TSTP Solution File: NUM819^5 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : NUM819^5 : TPTP v7.0.0. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n147.star.cs.uiowa.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory : 32218.625MB
% OS : Linux 3.10.0-693.2.2.el7.x86_64
% CPULimit : 300s
% DateTime : Mon Jan 8 13:11:50 EST 2018
% Result : Unknown 45.48s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM819^5 : TPTP v7.0.0. Bugfixed v5.2.0.
% 0.00/0.03 % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.02/0.23 % Computer : n147.star.cs.uiowa.edu
% 0.02/0.23 % Model : x86_64 x86_64
% 0.02/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% 0.02/0.23 % Memory : 32218.625MB
% 0.02/0.23 % OS : Linux 3.10.0-693.2.2.el7.x86_64
% 0.02/0.23 % CPULimit : 300
% 0.02/0.23 % DateTime : Fri Jan 5 14:32:34 CST 2018
% 0.06/0.23 % CPUTime :
% 0.06/0.25 Python 2.7.13
% 26.45/26.67 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% 26.45/26.67 FOF formula (<kernel.Constant object at 0x2b4a30caf878>, <kernel.Constant object at 0x2b4a30caf5a8>) of role type named c0_type
% 26.45/26.67 Using role type
% 26.45/26.67 Declaring c0:fofType
% 26.45/26.67 FOF formula (<kernel.Constant object at 0x2b4a30238f80>, <kernel.DependentProduct object at 0x2b4a30caf560>) of role type named cEVEN_type
% 26.45/26.67 Using role type
% 26.45/26.67 Declaring cEVEN:(fofType->Prop)
% 26.45/26.67 FOF formula (<kernel.Constant object at 0x2b4a30caf6c8>, <kernel.DependentProduct object at 0x2b4a30caf3b0>) of role type named cODD_type
% 26.45/26.67 Using role type
% 26.45/26.67 Declaring cODD:(fofType->Prop)
% 26.45/26.67 FOF formula (<kernel.Constant object at 0x2b4a30caf128>, <kernel.DependentProduct object at 0x2b4a30caf440>) of role type named cS_type
% 26.45/26.67 Using role type
% 26.45/26.67 Declaring cS:(fofType->fofType)
% 26.45/26.67 FOF formula (<kernel.Constant object at 0x2b4a30caf7e8>, <kernel.Sort object at 0x2b4a305e2b48>) of role type named cIND_type
% 26.45/26.67 Using role type
% 26.45/26.67 Declaring cIND:Prop
% 26.45/26.67 FOF formula (((eq Prop) cIND) (forall (Xp:(fofType->Prop)), (((and (Xp c0)) (forall (Xx:fofType), ((Xp Xx)->(Xp (cS Xx)))))->(forall (Xx:fofType), (Xp Xx))))) of role definition named cIND_def
% 26.45/26.67 A new definition: (((eq Prop) cIND) (forall (Xp:(fofType->Prop)), (((and (Xp c0)) (forall (Xx:fofType), ((Xp Xx)->(Xp (cS Xx)))))->(forall (Xx:fofType), (Xp Xx)))))
% 26.45/26.67 Defined: cIND:=(forall (Xp:(fofType->Prop)), (((and (Xp c0)) (forall (Xx:fofType), ((Xp Xx)->(Xp (cS Xx)))))->(forall (Xx:fofType), (Xp Xx))))
% 26.45/26.67 FOF formula (((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))))))) cIND)->(forall (Xn:fofType), ((or (cEVEN Xn)) (cODD Xn)))) of role conjecture named cEVEN_ODD_1
% 26.45/26.67 Conjecture to prove = (((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))))))) cIND)->(forall (Xn:fofType), ((or (cEVEN Xn)) (cODD Xn)))):Prop
% 26.45/26.67 We need to prove ['(((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))))))) cIND)->(forall (Xn:fofType), ((or (cEVEN Xn)) (cODD Xn))))']
% 26.45/26.67 Parameter fofType:Type.
% 26.45/26.67 Parameter c0:fofType.
% 26.45/26.67 Parameter cEVEN:(fofType->Prop).
% 26.45/26.67 Parameter cODD:(fofType->Prop).
% 26.45/26.67 Parameter cS:(fofType->fofType).
% 26.45/26.67 Definition cIND:=(forall (Xp:(fofType->Prop)), (((and (Xp c0)) (forall (Xx:fofType), ((Xp Xx)->(Xp (cS Xx)))))->(forall (Xx:fofType), (Xp Xx)))):Prop.
% 26.45/26.67 Trying to prove (((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))))))) cIND)->(forall (Xn:fofType), ((or (cEVEN Xn)) (cODD Xn))))
% 26.45/26.67 Found x6:(cEVEN c0)
% 26.45/26.67 Found x6 as proof of (cEVEN c0)
% 26.45/26.67 Found x6:(cEVEN c0)
% 26.45/26.67 Found x6 as proof of (cEVEN c0)
% 26.45/26.67 Found x6:(cEVEN c0)
% 26.45/26.67 Found x6 as proof of (cEVEN c0)
% 26.45/26.67 Found x6:(cEVEN c0)
% 26.45/26.67 Found x6 as proof of (cEVEN c0)
% 26.45/26.67 Found x6:(cEVEN c0)
% 26.45/26.67 Found x6 as proof of (cEVEN c0)
% 26.45/26.67 Found x6:(cEVEN c0)
% 26.45/26.67 Found x6 as proof of (cEVEN c0)
% 26.45/26.67 Found x6:(cEVEN c0)
% 26.45/26.67 Found x6 as proof of (cEVEN c0)
% 26.45/26.67 Found x6:(cEVEN c0)
% 26.45/26.67 Found x6 as proof of (cEVEN c0)
% 26.45/26.67 Found x6:(cEVEN c0)
% 26.45/26.67 Found x6 as proof of (cEVEN c0)
% 26.45/26.67 Found x6:(cEVEN c0)
% 26.45/26.67 Found x6 as proof of (cEVEN c0)
% 26.45/26.67 Found x6:(cEVEN c0)
% 26.45/26.67 Found x6 as proof of (cEVEN c0)
% 26.45/26.67 Found x6:(cEVEN c0)
% 26.45/26.67 Found x6 as proof of (cEVEN c0)
% 26.45/26.67 Found x6:(cEVEN c0)
% 26.45/26.67 Found x6 as proof of (cEVEN c0)
% 26.45/26.67 Found x6:(cEVEN c0)
% 26.45/26.67 Found x6 as proof of (cEVEN c0)
% 26.45/26.67 Found x6:(cEVEN c0)
% 26.45/26.67 Found x6 as proof of (cEVEN c0)
% 26.45/26.67 Found x6:(cEVEN c0)
% 26.45/26.67 Found x6 as proof of (cEVEN c0)
% 26.45/26.67 Found x6:(cEVEN c0)
% 26.45/26.67 Found x6 as proof of (cEVEN c0)
% 26.45/26.67 Found x6:(cEVEN c0)
% 26.45/26.67 Found x6 as proof of (cEVEN c0)
% 26.45/26.67 Found x6:(cEVEN c0)
% 26.45/26.67 Found x6 as proof of (cEVEN c0)
% 26.45/26.67 Found x6:(cEVEN c0)
% 26.45/26.67 Found (fun (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of (cEVEN c0)
% 26.45/26.67 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0))
% 26.75/26.97 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0)))
% 26.75/26.97 Found (and_rect30 (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 26.75/26.97 Found ((and_rect3 (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 26.75/26.97 Found (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 26.75/26.97 Found (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 26.75/26.97 Found x6:(cEVEN c0)
% 26.75/26.97 Found (fun (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of (cEVEN c0)
% 26.75/26.97 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0))
% 26.75/26.97 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0)))
% 26.75/26.97 Found (and_rect30 (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 26.75/26.97 Found ((and_rect3 (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 26.75/26.97 Found (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 26.75/26.97 Found (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 26.75/26.97 Found x6:(cEVEN c0)
% 26.75/26.97 Found (fun (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of (cEVEN c0)
% 26.75/26.97 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0))
% 26.75/26.97 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0)))
% 26.75/26.97 Found (and_rect30 (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 26.75/26.97 Found ((and_rect3 (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 26.75/26.97 Found (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 26.75/26.97 Found (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 27.12/27.36 Found x6:(cEVEN c0)
% 27.12/27.36 Found (fun (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of (cEVEN c0)
% 27.12/27.36 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0))
% 27.12/27.36 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0)))
% 27.12/27.36 Found (and_rect30 (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 27.12/27.36 Found ((and_rect3 (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 27.12/27.36 Found (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 27.12/27.36 Found (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 27.12/27.36 Found x6:(cEVEN c0)
% 27.12/27.36 Found (fun (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of (cEVEN c0)
% 27.12/27.36 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0))
% 27.12/27.36 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0)))
% 27.12/27.36 Found (and_rect30 (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 27.12/27.36 Found ((and_rect3 (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 27.12/27.36 Found (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 27.12/27.36 Found (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 27.12/27.36 Found x6:(cEVEN c0)
