx:fofType) (x6:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x50 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 269.85/270.20 Found (((conj0 (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))) (x50 c0)) (fun (Xx:fofType) (x6:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x50 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 269.85/270.20 Found ((((conj ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))) (x50 c0)) (fun (Xx:fofType) (x6:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x50 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 269.85/270.20 Found ((((conj ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))) (x50 c0)) (fun (Xx:fofType) (x6:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x50 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 269.85/270.20 Found x30:(cNUMBER Xn0)
% 269.85/270.20 Instantiate: Xn0:=Xn:fofType
% 269.85/270.20 Found x30 as proof of (cNUMBER Xn)
% 269.85/270.20 Found x30:=(x3 x20):(cNUMBER Xn0)
% 269.85/270.20 Found (x3 x20) as proof of (cNUMBER Xn)
% 269.85/270.20 Found (x3 x20) as proof of (cNUMBER Xn)
% 269.85/270.20 Found (fun (x9:(cODD (cS c0)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 269.85/270.20 Found (fun (x9:(cODD (cS c0)))=> (x3 x20)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 269.85/270.20 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 269.85/270.20 Instantiate: Xn0:=Xn:fofType
% 269.85/270.20 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 269.85/270.20 Found (x5 x20) as proof of (cNUMBER Xn)
% 269.85/270.20 Found (x5 x20) as proof of (cNUMBER Xn)
% 269.85/270.20 Found (x5 x20) as proof of (cNUMBER Xn)
% 269.85/270.20 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 269.85/270.20 Instantiate: Xn00:=Xn:fofType
% 269.85/270.20 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 269.85/270.20 Found (x3 x40) as proof of (cNUMBER Xn)
% 269.85/270.20 Found (x3 x40) as proof of (cNUMBER Xn)
% 269.85/270.20 Found (x3 x40) as proof of (cNUMBER Xn)
% 269.85/270.20 Found x30:=(x3 x20):(cNUMBER Xn0)
% 269.85/270.20 Found (x3 x20) as proof of (cNUMBER Xn)
% 269.85/270.20 Found (x3 x20) as proof of (cNUMBER Xn)
% 269.85/270.20 Found (fun (x9:(cODD (cS c0)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 269.85/270.20 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))
% 269.85/270.20 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)))
% 269.85/270.20 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 269.85/270.20 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 269.85/270.20 Found (x3 x20) as proof of (cNUMBER Xn)
% 269.85/270.20 Found (x3 x20) as proof of (cNUMBER Xn)
% 269.85/270.20 Found (x3 x20) as proof of (cNUMBER Xn)
% 269.85/270.20 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 269.85/270.20 Found x40 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 269.85/270.20 Found (x5 x40) as proof of (cNUMBER Xn)
% 269.85/270.20 Found (x5 x40) as proof of (cNUMBER Xn)
% 269.85/270.20 Found (x5 x40) as proof of (cNUMBER Xn)
% 269.85/270.20 Found x500:=(x50 c0):((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 269.85/270.20 Found (x50 c0) as proof of ((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 269.85/270.20 Found (x50 c0) as proof of ((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 269.85/270.20 Found x60:((or (cEVEN Xn0)) (cODD Xn0))
% 269.85/270.20 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 269.85/270.20 Found (x7 x60) as proof of (cNUMBER Xn)
% 269.85/270.20 Found (x7 x60) as proof of (cNUMBER Xn)
% 269.85/270.20 Found (fun (x7:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x7 x60)) as proof of (cNUMBER Xn)
% 269.85/270.20 Found (fun (x7:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x7 x60)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 270.14/270.52 Found x30:=(x3 x21):(cNUMBER Xn0)
% 270.14/270.52 Found (x3 x21) as proof of (cNUMBER Xn0)
% 270.14/270.52 Found (x3 x21) as proof of (cNUMBER Xn0)
% 270.14/270.52 Found x30:=(x3 x22):(cNUMBER Xn0)
% 270.14/270.52 Instantiate: Xn0:=Xn:fofType
% 270.14/270.52 Found (x3 x22) as proof of (cNUMBER Xn)
% 270.14/270.52 Found (fun (x5:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x3 x22)) as proof of (cNUMBER Xn)
% 270.14/270.52 Found (fun (x5:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x3 x22)) as proof of ((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn))
% 270.14/270.52 Found x30:=(x3 x20):(cNUMBER Xn0)
% 270.14/270.52 Found (x3 x20) as proof of (cNUMBER Xn)
% 270.14/270.52 Found (x3 x20) as proof of (cNUMBER Xn)
% 270.14/270.52 Found (fun (x7:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 270.14/270.52 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x3 x20)) as proof of ((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn))
% 270.14/270.52 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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))))))->((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn)))
% 270.14/270.52 Found x50:=(x5 x40):(cNUMBER Xn00)
% 270.14/270.52 Found (x5 x40) as proof of (cNUMBER Xn)
% 270.14/270.52 Found (x5 x40) as proof of (cNUMBER Xn)
% 270.14/270.52 Found (fun (x7:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 270.14/270.52 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x5 x40)) as proof of ((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn))
% 272.79/273.15 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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))))))->((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn)))
% 272.79/273.15 Found x30:=(x3 x22):(cNUMBER Xn0)
