TSTP Solution File: SYN056^5 by cocATP---0.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SYN056^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n092.star.cs.uiowa.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory : 32286.75MB
% OS : Linux 2.6.32-431.20.3.el6.x86_64
% CPULimit : 300s
% DateTime : Thu Jul 17 13:37:47 EDT 2014
% Result : Timeout 300.09s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : SYN056^5 : TPTP v6.1.0. Released v4.0.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n092.star.cs.uiowa.edu
% % Model : x86_64 x86_64
% % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% % Memory : 32286.75MB
% % OS : Linux 2.6.32-431.20.3.el6.x86_64
% % CPULimit : 300
% % DateTime : Thu Jul 17 08:03:21 CDT 2014
% % CPUTime: 300.09
% Python 2.7.5
% Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% FOF formula (<kernel.Constant object at 0x1d6a1b8>, <kernel.DependentProduct object at 0x1a5fbd8>) of role type named cR
% Using role type
% Declaring cR:(fofType->Prop)
% FOF formula (<kernel.Constant object at 0x1d6a758>, <kernel.DependentProduct object at 0x1d68cf8>) of role type named cP
% Using role type
% Declaring cP:(fofType->Prop)
% FOF formula (<kernel.Constant object at 0x1d6a098>, <kernel.DependentProduct object at 0x1d680e0>) of role type named cS
% Using role type
% Declaring cS:(fofType->Prop)
% FOF formula (<kernel.Constant object at 0x1fcbdd0>, <kernel.DependentProduct object at 0x1d68098>) of role type named cQ
% Using role type
% Declaring cQ:(fofType->Prop)
% FOF formula (((and ((and (((ex fofType) (fun (Xx:fofType)=> (cP Xx)))->((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))) (((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))->((ex fofType) (fun (Xx:fofType)=> (cP Xx)))))) (forall (Xx:fofType) (Xy:fofType), (((and (cP Xx)) (cQ Xy))->((and ((cR Xx)->(cS Xy))) ((cS Xy)->(cR Xx))))))->((and ((forall (Xx:fofType), ((cP Xx)->(cR Xx)))->(forall (Xx:fofType), ((cQ Xx)->(cS Xx))))) ((forall (Xx:fofType), ((cQ Xx)->(cS Xx)))->(forall (Xx:fofType), ((cP Xx)->(cR Xx)))))) of role conjecture named cPELL26
% Conjecture to prove = (((and ((and (((ex fofType) (fun (Xx:fofType)=> (cP Xx)))->((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))) (((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))->((ex fofType) (fun (Xx:fofType)=> (cP Xx)))))) (forall (Xx:fofType) (Xy:fofType), (((and (cP Xx)) (cQ Xy))->((and ((cR Xx)->(cS Xy))) ((cS Xy)->(cR Xx))))))->((and ((forall (Xx:fofType), ((cP Xx)->(cR Xx)))->(forall (Xx:fofType), ((cQ Xx)->(cS Xx))))) ((forall (Xx:fofType), ((cQ Xx)->(cS Xx)))->(forall (Xx:fofType), ((cP Xx)->(cR Xx)))))):Prop
% Parameter fofType_DUMMY:fofType.
% We need to prove ['(((and ((and (((ex fofType) (fun (Xx:fofType)=> (cP Xx)))->((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))) (((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))->((ex fofType) (fun (Xx:fofType)=> (cP Xx)))))) (forall (Xx:fofType) (Xy:fofType), (((and (cP Xx)) (cQ Xy))->((and ((cR Xx)->(cS Xy))) ((cS Xy)->(cR Xx))))))->((and ((forall (Xx:fofType), ((cP Xx)->(cR Xx)))->(forall (Xx:fofType), ((cQ Xx)->(cS Xx))))) ((forall (Xx:fofType), ((cQ Xx)->(cS Xx)))->(forall (Xx:fofType), ((cP Xx)->(cR Xx))))))']
% Parameter fofType:Type.
% Parameter cR:(fofType->Prop).
% Parameter cP:(fofType->Prop).
% Parameter cS:(fofType->Prop).
% Parameter cQ:(fofType->Prop).