% 27.12/27.36 Found (fun (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of (cEVEN c0)
% 27.12/27.36 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0))
% 27.12/27.36 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0)))
% 27.12/27.36 Found (and_rect30 (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 27.12/27.36 Found ((and_rect3 (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 27.12/27.36 Found (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 27.49/27.68 Found (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 27.49/27.68 Found x6:(cEVEN c0)
% 27.49/27.68 Found (fun (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of (cEVEN c0)
% 27.49/27.68 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0))
% 27.49/27.68 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0)))
% 27.49/27.68 Found (and_rect30 (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 27.49/27.68 Found ((and_rect3 (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 27.49/27.68 Found (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 27.49/27.68 Found (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 27.49/27.68 Found x6:(cEVEN c0)
% 27.49/27.68 Found (fun (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of (cEVEN c0)
% 27.49/27.68 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0))
% 27.49/27.68 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0)))
% 27.49/27.68 Found (and_rect30 (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 27.49/27.68 Found ((and_rect3 (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 27.49/27.68 Found (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 27.49/27.68 Found (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 27.49/27.68 Found x6:(cEVEN c0)
% 27.49/27.68 Found (fun (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of (cEVEN c0)
% 27.49/27.68 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0))
% 27.49/27.68 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0)))
% 27.49/27.68 Found (and_rect30 (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 27.49/27.68 Found ((and_rect3 (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 35.23/35.42 Found (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 35.23/35.42 Found (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 35.23/35.42 Found x6:(cEVEN c0)
% 35.23/35.42 Found x6 as proof of (cEVEN c0)
% 35.23/35.42 Found x6:(cEVEN c0)
% 35.23/35.42 Found x6 as proof of (cEVEN c0)
% 35.23/35.42 Found x6:(cEVEN c0)
% 35.23/35.42 Found x6 as proof of (cEVEN c0)
% 35.23/35.42 Found x6:(cEVEN c0)
% 35.23/35.42 Found x6 as proof of (cEVEN c0)
% 35.23/35.42 Found x6:(cEVEN c0)
% 35.23/35.42 Found x6 as proof of (cEVEN c0)
% 35.23/35.42 Found x6:(cEVEN c0)
% 35.23/35.42 Found x6 as proof of (cEVEN c0)
% 35.23/35.42 Found x6:(cEVEN c0)
% 35.23/35.42 Found x6 as proof of (cEVEN c0)
% 35.23/35.42 Found x6:(cEVEN c0)
% 35.23/35.42 Found x6 as proof of (cEVEN c0)
% 35.23/35.42 Found x6:(cEVEN c0)
% 35.23/35.42 Found x6 as proof of (cEVEN c0)
% 35.23/35.42 Found x6:(cEVEN c0)
% 35.23/35.42 Found x6 as proof of (cEVEN c0)
% 35.23/35.42 Found x6:(cEVEN c0)
% 35.23/35.42 Found x6 as proof of (cEVEN c0)
% 35.23/35.42 Found x6:(cEVEN c0)
% 35.23/35.42 Found x6 as proof of (cEVEN c0)
% 35.23/35.42 Found x6:(cEVEN c0)
% 35.23/35.42 Found x6 as proof of (cEVEN c0)
% 35.23/35.42 Found x6:(cEVEN c0)
% 35.23/35.42 Found x6 as proof of (cEVEN c0)
% 35.23/35.42 Found x6:(cEVEN c0)
% 35.23/35.42 Found x6 as proof of (cEVEN c0)
% 35.23/35.42 Found x6:(cEVEN c0)
% 35.23/35.42 Found x6 as proof of (cEVEN c0)
% 35.23/35.42 Found x6:(cEVEN c0)
% 35.23/35.42 Found x6 as proof of (cEVEN c0)
% 35.23/35.42 Found x6:(cEVEN c0)
% 35.23/35.42 Found x6 as proof of (cEVEN c0)
% 35.23/35.42 Found x6:(cEVEN c0)
% 35.23/35.42 Found x6 as proof of (cEVEN c0)
% 35.23/35.42 Found x6:(cEVEN c0)
% 35.23/35.42 Found x6 as proof of (cEVEN c0)
% 35.23/35.42 Found x6:(cEVEN c0)
% 35.23/35.42 Found x6 as proof of (cEVEN c0)
% 35.23/35.42 Found x6:(cEVEN c0)
% 35.23/35.42 Found x6 as proof of (cEVEN c0)
% 35.23/35.42 Found x6:(cEVEN c0)
% 35.23/35.42 Found x6 as proof of (cEVEN c0)
% 35.23/35.42 Found x6:(cEVEN c0)
% 35.23/35.42 Found x6 as proof of (cEVEN c0)
% 35.23/35.42 Found x6:(cEVEN c0)
% 35.23/35.42 Found x6 as proof of (cEVEN c0)
% 35.23/35.42 Found x6:(cEVEN c0)
% 35.23/35.42 Found x6 as proof of (cEVEN c0)
% 35.23/35.42 Found x6:(cEVEN c0)
% 35.23/35.42 Found x6 as proof of (cEVEN c0)
% 35.23/35.42 Found x6:(cEVEN c0)
% 35.23/35.42 Found x6 as proof of (cEVEN c0)
% 35.23/35.42 Found x6:(cEVEN c0)
% 35.23/35.42 Found x6 as proof of (cEVEN c0)
% 35.23/35.42 Found x6:(cEVEN c0)
% 35.23/35.42 Found (fun (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of (cEVEN c0)
% 35.23/35.42 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0))
% 35.23/35.42 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0)))
% 35.23/35.42 Found (and_rect30 (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 35.23/35.42 Found ((and_rect3 (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 35.23/35.42 Found (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 35.23/35.42 Found (fun (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6))) as proof of (cEVEN c0)
% 35.23/35.42 Found (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6))) as proof of ((cODD (cS c0))->(cEVEN c0))
% 35.27/35.48 Found (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6))) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cEVEN c0)))
% 35.27/35.48 Found (and_rect20 (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)))) as proof of (cEVEN c0)
% 35.27/35.48 Found ((and_rect2 (cEVEN c0)) (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)))) as proof of (cEVEN c0)
% 35.27/35.48 Found (((fun (P:Type) (x4:(((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) x4) x2)) (cEVEN c0)) (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)))) as proof of (cEVEN c0)
% 35.27/35.48 Found (((fun (P:Type) (x4:(((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) x4) x2)) (cEVEN c0)) (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)))) as proof of (cEVEN c0)
% 35.27/35.48 Found x6:(cEVEN c0)
% 35.27/35.48 Found (fun (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of (cEVEN c0)
% 35.27/35.48 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0))
% 35.27/35.48 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0)))
% 35.27/35.48 Found (and_rect30 (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 35.27/35.48 Found ((and_rect3 (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 35.27/35.48 Found (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 35.36/35.57 Found (fun (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6))) as proof of (cEVEN c0)
% 35.36/35.57 Found (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6))) as proof of ((cODD (cS c0))->(cEVEN c0))
% 35.36/35.57 Found (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6))) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cEVEN c0)))
% 35.36/35.57 Found (and_rect20 (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)))) as proof of (cEVEN c0)
% 35.36/35.57 Found ((and_rect2 (cEVEN c0)) (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)))) as proof of (cEVEN c0)
% 35.36/35.57 Found (((fun (P:Type) (x4:(((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) x4) x2)) (cEVEN c0)) (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)))) as proof of (cEVEN c0)
% 35.36/35.57 Found (((fun (P:Type) (x4:(((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) x4) x2)) (cEVEN c0)) (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)))) as proof of (cEVEN c0)
% 35.36/35.57 Found x6:(cEVEN c0)
% 35.36/35.57 Found (fun (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of (cEVEN c0)
% 35.36/35.57 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0))
% 35.36/35.57 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0)))
% 35.36/35.57 Found (and_rect30 (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 35.36/35.57 Found ((and_rect3 (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 35.36/35.57 Found (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 35.36/35.57 Found (fun (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6))) as proof of (cEVEN c0)