% 272.79/273.15 Instantiate: Xn0:=Xn:fofType
% 272.79/273.15 Found (x3 x22) as proof of (cNUMBER Xn)
% 272.79/273.15 Found (fun (x5:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x3 x22)) as proof of (cNUMBER Xn)
% 272.79/273.15 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x3 x22)) as proof of ((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn))
% 272.79/273.15 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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))))))->((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn)))
% 272.79/273.15 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 272.79/273.15 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 272.79/273.15 Found (x3 x20) as proof of (cNUMBER Xn)
% 272.79/273.15 Found (x3 x20) as proof of (cNUMBER Xn)
% 272.79/273.15 Found (x3 x20) as proof of (cNUMBER Xn)
% 272.79/273.15 Found x50:=(x5 x40):(cNUMBER Xn0)
% 272.79/273.15 Found (x5 x40) as proof of (cNUMBER Xn0)
% 272.79/273.15 Found (x5 x40) as proof of (cNUMBER Xn0)
% 272.79/273.15 Found x50:=(x5 x41):(cNUMBER Xn0)
% 272.79/273.15 Instantiate: Xn0:=Xn:fofType
% 272.79/273.15 Found (x5 x41) as proof of (cNUMBER Xn)
% 272.79/273.15 Found (fun (x9:(cODD (cS c0)))=> (x5 x41)) as proof of (cNUMBER Xn)
% 272.79/273.15 Found (fun (x9:(cODD (cS c0)))=> (x5 x41)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 272.79/273.15 Found x30:=(x3 x22):(cNUMBER Xn0)
% 272.79/273.15 Instantiate: Xn0:=Xn:fofType
% 272.79/273.15 Found (x3 x22) as proof of (cNUMBER Xn)
% 272.79/273.15 Found (fun (x3:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x3 x22)) as proof of (cNUMBER Xn)
% 272.79/273.15 Found (fun (x3:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x3 x22)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 272.79/273.15 Found x20:=(x2 x31):((or (cEVEN Xn0)) (cODD Xn0))
% 272.79/273.15 Found (x2 x31) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 272.79/273.15 Found (x2 x31) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 272.79/273.15 Found x9:(cEVEN c0)
% 272.79/273.15 Instantiate: Xn0:=c0:fofType
% 272.79/273.15 Found x9 as proof of (cEVEN Xn0)
% 272.79/273.15 Found (or_introl00 x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 272.79/273.15 Found ((or_introl0 (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 275.01/275.38 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 275.01/275.38 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))
% 275.01/275.38 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)))
% 275.01/275.38 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))))
% 275.01/275.38 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))
% 275.01/275.38 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))
% 275.01/275.38 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))
% 275.01/275.38 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))
% 275.01/275.38 Found x60:=(x6 x70):((or (cEVEN Xn00)) (cODD Xn00))
% 275.01/275.38 Instantiate: Xn00:=Xn:fofType
% 275.01/275.38 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 275.01/275.38 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 275.01/275.38 Found x40:=(x4 x50):((or (cEVEN Xn0)) (cODD Xn0))
% 275.01/275.38 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 275.01/275.38 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 275.01/275.38 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 275.01/275.38 Instantiate: Xn00:=Xn:fofType
% 275.01/275.38 Found (fun (x7:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> x40) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 275.01/275.38 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> x40) as proof of ((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 275.01/275.38 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:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS 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))))))->((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->((or (cEVEN Xn0)) (cODD Xn0))))
% 278.31/278.68 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 278.31/278.68 Instantiate: Xn0:=Xn:fofType
% 278.31/278.68 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 278.31/278.68 Found (x7 x20) as proof of (cNUMBER Xn)
% 278.31/278.68 Found (x7 x20) as proof of (cNUMBER Xn)
% 278.31/278.68 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x7 x20)) as proof of (cNUMBER Xn)
% 278.31/278.68 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x7 x20)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 278.31/278.68 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 278.31/278.68 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 278.31/278.68 Found (x3 x20) as proof of (cNUMBER Xn)
% 278.31/278.68 Found (x3 x20) as proof of (cNUMBER Xn)
% 278.31/278.68 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 278.31/278.68 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 278.31/278.68 Found x7:(cODD (cS c0))
% 278.31/278.68 Instantiate: Xn0:=(cS c0):fofType
% 278.31/278.68 Found x7 as proof of (cODD Xn0)
% 278.31/278.68 Found (or_intror00 x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 278.31/278.68 Found ((or_intror0 (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 278.31/278.68 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 278.31/278.68 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 278.31/278.68 Found x8:(cEVEN c0)
% 278.31/278.68 Instantiate: Xn0:=c0:fofType
% 278.31/278.68 Found x8 as proof of (cEVEN Xn0)