% Trying to prove (((and ((and (((ex fofType) (fun (Xx:fofType)=> (cP Xx)))->((ex fofType) (fun (Xx:fofType)=> (cQ Xx))))) (((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))->((ex fofType) (fun (Xx:fofType)=> (cP Xx)))))) (forall (Xx:fofType) (Xy:fofType), (((and (cP Xx)) (cQ Xy))->((and ((cR Xx)->(cS Xy))) ((cS Xy)->(cR Xx))))))->((and ((forall (Xx:fofType), ((cP Xx)->(cR Xx)))->(forall (Xx:fofType), ((cQ Xx)->(cS Xx))))) ((forall (Xx:fofType), ((cQ Xx)->(cS Xx)))->(forall (Xx:fofType), ((cP Xx)->(cR Xx))))))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found ex_intro0000:=(ex_intro000 x5):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (ex_intro000 x5) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found ((ex_intro00 Xx) x5) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (((ex_intro0 (fun (Xx:fofType)=> (cQ Xx))) Xx) x5) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found ((((ex_intro fofType) (fun (Xx:fofType)=> (cQ Xx))) Xx) x5) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found ((((ex_intro fofType) (fun (Xx:fofType)=> (cQ Xx))) Xx) x5) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found ex_intro0000:=(ex_intro000 x5):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (ex_intro000 x5) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found ((ex_intro00 Xx) x5) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (((ex_intro0 (fun (Xx:fofType)=> (cP Xx))) Xx) x5) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found ((((ex_intro fofType) (fun (Xx:fofType)=> (cP Xx))) Xx) x5) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found ((((ex_intro fofType) (fun (Xx:fofType)=> (cP Xx))) Xx) x5) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found ex_intro0000:=(ex_intro000 x00):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (ex_intro000 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found ((ex_intro00 Xx) x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (((ex_intro0 (fun (Xx:fofType)=> (cQ Xx))) Xx) x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found ((((ex_intro fofType) (fun (Xx:fofType)=> (cQ Xx))) Xx) x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found ((((ex_intro fofType) (fun (Xx:fofType)=> (cQ Xx))) Xx) x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found ex_intro0000:=(ex_intro000 x00):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (ex_intro000 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found ((ex_intro00 Xx) x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (((ex_intro0 (fun (Xx:fofType)=> (cP Xx))) Xx) x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found ((((ex_intro fofType) (fun (Xx:fofType)=> (cP Xx))) Xx) x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found ((((ex_intro fofType) (fun (Xx:fofType)=> (cP Xx))) Xx) x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found ex_intro0000:=(ex_intro000 x5):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (ex_intro000 x5) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found ((ex_intro00 Xx) x5) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (((ex_intro0 (fun (Xx:fofType)=> (cP Xx))) Xx) x5) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found ((((ex_intro fofType) (fun (Xx:fofType)=> (cP Xx))) Xx) x5) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found ((((ex_intro fofType) (fun (Xx:fofType)=> (cP Xx))) Xx) x5) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x2 ((((ex_intro fofType) (fun (Xx:fofType)=> (cP Xx))) Xx) x5)) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 ((((ex_intro fofType) (fun (Xx:fofType)=> (cP Xx))) Xx) x5)) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found ex_intro0000:=(ex_intro000 x5):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (ex_intro000 x5) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found ((ex_intro00 Xx) x5) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (((ex_intro0 (fun (Xx:fofType)=> (cQ Xx))) Xx) x5) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found ((((ex_intro fofType) (fun (Xx:fofType)=> (cQ Xx))) Xx) x5) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found ((((ex_intro fofType) (fun (Xx:fofType)=> (cQ Xx))) Xx) x5) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x3 ((((ex_intro fofType) (fun (Xx:fofType)=> (cQ Xx))) Xx) x5)) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 ((((ex_intro fofType) (fun (Xx:fofType)=> (cQ Xx))) Xx) x5)) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found ex_intro0000:=(ex_intro000 x3):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (ex_intro000 x3) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ((ex_intro00 Xx) x3) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (((ex_intro0 (fun (Xx0:fofType)=> (cP Xx0))) Xx) x3) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ((((ex_intro fofType) (fun (Xx0:fofType)=> (cP Xx0))) Xx) x3) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ((((ex_intro fofType) (fun (Xx0:fofType)=> (cP Xx0))) Xx) x3) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found ex_intro0000:=(ex_intro000 x3):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (ex_intro000 x3) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ((ex_intro00 Xx) x3) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (((ex_intro0 (fun (Xx0:fofType)=> (cP Xx0))) Xx) x3) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ((((ex_intro fofType) (fun (Xx0:fofType)=> (cP Xx0))) Xx) x3) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ((((ex_intro fofType) (fun (Xx0:fofType)=> (cP Xx0))) Xx) x3) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ex_intro0000:=(ex_intro000 