% 35.36/35.57 Found (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6))) as proof of ((cODD (cS c0))->(cEVEN c0))
% 35.36/35.57 Found (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6))) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cEVEN c0)))
% 35.36/35.57 Found (and_rect20 (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)))) as proof of (cEVEN c0)
% 35.36/35.57 Found ((and_rect2 (cEVEN c0)) (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)))) as proof of (cEVEN c0)
% 35.36/35.57 Found (((fun (P:Type) (x4:(((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) x4) x2)) (cEVEN c0)) (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)))) as proof of (cEVEN c0)
% 35.36/35.57 Found (((fun (P:Type) (x4:(((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) x4) x2)) (cEVEN c0)) (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)))) as proof of (cEVEN c0)
% 35.47/35.66 Found x6:(cEVEN c0)
% 35.47/35.66 Found (fun (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of (cEVEN c0)
% 35.47/35.66 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0))
% 35.47/35.66 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0)))
% 35.47/35.66 Found (and_rect30 (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 35.47/35.66 Found ((and_rect3 (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 35.47/35.66 Found (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 35.47/35.66 Found (fun (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6))) as proof of (cEVEN c0)
% 35.47/35.66 Found (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6))) as proof of ((cODD (cS c0))->(cEVEN c0))
% 35.47/35.66 Found (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6))) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cEVEN c0)))
% 35.47/35.66 Found (and_rect20 (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)))) as proof of (cEVEN c0)
% 35.47/35.66 Found ((and_rect2 (cEVEN c0)) (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)))) as proof of (cEVEN c0)
% 35.47/35.66 Found (((fun (P:Type) (x4:(((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) x4) x2)) (cEVEN c0)) (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)))) as proof of (cEVEN c0)
% 35.54/35.76 Found (((fun (P:Type) (x4:(((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) x4) x2)) (cEVEN c0)) (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)))) as proof of (cEVEN c0)
% 35.54/35.76 Found x6:(cEVEN c0)
% 35.54/35.76 Found (fun (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of (cEVEN c0)
% 35.54/35.76 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0))
% 35.54/35.76 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0)))
% 35.54/35.76 Found (and_rect30 (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 35.54/35.76 Found ((and_rect3 (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 35.54/35.76 Found (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 35.54/35.76 Found (fun (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6))) as proof of (cEVEN c0)
% 35.54/35.76 Found (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6))) as proof of ((cODD (cS c0))->(cEVEN c0))
% 35.54/35.76 Found (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6))) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cEVEN c0)))
% 35.54/35.76 Found (and_rect20 (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)))) as proof of (cEVEN c0)
% 37.94/38.13 Found ((and_rect2 (cEVEN c0)) (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)))) as proof of (cEVEN c0)
% 37.94/38.13 Found (((fun (P:Type) (x4:(((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) x4) x2)) (cEVEN c0)) (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)))) as proof of (cEVEN c0)
% 37.94/38.13 Found (((fun (P:Type) (x4:(((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) x4) x2)) (cEVEN c0)) (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)))) as proof of (cEVEN c0)
% 37.94/38.13 Found x6:(cEVEN c0)
% 37.94/38.13 Found (fun (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of (cEVEN c0)
% 37.94/38.13 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0))
% 37.94/38.13 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0)))
% 37.94/38.13 Found (and_rect30 (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 37.94/38.13 Found ((and_rect3 (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 37.94/38.13 Found (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 37.94/38.13 Found (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 37.94/38.13 Found x6:(cEVEN c0)
% 37.94/38.13 Found (fun (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of (cEVEN c0)
% 37.94/38.13 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0))
% 37.94/38.13 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0)))
% 37.94/38.13 Found (and_rect30 (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 38.16/38.36 Found ((and_rect3 (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 38.16/38.36 Found (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 38.16/38.36 Found (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 38.16/38.36 Found x6:(cEVEN c0)
% 38.16/38.36 Found (fun (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of (cEVEN c0)
% 38.16/38.36 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0))
% 38.16/38.36 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0)))
% 38.16/38.36 Found (and_rect30 (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 38.16/38.36 Found ((and_rect3 (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 38.16/38.36 Found (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 38.16/38.36 Found (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 38.16/38.36 Found x6:(cEVEN c0)
% 38.16/38.36 Found (fun (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of (cEVEN c0)
% 38.16/38.36 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0))
% 38.16/38.36 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0)))
% 38.16/38.36 Found (and_rect30 (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 38.16/38.36 Found ((and_rect3 (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 38.16/38.36 Found (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 38.16/38.36 Found (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 38.16/38.36 Found x6:(cEVEN c0)
% 38.16/38.36 Found (fun (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of (cEVEN c0)
% 38.16/38.36 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0))
% 38.28/38.48 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0)))
% 38.28/38.48 Found (and_rect30 (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 38.28/38.48 Found ((and_rect3 (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 38.28/38.48 Found (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 38.28/38.48 Found (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 38.28/38.48 Found x6:(cEVEN c0)
% 38.28/38.48 Found (fun (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of (cEVEN c0)
% 38.28/38.48 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0))
% 38.28/38.48 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0)))
% 38.28/38.48 Found (and_rect30 (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 38.28/38.48 Found ((and_rect3 (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 38.28/38.48 Found (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 38.28/38.48 Found (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 38.28/38.48 Found x6:(cEVEN c0)
% 38.28/38.48 Found (fun (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of (cEVEN c0)
% 38.28/38.48 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0))
% 38.28/38.48 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0)))
% 38.28/38.48 Found (and_rect30 (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 38.28/38.48 Found ((and_rect3 (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 38.28/38.48 Found (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 38.28/38.48 Found (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 38.40/38.63 Found x6:(cEVEN c0)