% 278.31/278.68 Found (or_introl00 x8) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 278.31/278.68 Found ((or_introl0 (cODD Xn0)) x8) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 278.31/278.68 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x8) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 278.31/278.68 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x8) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 278.31/278.68 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 278.31/278.68 Instantiate: Xn00:=Xn:fofType
% 278.31/278.68 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 278.31/278.68 Found (x3 x60) as proof of (cNUMBER Xn)
% 278.31/278.68 Found (x3 x60) as proof of (cNUMBER Xn)
% 278.31/278.68 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x60)) as proof of (cNUMBER Xn)
% 278.31/278.68 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x60)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 278.31/278.68 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 278.31/278.68 Found x60 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 278.31/278.68 Found (x7 x60) as proof of (cNUMBER Xn)
% 278.31/278.68 Found (x7 x60) as proof of (cNUMBER Xn)
% 278.31/278.68 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x7 x60)) as proof of (cNUMBER Xn)
% 278.31/278.68 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x7 x60)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 278.31/278.68 Found x70:(cNUMBER Xn0)
% 278.31/278.68 Instantiate: Xn0:=Xn:fofType
% 278.31/278.68 Found (fun (x9:(cODD (cS c0)))=> x70) as proof of (cNUMBER Xn)
% 278.31/278.68 Found (fun (x9:(cODD (cS c0)))=> x70) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 278.31/278.68 Found x70:(cNUMBER Xn0)
% 278.31/278.68 Instantiate: Xn0:=Xn:fofType
% 278.31/278.68 Found (fun (x9:(cODD (cS c0)))=> x70) as proof of (cNUMBER Xn)
% 278.31/278.68 Found (fun (x9:(cODD (cS c0)))=> x70) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 278.31/278.68 Found x71:(cNUMBER Xn0)
% 278.31/278.68 Instantiate: Xn0:=Xn:fofType
% 278.31/278.68 Found (fun (x9:(cODD (cS c0)))=> x71) as proof of (cNUMBER Xn)
% 278.31/278.68 Found (fun (x9:(cODD (cS c0)))=> x71) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 278.31/278.68 Found x50:=(x5 x40):(cNUMBER Xn0)
% 278.31/278.68 Instantiate: Xn0:=Xn:fofType
% 278.31/278.68 Found (x5 x40) as proof of (cNUMBER Xn)
% 278.31/278.68 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 278.31/278.68 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))
% 278.31/278.68 Found x300:=(x30 (cS Xx)):((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))
% 278.31/278.68 Found (x30 (cS Xx)) as proof of ((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))
% 278.31/278.68 Found (fun (x6:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx))) as proof of ((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))
% 280.70/281.06 Found (fun (Xx:fofType) (x6:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx))) as proof of (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))
% 280.70/281.06 Found (fun (Xx:fofType) (x6:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx))) as proof of (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))
% 280.70/281.06 Found ((conj00 (x30 c0)) (fun (Xx:fofType) (x6:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 280.70/281.06 Found (((conj0 (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))) (x30 c0)) (fun (Xx:fofType) (x6:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 280.70/281.06 Found ((((conj ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))) (x30 c0)) (fun (Xx:fofType) (x6:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 280.70/281.06 Found ((((conj ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))) (x30 c0)) (fun (Xx:fofType) (x6:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 280.70/281.06 Found x50:(cNUMBER Xn0)
% 280.70/281.06 Instantiate: Xn0:=Xn:fofType
% 280.70/281.06 Found x50 as proof of (cNUMBER Xn)
% 280.70/281.06 Found x300:=(x30 c0):((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 280.70/281.06 Found (x30 c0) as proof of ((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 280.70/281.06 Found (x30 c0) as proof of ((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 280.70/281.06 Found x50:=(x5 x40):(cNUMBER Xn0)
% 280.70/281.06 Instantiate: Xn0:=Xn:fofType
% 280.70/281.06 Found (x5 x40) as proof of (cNUMBER Xn)
% 280.70/281.06 Found (x5 x40) as proof of (cNUMBER Xn)
% 280.70/281.06 Found x50:=(x5 x40):(cNUMBER Xn0)
% 280.70/281.06 Instantiate: Xn0:=Xn:fofType
% 280.70/281.06 Found (x5 x40) as proof of (cNUMBER Xn)
% 280.70/281.06 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 280.70/281.06 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))
% 280.70/281.06 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)))
% 280.70/281.06 Found x9:(cODD (cS c0))
% 280.70/281.06 Instantiate: Xn0:=(cS c0):fofType
% 280.70/281.06 Found x9 as proof of (cODD Xn0)
% 280.70/281.06 Found (or_intror00 x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 280.70/281.06 Found ((or_intror0 (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 280.70/281.06 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 280.70/281.06 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 280.70/281.06 Found (x7 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9)) as proof of (cNUMBER Xn0)
% 280.70/281.06 Found (fun (x9:(cODD (cS c0)))=> (x7 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9))) as proof of (cNUMBER Xn0)
% 280.70/281.06 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))
% 281.52/281.94 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)))
% 281.52/281.94 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)