x3):((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found (ex_intro000 x3) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found ((ex_intro00 Xx) x3) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found (((ex_intro0 (fun (Xx0:fofType)=> (cQ Xx0))) Xx) x3) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found ((((ex_intro fofType) (fun (Xx0:fofType)=> (cQ Xx0))) Xx) x3) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found ((((ex_intro fofType) (fun (Xx0:fofType)=> (cQ Xx0))) Xx) x3) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found ex_intro0000:=(ex_intro000 x00):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (ex_intro000 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found ((ex_intro00 Xx) x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (((ex_intro0 (fun (Xx:fofType)=> (cP Xx))) Xx) x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found ((((ex_intro fofType) (fun (Xx:fofType)=> (cP Xx))) Xx) x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found ((((ex_intro fofType) (fun (Xx:fofType)=> (cP Xx))) Xx) x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x2 ((((ex_intro fofType) (fun (Xx:fofType)=> (cP Xx))) Xx) x00)) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 ((((ex_intro fofType) (fun (Xx:fofType)=> (cP Xx))) Xx) x00)) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found ex_intro0000:=(ex_intro000 x00):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (ex_intro000 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found ((ex_intro00 Xx) x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (((ex_intro0 (fun (Xx:fofType)=> (cQ Xx))) Xx) x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found ((((ex_intro fofType) (fun (Xx:fofType)=> (cQ Xx))) Xx) x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found ((((ex_intro fofType) (fun (Xx:fofType)=> (cQ Xx))) Xx) x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x3 ((((ex_intro fofType) (fun (Xx:fofType)=> (cQ Xx))) Xx) x00)) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 ((((ex_intro fofType) (fun (Xx:fofType)=> (cQ Xx))) Xx) x00)) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found ex_intro0000:=(ex_intro000 x00):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (ex_intro000 x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ((ex_intro00 Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (((ex_intro0 (fun (Xx0:fofType)=> (cP Xx0))) Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ((((ex_intro fofType) (fun (Xx0:fofType)=> (cP Xx0))) Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ((((ex_intro fofType) (fun (Xx0:fofType)=> (cP Xx0))) Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x40:=(x4 x50):((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found (x4 x50) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found (x4 x50) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found x50:=(x5 x40):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x5 x40) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x5 x40) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x50:=(x5 x40):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x5 x40) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x5 x40) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found ex_intro0000:=(ex_intro000 x00):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (ex_intro000 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found ((ex_intro00 Xx) x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (((ex_intro0 (fun (Xx:fofType)=> (cQ Xx))) Xx) x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found ((((ex_intro fofType) (fun (Xx:fofType)=> (cQ Xx))) Xx) x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found ((((ex_intro fofType) (fun (Xx:fofType)=> (cQ Xx))) Xx) x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found ex_intro0000:=(ex_intro000 x00):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (ex_intro000 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found ((ex_intro00 Xx) x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (((ex_intro0 (fun (Xx:fofType)=> (cP Xx))) Xx) x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found ((((ex_intro fofType) (fun (Xx:fofType)=> (cP Xx))) Xx) x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found ((((ex_intro fofType) (fun (Xx:fofType)=> (cP Xx))) Xx) x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found ex_intro0000:=(ex_intro000 x00):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (ex_intro000 x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ((ex_intro00 Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (((ex_intro0 (fun (Xx0:fofType)=> (cP Xx0))) Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ((((ex_intro fofType) (fun (Xx0:fofType)=> (cP Xx0))) Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ((((ex_intro fofType) (fun (Xx0:fofType)=> (cP Xx0))) Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ex_intro0000:=(ex_intro000 x00):((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found (ex_intro000 x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found ((ex_intro00 Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found (((ex_intro0 (fun (Xx0:fofType)=> (cQ Xx0))) Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found ((((ex_intro fofType) (fun (Xx0:fofType)=> (cQ Xx0))) Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found ((((ex_intro fofType) (fun (Xx0:fofType)=> (cQ Xx0))) Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found ex_intro0000:=(ex_intro000 x00):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (ex_intro000 