% 38.40/38.63 Found (fun (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of (cEVEN c0)
% 38.40/38.63 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0))
% 38.40/38.63 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0)))
% 38.40/38.63 Found (and_rect30 (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 38.40/38.63 Found ((and_rect3 (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 38.40/38.63 Found (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 38.40/38.63 Found (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 38.40/38.63 Found x6:(cEVEN c0)
% 38.40/38.63 Found (fun (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of (cEVEN c0)
% 38.40/38.63 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0))
% 38.40/38.63 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0)))
% 38.40/38.63 Found (and_rect30 (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 38.40/38.63 Found ((and_rect3 (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 38.40/38.63 Found (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 38.40/38.63 Found (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 38.40/38.63 Found x6:(cEVEN c0)
% 38.40/38.63 Found (fun (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of (cEVEN c0)
% 38.40/38.63 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0))
% 38.40/38.63 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0)))
% 38.40/38.63 Found (and_rect30 (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 38.40/38.63 Found ((and_rect3 (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 38.40/38.63 Found (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 38.57/38.77 Found (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 38.57/38.77 Found x6:(cEVEN c0)
% 38.57/38.77 Found (fun (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of (cEVEN c0)
% 38.57/38.77 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0))
% 38.57/38.77 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0)))
% 38.57/38.77 Found (and_rect30 (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 38.57/38.77 Found ((and_rect3 (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 38.57/38.77 Found (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 38.57/38.77 Found (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 38.57/38.77 Found x6:(cEVEN c0)
% 38.57/38.77 Found (fun (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of (cEVEN c0)
% 38.57/38.77 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0))
% 38.57/38.77 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0)))
% 38.57/38.77 Found (and_rect30 (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 38.57/38.77 Found ((and_rect3 (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 38.57/38.77 Found (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 38.57/38.77 Found (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 38.57/38.77 Found x6:(cEVEN c0)
% 38.57/38.77 Found (fun (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of (cEVEN c0)
% 38.57/38.77 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0))
% 38.57/38.77 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0)))
% 38.57/38.77 Found (and_rect30 (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 38.57/38.77 Found ((and_rect3 (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 38.57/38.77 Found (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 38.69/38.90 Found (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 38.69/38.90 Found x6:(cEVEN c0)
% 38.69/38.90 Found (fun (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of (cEVEN c0)
% 38.69/38.90 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0))
% 38.69/38.90 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0)))
% 38.69/38.90 Found (and_rect30 (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 38.69/38.90 Found ((and_rect3 (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 38.69/38.90 Found (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 38.69/38.90 Found (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 38.69/38.90 Found x6:(cEVEN c0)
% 38.69/38.90 Found (fun (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of (cEVEN c0)
% 38.69/38.90 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0))
% 38.69/38.90 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0)))
% 38.69/38.90 Found (and_rect30 (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 38.69/38.90 Found ((and_rect3 (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 38.69/38.90 Found (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 38.69/38.90 Found (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 38.69/38.90 Found x6:(cEVEN c0)
% 38.69/38.90 Found (fun (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of (cEVEN c0)
% 38.69/38.90 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0))
% 38.69/38.90 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0)))
% 38.83/39.04 Found (and_rect30 (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 38.83/39.04 Found ((and_rect3 (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 38.83/39.04 Found (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 38.83/39.04 Found (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 38.83/39.04 Found x6:(cEVEN c0)
% 38.83/39.04 Found (fun (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of (cEVEN c0)
% 38.83/39.04 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0))
% 38.83/39.04 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0)))
% 38.83/39.04 Found (and_rect30 (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 38.83/39.04 Found ((and_rect3 (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 38.83/39.04 Found (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 38.83/39.04 Found (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 38.83/39.04 Found x6:(cEVEN c0)
% 38.83/39.04 Found (fun (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of (cEVEN c0)
% 38.83/39.04 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0))
% 38.83/39.04 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0)))
% 38.83/39.04 Found (and_rect30 (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 38.83/39.04 Found ((and_rect3 (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 38.83/39.04 Found (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 38.83/39.04 Found (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 38.83/39.04 Found x6:(cEVEN c0)
% 38.83/39.04 Found (fun (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of (cEVEN c0)
% 38.83/39.04 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0))
% 39.77/39.98 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0)))
% 39.77/39.98 Found (and_rect30 (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 39.77/39.98 Found ((and_rect3 (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 39.77/39.98 Found (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 39.77/39.98 Found (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 39.77/39.98 Found x6:(cEVEN c0)
% 39.77/39.98 Found (fun (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of (cEVEN c0)
% 39.77/39.98 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0))
% 39.77/39.98 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0)))
% 39.77/39.98 Found (and_rect30 (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 39.77/39.98 Found ((and_rect3 (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 39.77/39.98 Found (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 39.77/39.98 Found (fun (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6))) as proof of (cEVEN c0)
% 39.77/39.98 Found (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6))) as proof of ((cODD (cS c0))->(cEVEN c0))
% 39.77/39.98 Found (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6))) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cEVEN c0)))
% 39.77/39.98 Found (and_rect20 (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)))) as proof of (cEVEN c0)
% 39.77/39.98 Found ((and_rect2 (cEVEN c0)) (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)))) as proof of (cEVEN c0)