% 281.52/281.94 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)
% 281.52/281.94 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) 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)
% 281.52/281.94 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) 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)
% 281.52/281.94 Found x70:(cNUMBER Xn0)
% 281.52/281.94 Instantiate: Xn0:=Xn:fofType
% 281.52/281.94 Found x70 as proof of (cNUMBER Xn)
% 281.52/281.94 Found x32:(cNUMBER Xn0)
% 281.52/281.94 Instantiate: Xn0:=Xn:fofType
% 281.52/281.94 Found (fun (x5:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> x32) as proof of (cNUMBER Xn)
% 281.52/281.94 Found (fun (x5:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> x32) as proof of ((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn))
% 281.52/281.94 Found x300:=(x30 (cS Xx)):((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))
% 281.52/281.94 Found (x30 (cS Xx)) as proof of ((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))
% 281.52/281.94 Found (fun (x8:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx))) as proof of ((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))
% 281.52/281.94 Found (fun (Xx:fofType) (x8:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx))) as proof of (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))
% 281.52/281.94 Found (fun (Xx:fofType) (x8:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx))) as proof of (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))
% 281.52/281.94 Found ((conj00 (x30 c0)) (fun (Xx:fofType) (x8:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 281.52/281.94 Found (((conj0 (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))) (x30 c0)) (fun (Xx:fofType) (x8:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 281.52/281.94 Found ((((conj ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))) (x30 c0)) (fun (Xx:fofType) (x8:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 285.62/285.97 Found ((((conj ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))) (x30 c0)) (fun (Xx:fofType) (x8:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 285.62/285.97 Found x32:(cNUMBER Xn0)
% 285.62/285.97 Instantiate: Xn0:=Xn:fofType
% 285.62/285.97 Found (fun (x5:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> x32) as proof of (cNUMBER Xn)
% 285.62/285.97 Found (fun (x5:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> x32) as proof of ((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn))
% 285.62/285.97 Found x300:=(x30 (cS Xx)):((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))
% 285.62/285.97 Found (x30 (cS Xx)) as proof of ((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))
% 285.62/285.97 Found (fun (x6:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx))) as proof of ((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))
% 285.62/285.97 Found (fun (Xx:fofType) (x6:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx))) as proof of (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))
% 285.62/285.97 Found (fun (Xx:fofType) (x6:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx))) as proof of (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))
% 285.62/285.97 Found ((conj00 (x30 c0)) (fun (Xx:fofType) (x6:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 285.62/285.97 Found (((conj0 (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))) (x30 c0)) (fun (Xx:fofType) (x6:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 285.62/285.97 Found ((((conj ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))) (x30 c0)) (fun (Xx:fofType) (x6:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 285.62/285.97 Found ((((conj ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx))))))) (x30 c0)) (fun (Xx:fofType) (x6:((and (cNUMBER Xx)) (cNUMBER (cS Xx))))=> (x30 (cS Xx)))) as proof of ((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))
% 285.62/285.97 Found x50:(cNUMBER Xn0)
% 285.62/285.97 Instantiate: Xn0:=Xn:fofType
% 285.62/285.97 Found (fun (x9:(cODD (cS c0)))=> x50) as proof of (cNUMBER Xn)
% 285.62/285.97 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))
% 285.62/285.97 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)))
% 289.01/289.37 Found x50:(cNUMBER Xn0)
% 289.01/289.37 Instantiate: Xn0:=Xn:fofType
% 289.01/289.37 Found (fun (x9:(cODD (cS c0)))=> x50) as proof of (cNUMBER Xn)
% 289.01/289.37 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))
% 289.01/289.37 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)))
% 289.01/289.37 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 289.01/289.37 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 289.01/289.37 Found (x5 x40) as proof of (cNUMBER Xn)
% 289.01/289.37 Found (x5 x40) as proof of (cNUMBER Xn)
% 289.01/289.37 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 289.01/289.37 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))
% 289.01/289.37 Found x50:=(x5 x40):(cNUMBER Xn0)
% 289.01/289.37 Found (x5 x40) as proof of (cNUMBER Xn0)
% 289.01/289.37 Found (x5 x40) as proof of (cNUMBER Xn0)
% 289.01/289.37 Found x50:=(x5 x41):(cNUMBER Xn0)
% 289.01/289.37 Instantiate: Xn0:=Xn:fofType
% 289.01/289.37 Found (x5 x41) as proof of (cNUMBER Xn)
% 289.01/289.37 Found (x5 x41) as proof of (cNUMBER Xn)
% 289.01/289.37 Found x50:=(x5 x41):(cNUMBER Xn0)
% 289.01/289.37 Found (x5 x41) as proof of (cNUMBER Xn)
% 289.01/289.37 Found (x5 x41) as proof of (cNUMBER Xn)
% 289.01/289.37 Found (x5 x41) as proof of (cNUMBER Xn)
% 289.01/289.37 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 289.01/289.37 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 289.01/289.37 Found (x5 x40) as proof of (cNUMBER Xn)
% 289.01/289.37 Found (x5 x40) as proof of (cNUMBER Xn)
% 289.01/289.37 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 289.01/289.37 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))
% 289.01/289.37 Found x30:=(x3 x20):(cNUMBER Xn0)
% 289.01/289.37 Instantiate: Xn0:=Xn:fofType
% 289.01/289.37 Found (x3 x20) as proof of (cNUMBER Xn)
% 289.01/289.37 Found (fun (x9:(cODD (cS c0)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 289.01/289.37 Found (fun (x9:(cODD (cS c0)))=> (x3 x20)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 289.01/289.37 Found x30:=(x3 x20):(cNUMBER Xn0)
% 289.01/289.37 Found (x3 x20) as proof of (cNUMBER Xn0)
% 289.01/289.37 Found (x3 x20) as proof of (cNUMBER Xn0)
% 289.01/289.37 Found x30:=(x3 x21):(cNUMBER Xn0)
% 289.01/289.37 Instantiate: Xn0:=Xn:fofType
% 289.01/289.37 Found (x3 x21) as proof of (cNUMBER Xn)
% 289.01/289.37 Found (x3 x21) as proof of (cNUMBER Xn)
% 289.01/289.37 Found x30:=(x3 x20):(cNUMBER Xn0)
% 289.01/289.37 Found (x3 x20) as proof of (cNUMBER Xn)
% 289.01/289.37 Found (x3 x20) as proof of (cNUMBER Xn)
% 289.01/289.37 Found (x3 x20) as proof of (cNUMBER Xn)
% 289.01/289.37 Found x30:=(x3 x20):(cNUMBER Xn0)
% 289.01/289.37 Instantiate: Xn0:=Xn:fofType
% 289.01/289.37 Found (x3 x20) as proof of (cNUMBER Xn)
% 289.01/289.37 Found (fun (x9:(cODD (cS c0)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 289.01/289.37 Found (fun (x9:(cODD (cS c0)))=> (x3 x20)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 289.01/289.37 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 289.01/289.37 Instantiate: Xn0:=Xn:fofType
% 289.01/289.37 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 289.01/289.38 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 289.01/289.38 Found x40:=(x4 x50):((or (cEVEN Xn00)) (cODD Xn00))
% 289.01/289.38 Instantiate: Xn00:=Xn:fofType
% 289.01/289.38 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 289.01/289.38 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 289.01/289.38 Found x50:=(x5 x40):(cNUMBER Xn0)
% 289.01/289.38 Instantiate: Xn0:=Xn:fofType
% 289.01/289.38 Found (x5 x40) as proof of (cNUMBER Xn)
% 289.01/289.38 Found (x5 x40) as proof of (cNUMBER Xn)
% 289.01/289.38 Found x50:=(x5 x40):(cNUMBER Xn0)
% 289.01/289.38 Instantiate: Xn0:=Xn:fofType
% 289.01/289.38 Found (x5 x40) as proof of (cNUMBER Xn)
% 289.01/289.38 Found (x5 x40) as proof of (cNUMBER Xn)
% 289.01/289.38 Found x30:=(x3 x20):(cNUMBER Xn0)
% 289.01/289.38 Instantiate: Xn0:=Xn:fofType
% 289.01/289.38 Found (x3 x20) as proof of (cNUMBER Xn)
% 289.01/289.38 Found (x3 x20) as proof of (cNUMBER Xn)
% 289.01/289.38 Found x300:=(x30 c0):((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 289.01/289.38 Found (x30 c0) as proof of ((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 289.01/289.38 Found (x30 c0) as proof of ((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 289.01/289.38 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 289.01/289.38 Instantiate: Xn0:=Xn:fofType
% 289.01/289.38 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 289.05/289.43 Found (x5 x20) as proof of (cNUMBER Xn)
% 289.05/289.43 Found (x5 x20) as proof of (cNUMBER Xn)
% 289.05/289.43 Found (fun (x7:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x5 x20)) as proof of (cNUMBER Xn)
% 289.05/289.43 Found (fun (x7:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x5 x20)) as proof of ((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn))
% 289.05/289.43 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 289.05/289.43 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 289.05/289.43 Found (x3 x20) as proof of (cNUMBER Xn)
% 289.05/289.43 Found (x3 x20) as proof of (cNUMBER Xn)
% 289.05/289.43 Found (fun (x7:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 289.05/289.43 Found (fun (x7:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x3 x20)) as proof of ((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn))
% 289.05/289.43 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 289.05/289.43 Instantiate: Xn0:=Xn:fofType
% 289.05/289.43 Found x40 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 289.05/289.43 Found (x7 x40) as proof of (cNUMBER Xn)
% 289.05/289.43 Found (x7 x40) as proof of (cNUMBER Xn)
% 289.05/289.43 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x7 x40)) as proof of (cNUMBER Xn)
% 289.05/289.43 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))
% 289.05/289.43 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)))
% 289.05/289.43 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 289.05/289.43 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 289.05/289.43 Found (x5 x40) as proof of (cNUMBER Xn)
% 289.05/289.43 Found (x5 x40) as proof of (cNUMBER Xn)
% 289.05/289.43 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 289.05/289.43 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))
% 289.05/289.43 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)))
% 289.05/289.43 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 289.05/289.43 Instantiate: Xn00:=Xn:fofType
% 289.05/289.43 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 289.05/289.43 Found (x3 x40) as proof of (cNUMBER Xn)
% 289.05/289.43 Found (x3 x40) as proof of (cNUMBER Xn)
% 289.05/289.43 Found (fun (x7:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x3 x40)) as proof of (cNUMBER Xn)
% 289.05/289.43 Found (fun (x7:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x3 x40)) as proof of ((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn))