% 39.77/39.98 Found (((fun (P:Type) (x4:(((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) x4) x2)) (cEVEN c0)) (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)))) as proof of (cEVEN c0)
% 39.77/39.98 Found (fun (x3:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (((fun (P:Type) (x4:(((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) x4) x2)) (cEVEN c0)) (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6))))) as proof of (cEVEN c0)
% 39.77/39.98 Found (fun (x2:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x3:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (((fun (P:Type) (x4:(((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) x4) x2)) (cEVEN c0)) (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6))))) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cEVEN c0))
% 39.77/39.98 Found (fun (x2:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x3:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (((fun (P:Type) (x4:(((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) x4) x2)) (cEVEN c0)) (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6))))) 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)))))->(cEVEN c0)))
% 39.77/39.98 Found (and_rect10 (fun (x2:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x3:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (((fun (P:Type) (x4:(((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) x4) x2)) (cEVEN c0)) (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)))))) as proof of (cEVEN c0)
% 39.77/39.98 Found ((and_rect1 (cEVEN c0)) (fun (x2:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x3:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (((fun (P:Type) (x4:(((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) x4) x2)) (cEVEN c0)) (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)))))) as proof of (cEVEN c0)
% 39.77/39.98 Found (((fun (P:Type) (x2:(((and ((and (cEVEN c0)) (forall (Xn0: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) x2) x0)) (cEVEN c0)) (fun (x2:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x3:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (((fun (P:Type) (x4:(((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) x4) x2)) (cEVEN c0)) (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)))))) as proof of (cEVEN c0)
% 39.77/39.98 Found (((fun (P:Type) (x2:(((and ((and (cEVEN c0)) (forall (Xn0: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) x2) x0)) (cEVEN c0)) (fun (x2:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x3:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (((fun (P:Type) (x4:(((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) x4) x2)) (cEVEN c0)) (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)))))) as proof of (cEVEN c0)
% 39.87/40.06 Found x6:(cEVEN c0)
% 39.87/40.06 Found (fun (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of (cEVEN c0)
% 39.87/40.06 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0))
% 39.87/40.06 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0)))
% 39.87/40.06 Found (and_rect30 (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 39.87/40.06 Found ((and_rect3 (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 39.87/40.06 Found (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 39.87/40.06 Found (fun (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6))) as proof of (cEVEN c0)
% 39.87/40.06 Found (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6))) as proof of ((cODD (cS c0))->(cEVEN c0))
% 39.87/40.06 Found (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6))) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cEVEN c0)))
% 39.87/40.06 Found (and_rect20 (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)))) as proof of (cEVEN c0)
% 39.87/40.06 Found ((and_rect2 (cEVEN c0)) (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)))) as proof of (cEVEN c0)
% 39.87/40.06 Found (((fun (P:Type) (x4:(((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) x4) x2)) (cEVEN c0)) (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)))) as proof of (cEVEN c0)
% 39.87/40.06 Found (fun (x3:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (((fun (P:Type) (x4:(((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) x4) x2)) (cEVEN c0)) (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6))))) as proof of (cEVEN c0)
% 39.87/40.06 Found (fun (x2:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x3:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (((fun (P:Type) (x4:(((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) x4) x2)) (cEVEN c0)) (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6))))) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cEVEN c0))
% 39.87/40.06 Found (fun (x2:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x3:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (((fun (P:Type) (x4:(((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) x4) x2)) (cEVEN c0)) (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6))))) 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)))))->(cEVEN c0)))
% 39.87/40.06 Found (and_rect10 (fun (x2:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x3:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (((fun (P:Type) (x4:(((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) x4) x2)) (cEVEN c0)) (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)))))) as proof of (cEVEN c0)
% 41.58/41.79 Found ((and_rect1 (cEVEN c0)) (fun (x2:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x3:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (((fun (P:Type) (x4:(((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) x4) x2)) (cEVEN c0)) (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)))))) as proof of (cEVEN c0)
% 41.58/41.79 Found (((fun (P:Type) (x2:(((and ((and (cEVEN c0)) (forall (Xn0: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) x2) x0)) (cEVEN c0)) (fun (x2:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x3:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (((fun (P:Type) (x4:(((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) x4) x2)) (cEVEN c0)) (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)))))) as proof of (cEVEN c0)
% 41.58/41.79 Found (((fun (P:Type) (x2:(((and ((and (cEVEN c0)) (forall (Xn0: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) x2) x0)) (cEVEN c0)) (fun (x2:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x3:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (((fun (P:Type) (x4:(((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) x4) x2)) (cEVEN c0)) (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)))))) as proof of (cEVEN c0)
% 41.58/41.79 Found x6:(cEVEN c0)
% 41.58/41.79 Found (fun (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of (cEVEN c0)
% 41.58/41.79 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0))
% 41.58/41.79 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0)))
% 41.58/41.79 Found (and_rect30 (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 41.58/41.79 Found ((and_rect3 (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 41.58/41.79 Found (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 41.58/41.79 Found (fun (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6))) as proof of (cEVEN c0)
% 41.58/41.79 Found (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6))) as proof of ((cODD (cS c0))->(cEVEN c0))
% 41.58/41.79 Found (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6))) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cEVEN c0)))
% 41.58/41.79 Found (and_rect20 (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)))) as proof of (cEVEN c0)
% 41.58/41.79 Found ((and_rect2 (cEVEN c0)) (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)))) as proof of (cEVEN c0)
% 41.58/41.79 Found (((fun (P:Type) (x4:(((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) x4) x2)) (cEVEN c0)) (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)))) as proof of (cEVEN c0)
% 41.58/41.79 Found (((fun (P:Type) (x4:(((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) x4) x2)) (cEVEN c0)) (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)))) as proof of (cEVEN c0)
% 41.66/41.86 Found x6:(cEVEN c0)
% 41.66/41.86 Found (fun (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of (cEVEN c0)
% 41.66/41.86 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0))
% 41.66/41.86 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0)))
% 41.66/41.86 Found (and_rect30 (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 41.66/41.86 Found ((and_rect3 (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 41.66/41.86 Found (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 41.66/41.86 Found (fun (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6))) as proof of (cEVEN c0)
% 41.66/41.86 Found (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6))) as proof of ((cODD (cS c0))->(cEVEN c0))
% 41.66/41.86 Found (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6))) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cEVEN c0)))
% 41.66/41.86 Found (and_rect20 (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)))) as proof of (cEVEN c0)
% 41.66/41.86 Found ((and_rect2 (cEVEN c0)) (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)))) as proof of (cEVEN c0)
% 41.66/41.86 Found (((fun (P:Type) (x4:(((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) x4) x2)) (cEVEN c0)) (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)))) as proof of (cEVEN c0)
% 41.77/41.98 Found (((fun (P:Type) (x4:(((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) x4) x2)) (cEVEN c0)) (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)))) as proof of (cEVEN c0)
% 41.77/41.98 Found x6:(cEVEN c0)
% 41.77/41.98 Found (fun (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of (cEVEN c0)
% 41.77/41.98 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0))
% 41.77/41.98 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0)))
% 41.77/41.98 Found (and_rect30 (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 41.77/41.98 Found ((and_rect3 (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 41.77/41.98 Found (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 41.77/41.98 Found (fun (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6))) as proof of (cEVEN c0)
% 41.77/41.98 Found (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6))) as proof of ((cODD (cS c0))->(cEVEN c0))
% 41.77/41.98 Found (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6))) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cEVEN c0)))
% 41.77/41.98 Found (and_rect20 (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)))) as proof of (cEVEN c0)
% 41.77/41.98 Found ((and_rect2 (cEVEN c0)) (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)))) as proof of (cEVEN c0)
% 41.83/42.04 Found (((fun (P:Type) (x4:(((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) x4) x2)) (cEVEN c0)) (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)))) as proof of (cEVEN c0)
% 41.83/42.04 Found (((fun (P:Type) (x4:(((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) x4) x2)) (cEVEN c0)) (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)))) as proof of (cEVEN c0)
% 41.83/42.04 Found x6:(cEVEN c0)
% 41.83/42.04 Found (fun (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of (cEVEN c0)
% 41.83/42.04 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0))
% 41.83/42.04 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0)))
% 41.83/42.04 Found (and_rect30 (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 41.83/42.04 Found ((and_rect3 (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 41.83/42.04 Found (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 41.83/42.04 Found (fun (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6))) as proof of (cEVEN c0)
% 41.83/42.04 Found (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6))) as proof of ((cODD (cS c0))->(cEVEN c0))
% 41.83/42.04 Found (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6))) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cEVEN c0)))
% 41.87/42.10 Found (and_rect20 (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)))) as proof of (cEVEN c0)
% 41.87/42.10 Found ((and_rect2 (cEVEN c0)) (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)))) as proof of (cEVEN c0)
% 41.87/42.10 Found (((fun (P:Type) (x4:(((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) x4) x2)) (cEVEN c0)) (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)))) as proof of (cEVEN c0)
% 41.87/42.10 Found (((fun (P:Type) (x4:(((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) x4) x2)) (cEVEN c0)) (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)))) as proof of (cEVEN c0)
% 41.87/42.10 Found x6:(cEVEN c0)
% 41.87/42.10 Found (fun (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of (cEVEN c0)
% 41.87/42.10 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0))
% 41.87/42.10 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0)))
% 41.87/42.10 Found (and_rect30 (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 41.87/42.10 Found ((and_rect3 (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 41.87/42.10 Found (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 41.87/42.10 Found (fun (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6))) as proof of (cEVEN c0)
% 41.96/42.16 Found (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6))) as proof of ((cODD (cS c0))->(cEVEN c0))
% 41.96/42.16 Found (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6))) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cEVEN c0)))
% 41.96/42.16 Found (and_rect20 (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)))) as proof of (cEVEN c0)
% 41.96/42.16 Found ((and_rect2 (cEVEN c0)) (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)))) as proof of (cEVEN c0)
% 41.96/42.16 Found (((fun (P:Type) (x4:(((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) x4) x2)) (cEVEN c0)) (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)))) as proof of (cEVEN c0)
% 41.96/42.16 Found (((fun (P:Type) (x4:(((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) x4) x2)) (cEVEN c0)) (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)))) as proof of (cEVEN c0)
% 41.96/42.16 Found x6:(cEVEN c0)
% 41.96/42.16 Found (fun (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of (cEVEN c0)
% 41.96/42.16 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0))
% 41.96/42.16 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0)))
% 41.96/42.16 Found (and_rect30 (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 41.96/42.16 Found ((and_rect3 (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 41.96/42.16 Found (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 41.96/42.16 Found (fun (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6))) as proof of (cEVEN c0)
% 41.96/42.16 Found (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6))) as proof of ((cODD (cS c0))->(cEVEN c0))
% 41.96/42.16 Found (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6))) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cEVEN c0)))
% 41.96/42.16 Found (and_rect20 (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)))) as proof of (cEVEN c0)
% 41.96/42.16 Found ((and_rect2 (cEVEN c0)) (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)))) as proof of (cEVEN c0)
% 41.96/42.16 Found (((fun (P:Type) (x4:(((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) x4) x2)) (cEVEN c0)) (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)))) as proof of (cEVEN c0)
% 41.96/42.16 Found (((fun (P:Type) (x4:(((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) x4) x2)) (cEVEN c0)) (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)))) as proof of (cEVEN c0)
% 42.00/42.22 Found x6:(cEVEN c0)
% 42.00/42.22 Found (fun (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of (cEVEN c0)
% 42.00/42.22 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0))
% 42.00/42.22 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0)))
% 42.00/42.22 Found (and_rect30 (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 42.00/42.22 Found ((and_rect3 (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 42.00/42.22 Found (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 42.00/42.22 Found (fun (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6))) as proof of (cEVEN c0)