% 292.78/293.16 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 292.78/293.16 Found x40 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 292.78/293.16 Found (x5 x40) as proof of (cNUMBER Xn)
% 292.78/293.16 Found (x5 x40) as proof of (cNUMBER Xn)
% 292.78/293.16 Found (fun (x7:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 292.78/293.16 Found (fun (x7:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x5 x40)) as proof of ((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn))
% 292.78/293.16 Found x30:=(x3 x20):(cNUMBER Xn0)
% 292.78/293.16 Found (x3 x20) as proof of (cNUMBER Xn)
% 292.78/293.16 Found (x3 x20) as proof of (cNUMBER Xn)
% 292.78/293.16 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 292.78/293.16 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))
% 292.78/293.16 Found x70:=(x7 x60):(cNUMBER Xn0)
% 292.78/293.16 Instantiate: Xn0:=Xn:fofType
% 292.78/293.16 Found (x7 x60) as proof of (cNUMBER Xn)
% 292.78/293.16 Found (fun (x7:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x7 x60)) as proof of (cNUMBER Xn)
% 292.78/293.16 Found (fun (x7:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x7 x60)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 292.78/293.16 Found x30:=(x3 x20):(cNUMBER Xn0)
% 292.78/293.16 Instantiate: Xn0:=Xn:fofType
% 292.78/293.16 Found (x3 x20) as proof of (cNUMBER Xn)
% 292.78/293.16 Found (x3 x20) as proof of (cNUMBER Xn)
% 292.78/293.16 Found x9:(cODD (cS c0))
% 292.78/293.16 Instantiate: Xn0:=(cS c0):fofType
% 292.78/293.16 Found x9 as proof of (cODD Xn0)
% 292.78/293.16 Found (or_intror00 x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 292.78/293.16 Found ((or_intror0 (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 292.78/293.16 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 292.78/293.16 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 292.78/293.16 Found (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9)) as proof of (cNUMBER Xn0)
% 292.78/293.16 Found (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9)) as proof of (cNUMBER Xn0)
% 292.78/293.16 Found x50:=(x5 x41):(cNUMBER Xn0)
% 292.78/293.16 Found (x5 x41) as proof of (cNUMBER Xn)
% 292.78/293.16 Found (x5 x41) as proof of (cNUMBER Xn)
% 292.78/293.16 Found (fun (x9:(cODD (cS c0)))=> (x5 x41)) as proof of (cNUMBER Xn)
% 292.78/293.16 Found (fun (x9:(cODD (cS c0)))=> (x5 x41)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 292.78/293.16 Found x70:=(x7 x60):(cNUMBER Xn0)
% 292.78/293.16 Instantiate: Xn0:=Xn:fofType
% 292.78/293.16 Found (x7 x60) as proof of (cNUMBER Xn)
% 292.78/293.16 Found (x7 x60) as proof of (cNUMBER Xn)
% 292.78/293.16 Found x70:=(x7 x60):(cNUMBER Xn0)
% 292.78/293.16 Found (x7 x60) as proof of (cNUMBER Xn0)
% 292.78/293.16 Found (x7 x60) as proof of (cNUMBER Xn0)
% 292.78/293.16 Found x70:=(x7 x61):(cNUMBER Xn0)
% 292.78/293.16 Instantiate: Xn0:=Xn:fofType
% 292.78/293.16 Found (x7 x61) as proof of (cNUMBER Xn)
% 292.78/293.16 Found (fun (x9:(cODD (cS c0)))=> (x7 x61)) as proof of (cNUMBER Xn)
% 292.78/293.16 Found (fun (x9:(cODD (cS c0)))=> (x7 x61)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 292.78/293.16 Found x500:=(x50 c0):((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 292.78/293.16 Found (x50 c0) as proof of ((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 292.78/293.16 Found (x50 c0) as proof of ((and (cNUMBER c0)) (cNUMBER (cS c0)))
% 292.78/293.16 Found x11:(cEVEN c0)
% 292.78/293.16 Instantiate: Xn0:=c0:fofType
% 292.78/293.16 Found x11 as proof of (cEVEN Xn0)
% 292.78/293.16 Found (or_introl00 x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 292.78/293.16 Found ((or_introl0 (cODD Xn0)) x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 292.78/293.16 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 292.78/293.16 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 292.78/293.16 Found x7:(cODD (cS c0))
% 294.17/294.53 Instantiate: Xn0:=(cS c0):fofType
% 294.17/294.53 Found x7 as proof of (cODD Xn0)
% 294.17/294.53 Found (or_intror00 x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 294.17/294.53 Found ((or_intror0 (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 294.17/294.53 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 294.17/294.53 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 294.17/294.53 Found x9:(cODD (cS c0))
% 294.17/294.53 Instantiate: Xn0:=(cS c0):fofType
% 294.17/294.53 Found x9 as proof of (cODD Xn0)
% 294.17/294.53 Found (or_intror00 x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 294.17/294.53 Found ((or_intror0 (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 294.17/294.53 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 294.17/294.53 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 294.17/294.53 Found (x5 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9)) as proof of (cNUMBER Xn0)
% 294.17/294.53 Found (x5 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9)) as proof of (cNUMBER Xn0)
% 294.17/294.53 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 294.17/294.53 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 294.17/294.53 Found (x3 x20) as proof of (cNUMBER Xn)
% 294.17/294.53 Found (x3 x20) as proof of (cNUMBER Xn)
% 294.17/294.53 Found (fun (x9:(cODD (cS c0)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 294.17/294.53 Found (fun (x9:(cODD (cS c0)))=> (x3 x20)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 294.17/294.53 Found x9:(cODD (cS c0))
% 294.17/294.53 Instantiate: Xn0:=(cS c0):fofType
% 294.17/294.53 Found (fun (x9:(cODD (cS c0)))=> x9) as proof of (cODD Xn0)
% 294.17/294.53 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))