% 42.00/42.22 Found (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6))) as proof of ((cODD (cS c0))->(cEVEN c0))
% 42.00/42.22 Found (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6))) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cEVEN c0)))
% 42.00/42.22 Found (and_rect20 (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)))) as proof of (cEVEN c0)
% 42.00/42.22 Found ((and_rect2 (cEVEN c0)) (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)))) as proof of (cEVEN c0)
% 42.00/42.22 Found (((fun (P:Type) (x4:(((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) x4) x2)) (cEVEN c0)) (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)))) as proof of (cEVEN c0)
% 42.08/42.30 Found (((fun (P:Type) (x4:(((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) x4) x2)) (cEVEN c0)) (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)))) as proof of (cEVEN c0)
% 42.08/42.30 Found x6:(cEVEN c0)
% 42.08/42.30 Found (fun (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of (cEVEN c0)
% 42.08/42.30 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0))
% 42.08/42.30 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0)))
% 42.08/42.30 Found (and_rect30 (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 42.08/42.30 Found ((and_rect3 (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 42.08/42.30 Found (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 42.08/42.30 Found (fun (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6))) as proof of (cEVEN c0)
% 42.08/42.30 Found (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6))) as proof of ((cODD (cS c0))->(cEVEN c0))
% 42.08/42.30 Found (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6))) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cEVEN c0)))
% 42.08/42.30 Found (and_rect20 (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)))) as proof of (cEVEN c0)
% 42.08/42.30 Found ((and_rect2 (cEVEN c0)) (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)))) as proof of (cEVEN c0)
% 42.18/42.36 Found (((fun (P:Type) (x4:(((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) x4) x2)) (cEVEN c0)) (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)))) as proof of (cEVEN c0)
% 42.18/42.36 Found (((fun (P:Type) (x4:(((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) x4) x2)) (cEVEN c0)) (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)))) as proof of (cEVEN c0)
% 42.18/42.36 Found x6:(cEVEN c0)
% 42.18/42.36 Found (fun (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of (cEVEN c0)
% 42.18/42.36 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0))
% 42.18/42.36 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0)))
% 42.18/42.36 Found (and_rect30 (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 42.18/42.36 Found ((and_rect3 (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 42.18/42.36 Found (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 42.18/42.36 Found (fun (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6))) as proof of (cEVEN c0)
% 42.18/42.36 Found (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6))) as proof of ((cODD (cS c0))->(cEVEN c0))
% 42.18/42.36 Found (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6))) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cEVEN c0)))
% 43.62/43.81 Found (and_rect20 (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)))) as proof of (cEVEN c0)
% 43.62/43.81 Found ((and_rect2 (cEVEN c0)) (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)))) as proof of (cEVEN c0)
% 43.62/43.81 Found (((fun (P:Type) (x4:(((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) x4) x2)) (cEVEN c0)) (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)))) as proof of (cEVEN c0)
% 43.62/43.81 Found (((fun (P:Type) (x4:(((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) x4) x2)) (cEVEN c0)) (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)))) as proof of (cEVEN c0)
% 43.62/43.81 Found x6:(cEVEN c0)
% 43.62/43.81 Found (fun (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of (cEVEN c0)
% 43.62/43.81 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0))
% 43.62/43.81 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0)))
% 43.62/43.81 Found (and_rect30 (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 43.62/43.81 Found ((and_rect3 (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 43.62/43.81 Found (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 43.62/43.81 Found (fun (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6))) as proof of (cEVEN c0)
% 43.62/43.81 Found (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6))) as proof of ((cODD (cS c0))->(cEVEN c0))
% 43.62/43.81 Found (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6))) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cEVEN c0)))
% 43.62/43.81 Found (and_rect20 (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)))) as proof of (cEVEN c0)
% 43.62/43.81 Found ((and_rect2 (cEVEN c0)) (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)))) as proof of (cEVEN c0)
% 43.62/43.81 Found (((fun (P:Type) (x4:(((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) x4) x2)) (cEVEN c0)) (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)))) as proof of (cEVEN c0)
% 43.62/43.81 Found (fun (x3:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (((fun (P:Type) (x4:(((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) x4) x2)) (cEVEN c0)) (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6))))) as proof of (cEVEN c0)
% 43.62/43.81 Found (fun (x2:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x3:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (((fun (P:Type) (x4:(((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) x4) x2)) (cEVEN c0)) (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6))))) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cEVEN c0))
% 43.62/43.81 Found (fun (x2:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x3:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (((fun (P:Type) (x4:(((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) x4) x2)) (cEVEN c0)) (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6))))) 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)))))->(cEVEN c0)))
% 43.62/43.81 Found (and_rect10 (fun (x2:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x3:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (((fun (P:Type) (x4:(((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) x4) x2)) (cEVEN c0)) (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)))))) as proof of (cEVEN c0)
% 43.62/43.81 Found ((and_rect1 (cEVEN c0)) (fun (x2:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x3:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (((fun (P:Type) (x4:(((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) x4) x2)) (cEVEN c0)) (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)))))) as proof of (cEVEN c0)
% 43.62/43.81 Found (((fun (P:Type) (x2:(((and ((and (cEVEN c0)) (forall (Xn0: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) x2) x0)) (cEVEN c0)) (fun (x2:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x3:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (((fun (P:Type) (x4:(((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) x4) x2)) (cEVEN c0)) (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)))))) as proof of (cEVEN c0)
% 43.67/43.87 Found (((fun (P:Type) (x2:(((and ((and (cEVEN c0)) (forall (Xn0: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) x2) x0)) (cEVEN c0)) (fun (x2:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x3:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (((fun (P:Type) (x4:(((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) x4) x2)) (cEVEN c0)) (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)))))) as proof of (cEVEN c0)
% 43.67/43.87 Found x6:(cEVEN c0)
% 43.67/43.87 Found (fun (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of (cEVEN c0)
% 43.67/43.87 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0))