% 294.17/294.53 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)))
% 294.17/294.53 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)
% 294.17/294.53 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)
% 294.17/294.53 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)
% 294.17/294.53 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)
% 294.17/294.53 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))
% 294.17/294.53 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)))
% 294.17/294.55 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)
% 294.17/294.55 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)
% 294.17/294.55 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))))))) (x9:(cODD (cS c0)))=> x9)))) as proof of (cODD Xn0)
% 294.17/294.55 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))))))) (x9:(cODD (cS c0)))=> x9)))) as proof of (cODD Xn0)
% 294.17/294.55 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))))))) (x9:(cODD (cS c0)))=> x9))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 294.38/294.77 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))))))) (x9:(cODD (cS c0)))=> x9))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 294.38/294.77 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))))))) (x9:(cODD (cS c0)))=> x9))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 294.38/294.77 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))))))) (x9:(cODD (cS c0)))=> x9))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 294.38/294.77 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 294.38/294.77 Instantiate: Xn0:=Xn00:fofType
% 294.38/294.77 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 294.38/294.77 Found x30:(cNUMBER Xn0)
% 294.38/294.77 Instantiate: Xn00:=Xn0:fofType
% 294.38/294.77 Found x30 as proof of (cNUMBER Xn00)
% 294.38/294.77 Found x60:=(x6 x70):((or (cEVEN Xn00)) (cODD Xn00))
% 294.38/294.77 Instantiate: Xn00:=Xn:fofType
% 294.38/294.77 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 296.40/296.77 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 296.40/296.77 Found x30:=(x3 x21):(cNUMBER Xn0)
% 296.40/296.77 Found (x3 x21) as proof of (cNUMBER Xn0)
% 296.40/296.77 Found (x3 x21) as proof of (cNUMBER Xn0)
% 296.40/296.77 Found x30:=(x3 x22):(cNUMBER Xn0)
% 296.40/296.77 Instantiate: Xn0:=Xn:fofType
% 296.40/296.77 Found (x3 x22) as proof of (cNUMBER Xn)
% 296.40/296.77 Found (fun (x5:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x3 x22)) as proof of (cNUMBER Xn)
% 296.40/296.77 Found (fun (x5:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x3 x22)) as proof of ((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn))
% 296.40/296.77 Found x50:=(x5 x41):(cNUMBER Xn0)
% 296.40/296.77 Found (x5 x41) as proof of (cNUMBER Xn0)
% 296.40/296.77 Found (x5 x41) as proof of (cNUMBER Xn0)
% 296.40/296.77 Found x50:=(x5 x42):(cNUMBER Xn0)
% 296.40/296.77 Instantiate: Xn0:=Xn:fofType
% 296.40/296.77 Found (x5 x42) as proof of (cNUMBER Xn)
% 296.40/296.77 Found (x5 x42) as proof of (cNUMBER Xn)
% 296.40/296.77 Found x50:=(x5 x40):(cNUMBER Xn0)
% 296.40/296.77 Found (x5 x40) as proof of (cNUMBER Xn)
% 296.40/296.77 Found (x5 x40) as proof of (cNUMBER Xn)
% 296.40/296.77 Found (x5 x40) as proof of (cNUMBER Xn)
% 296.40/296.77 Found x60:=(x6 x70):((or (cEVEN Xn0)) (cODD Xn0))
% 296.40/296.77 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 296.40/296.77 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 296.40/296.77 Found x50:=(x5 x40):(cNUMBER Xn0)
% 296.40/296.77 Instantiate: Xn0:=Xn:fofType
% 296.40/296.77 Found (x5 x40) as proof of (cNUMBER Xn)
% 296.40/296.77 Found (x5 x40) as proof of (cNUMBER Xn)
% 296.40/296.77 Found x30:=(x3 x21):(cNUMBER Xn0)
% 296.40/296.77 Found (x3 x21) as proof of (cNUMBER Xn0)
% 296.40/296.77 Found (x3 x21) as proof of (cNUMBER Xn0)
% 296.40/296.77 Found x30:=(x3 x22):(cNUMBER Xn0)
% 296.40/296.77 Instantiate: Xn0:=Xn:fofType
% 296.40/296.77 Found (x3 x22) as proof of (cNUMBER Xn)
% 296.40/296.77 Found (fun (x5:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x3 x22)) as proof of (cNUMBER Xn)
% 296.40/296.77 Found (fun (x5:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x3 x22)) as proof of ((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn))
% 296.40/296.77 Found x30:(cNUMBER Xn0)
% 296.40/296.77 Instantiate: Xn00:=Xn0:fofType
% 296.40/296.77 Found x30 as proof of (cNUMBER Xn00)
% 296.40/296.77 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 296.40/296.77 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 296.40/296.77 Found (x3 x20) as proof of (cNUMBER Xn)
% 296.40/296.77 Found (x3 x20) as proof of (cNUMBER Xn)
% 296.40/296.77 Found (x3 x20) as proof of (cNUMBER Xn)
% 296.40/296.77 Found x9:(cODD (cS c0))
% 296.40/296.77 Instantiate: Xn0:=(cS c0):fofType
% 296.40/296.77 Found x9 as proof of (cODD Xn0)
% 296.40/296.77 Found (or_intror00 x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 296.40/296.77 Found ((or_intror0 (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 296.40/296.77 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 296.40/296.77 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 296.40/296.77 Found (x7 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9)) as proof of (cNUMBER Xn0)
% 296.40/296.77 Found (x7 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x9)) as proof of (cNUMBER Xn0)
% 296.40/296.77 Found x50:=(x5 x41):(cNUMBER Xn0)
% 296.40/296.77 Instantiate: Xn0:=Xn:fofType
% 296.40/296.77 Found (x5 x41) as proof of (cNUMBER Xn)
% 296.40/296.77 Found (x5 x41) as proof of (cNUMBER Xn)
% 296.40/296.77 Found or_introl00:=(or_introl0 (cEVEN Xn0)):((cODD (cS c0))->((or (cODD (cS c0))) (cEVEN Xn0)))
% 296.40/296.77 Found (or_introl0 (cEVEN Xn0)) as proof of ((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0)))
% 296.40/296.77 Found ((or_introl (cODD (cS c0))) (cEVEN Xn0)) as proof of ((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0)))
% 296.40/296.77 Found ((or_introl (cODD (cS c0))) (cEVEN Xn0)) as proof of ((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0)))
% 296.40/296.77 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)))
% 296.40/296.77 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))))
% 296.40/296.77 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))
% 296.40/296.77 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))
% 296.40/296.77 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))
% 296.40/296.77 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))
% 296.40/296.77 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)))
% 296.40/296.77 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))))
% 296.40/296.77 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))
% 296.40/296.78 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))
% 296.40/296.78 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))
% 296.40/296.78 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))
% 296.40/296.78 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))
% 297.49/297.86 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))
% 297.49/297.86 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))
% 297.49/297.86 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))
% 297.49/297.86 Found x20:=(x2 x31):((or (cEVEN Xn0)) (cODD Xn0))
% 297.49/297.86 Found (x2 x31) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 297.49/297.86 Found (x2 x31) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 297.49/297.86 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 297.49/297.86 Instantiate: Xn0:=Xn00:fofType
% 297.49/297.86 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 297.49/297.86 Found x20:=(x2 x31):((or (cEVEN Xn0)) (cODD Xn0))
% 297.49/297.86 Found (x2 x31) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 297.49/297.86 Found (x2 x31) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 297.49/297.86 Found x7:(cODD (cS c0))
% 297.49/297.86 Instantiate: Xn0:=(cS c0):fofType
% 297.49/297.86 Found x7 as proof of (cODD Xn0)
% 297.49/297.86 Found (or_introl00 x7) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 297.49/297.86 Found ((or_introl0 (cEVEN Xn0)) x7) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 299.26/299.64 Found (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 299.26/299.64 Found (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 299.26/299.64 Found (or_comm_i00 (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 299.26/299.64 Found ((or_comm_i0 (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 299.26/299.64 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 299.26/299.64 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 299.26/299.64 Found x30:=(x3 x20):(cNUMBER Xn0)
% 299.26/299.64 Found (x3 x20) as proof of (cNUMBER Xn)
% 299.26/299.64 Found (x3 x20) as proof of (cNUMBER Xn)
% 299.26/299.64 Found (fun (x5:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 299.26/299.64 Found (fun (x5:(((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx))))))=> (x3 x20)) as proof of ((((and ((and (cNUMBER c0)) (cNUMBER (cS c0)))) (forall (Xx:fofType), (((and (cNUMBER Xx)) (cNUMBER (cS Xx)))->((and (cNUMBER (cS Xx))) (cNUMBER (cS (cS Xx)))))))->(forall (Xx:fofType), ((and (cNUMBER Xx)) (cNUMBER (cS Xx)))))->(cNUMBER Xn))
% 299.26/299.64 Found x40:=(x4 x50):((or (cEVEN Xn0)) (cODD Xn0))
% 299.26/299.64 Found (x4 x50) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 299.26/299.64 Found (x4 x50) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 299.26/299.64 Found (x4 x50) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 299.26/299.64 Found x60:=(x6 x70):((or (cEVEN Xn00)) (cODD Xn00))
% 299.26/299.64 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 299.26/299.64 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 299.26/299.64 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 299.26/299.64 Found x70:=(x7 x61):(cNUMBER Xn0)
% 299.26/299.64 Instantiate: Xn0:=Xn:fofType
% 299.26/299.64 Found (x7 x61) as proof of (cNUMBER Xn)
% 299.26/299.64 Found (fun (x9:(cODD (cS c0)))=> (x7 x61)) as proof of (cNUMBER Xn)
% 299.26/299.64 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))
% 299.26/299.64 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)))
% 299.26/299.64 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 299.26/299.64 Instantiate: Xn0:=Xn:fofType
% 299.26/299.64 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 299.26/299.64 Found (x7 x20) as proof of (cNUMBER Xn)
% 299.26/299.64 Found (x7 x20) as proof of (cNUMBER Xn)
% 299.26/299.64 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x7 x20)) as proof of (cNUMBER Xn)
% 299.26/299.64 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))
% 299.26/299.64 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)))
% 299.26/299.64 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 299.26/299.64 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 299.26/299.64 Found (x3 x20) as proof of (cNUMBER Xn)
% 299.26/299.64 Found (x3 x20) as proof of (cNUMBER Xn)
% 299.26/299.64 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 299.26/299.64 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))
% 299.26/299.64 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
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