% 43.67/43.87 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0)))
% 43.67/43.87 Found (and_rect30 (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 43.67/43.87 Found ((and_rect3 (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 43.67/43.87 Found (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 43.67/43.87 Found (fun (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6))) as proof of (cEVEN c0)
% 43.67/43.87 Found (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6))) as proof of ((cODD (cS c0))->(cEVEN c0))
% 43.67/43.87 Found (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6))) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cEVEN c0)))
% 43.67/43.87 Found (and_rect20 (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)))) as proof of (cEVEN c0)
% 43.67/43.88 Found ((and_rect2 (cEVEN c0)) (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)))) as proof of (cEVEN c0)
% 43.67/43.88 Found (((fun (P:Type) (x4:(((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) x4) x2)) (cEVEN c0)) (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)))) as proof of (cEVEN c0)
% 43.67/43.88 Found (fun (x3:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (((fun (P:Type) (x4:(((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) x4) x2)) (cEVEN c0)) (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6))))) as proof of (cEVEN c0)
% 43.67/43.88 Found (fun (x2:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x3:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (((fun (P:Type) (x4:(((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) x4) x2)) (cEVEN c0)) (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6))))) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cEVEN c0))
% 43.67/43.88 Found (fun (x2:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x3:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (((fun (P:Type) (x4:(((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) x4) x2)) (cEVEN c0)) (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6))))) 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)))))->(cEVEN c0)))
% 43.67/43.88 Found (and_rect10 (fun (x2:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x3:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (((fun (P:Type) (x4:(((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) x4) x2)) (cEVEN c0)) (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)))))) as proof of (cEVEN c0)
% 43.67/43.88 Found ((and_rect1 (cEVEN c0)) (fun (x2:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x3:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (((fun (P:Type) (x4:(((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) x4) x2)) (cEVEN c0)) (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)))))) as proof of (cEVEN c0)
% 43.67/43.88 Found (((fun (P:Type) (x2:(((and ((and (cEVEN c0)) (forall (Xn0: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) x2) x0)) (cEVEN c0)) (fun (x2:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x3:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (((fun (P:Type) (x4:(((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) x4) x2)) (cEVEN c0)) (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)))))) as proof of (cEVEN c0)
% 43.67/43.88 Found (((fun (P:Type) (x2:(((and ((and (cEVEN c0)) (forall (Xn0: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) x2) x0)) (cEVEN c0)) (fun (x2:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x3:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (((fun (P:Type) (x4:(((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) x4) x2)) (cEVEN c0)) (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)))))) as proof of (cEVEN c0)
% 43.67/43.94 Found x6:(cEVEN c0)
% 43.67/43.94 Found (fun (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of (cEVEN c0)
% 43.67/43.94 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0))
% 43.67/43.94 Found (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6) as proof of ((cEVEN c0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cEVEN c0)))
% 43.67/43.94 Found (and_rect30 (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 43.67/43.94 Found ((and_rect3 (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 43.67/43.94 Found (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)) as proof of (cEVEN c0)
% 43.67/43.94 Found (fun (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6))) as proof of (cEVEN c0)
% 43.67/43.94 Found (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6))) as proof of ((cODD (cS c0))->(cEVEN c0))
% 43.67/43.94 Found (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6))) as proof of (((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cEVEN c0)))
% 43.67/43.94 Found (and_rect20 (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)))) as proof of (cEVEN c0)
% 43.67/43.94 Found ((and_rect2 (cEVEN c0)) (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)))) as proof of (cEVEN c0)
% 43.67/43.94 Found (((fun (P:Type) (x4:(((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) x4) x2)) (cEVEN c0)) (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)))) as proof of (cEVEN c0)
% 43.67/43.94 Found (fun (x3:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (((fun (P:Type) (x4:(((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) x4) x2)) (cEVEN c0)) (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6))))) as proof of (cEVEN c0)
% 43.67/43.94 Found (fun (x2:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x3:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (((fun (P:Type) (x4:(((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) x4) x2)) (cEVEN c0)) (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6))))) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cEVEN c0))
% 43.67/43.94 Found (fun (x2:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x3:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (((fun (P:Type) (x4:(((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) x4) x2)) (cEVEN c0)) (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6))))) 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)))))->(cEVEN c0)))
% 43.67/43.94 Found (and_rect10 (fun (x2:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x3:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (((fun (P:Type) (x4:(((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) x4) x2)) (cEVEN c0)) (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)))))) as proof of (cEVEN c0)
% 45.37/45.61 Found ((and_rect1 (cEVEN c0)) (fun (x2:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x3:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (((fun (P:Type) (x4:(((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) x4) x2)) (cEVEN c0)) (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)))))) as proof of (cEVEN c0)
% 45.37/45.61 Found (((fun (P:Type) (x2:(((and ((and (cEVEN c0)) (forall (Xn0: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) x2) x0)) (cEVEN c0)) (fun (x2:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x3:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (((fun (P:Type) (x4:(((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) x4) x2)) (cEVEN c0)) (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)))))) as proof of (cEVEN c0)
% 45.37/45.61 Found (((fun (P:Type) (x2:(((and ((and (cEVEN c0)) (forall (Xn0: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) x2) x0)) (cEVEN c0)) (fun (x2:((and ((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x3:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (((fun (P:Type) (x4:(((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) x4) x2)) (cEVEN c0)) (fun (x4:((and (cEVEN c0)) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x5:(cODD (cS c0)))=> (((fun (P:Type) (x6:((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) x6) x4)) (cEVEN c0)) (fun (x6:(cEVEN c0)) (x7:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x6)))))) as proof of (cEVEN c0)
% 45.37/45.61 % SZS status GaveUp for /export/starexec/sandbox/benchmark/theBenchmark.p
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