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found ((ex_intro00 Xx) x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (((ex_intro0 (fun (Xx:fofType)=> (cQ Xx))) Xx) x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found ((((ex_intro fofType) (fun (Xx:fofType)=> (cQ Xx))) Xx) x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found ((((ex_intro fofType) (fun (Xx:fofType)=> (cQ Xx))) Xx) x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found ex_intro0000:=(ex_intro000 x00):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (ex_intro000 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found ((ex_intro00 Xx) x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (((ex_intro0 (fun (Xx:fofType)=> (cP Xx))) Xx) x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found ((((ex_intro fofType) (fun (Xx:fofType)=> (cP Xx))) Xx) x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found ((((ex_intro fofType) (fun (Xx:fofType)=> (cP Xx))) Xx) x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found ex_intro0000:=(ex_intro000 x00):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (ex_intro000 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found ((ex_intro00 Xx) x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (((ex_intro0 (fun (Xx:fofType)=> (cP Xx))) Xx) x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found ((((ex_intro fofType) (fun (Xx:fofType)=> (cP Xx))) Xx) x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found ((((ex_intro fofType) (fun (Xx:fofType)=> (cP Xx))) Xx) x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found ex_intro0000:=(ex_intro000 x00):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (ex_intro000 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found ((ex_intro00 Xx) x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (((ex_intro0 (fun (Xx:fofType)=> (cQ Xx))) Xx) x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found ((((ex_intro fofType) (fun (Xx:fofType)=> (cQ Xx))) Xx) x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found ((((ex_intro fofType) (fun (Xx:fofType)=> (cQ Xx))) Xx) x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x40):((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found (x3 x40) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found (x3 x40) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found x40:=(x4 x30):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x4 x30) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x4 x30) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x40:=(x4 x30):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x4 x30) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x4 x30) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found ex_intro0000:=(ex_intro000 x1):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (ex_intro000 x1) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ((ex_intro00 Xx) x1) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (((ex_intro0 (fun (Xx0:fofType)=> (cP Xx0))) Xx) x1) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ((((ex_intro fofType) (fun (Xx0:fofType)=> (cP Xx0))) Xx) x1) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ((((ex_intro fofType) (fun (Xx0:fofType)=> (cP Xx0))) Xx) x1) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x50:=(x5 x40):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x5 x40) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x5 x40) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x40:=(x4 x50):((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found (x4 x50) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found (x4 x50) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found ex_intro0000:=(ex_intro000 x3):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (ex_intro000 x3) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ((ex_intro00 Xx) x3) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (((ex_intro0 (fun (Xx0:fofType)=> (cP Xx0))) Xx) x3) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ((((ex_intro fofType) (fun (Xx0:fofType)=> (cP Xx0))) Xx) x3) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ((((ex_intro fofType) (fun (Xx0:fofType)=> (cP Xx0))) Xx) x3) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x4 ((((ex_intro fofType) (fun (Xx0:fofType)=> (cP Xx0))) Xx) x3)) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found (x4 ((((ex_intro fofType) (fun (Xx0:fofType)=> (cP Xx0))) Xx) x3)) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found ex_intro0000:=(ex_intro000 x1):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (ex_intro000 x1) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ((ex_intro00 Xx) x1) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (((ex_intro0 (fun (Xx0:fofType)=> (cP Xx0))) Xx) x1) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ((((ex_intro fofType) (fun (Xx0:fofType)=> (cP Xx0))) Xx) x1) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ((((ex_intro fofType) (fun (Xx0:fofType)=> (cP Xx0))) Xx) x1) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found ex_intro0000:=(ex_intro000 x3):((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found (ex_intro000 x3) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found ((ex_intro00 Xx) x3) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found (((ex_intro0 (fun (Xx0:fofType)=> (cQ Xx0))) Xx) x3) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found ((((ex_intro fofType) (fun (Xx0:fofType)=> (cQ Xx0))) Xx) x3) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found ((((ex_intro fofType) (fun (Xx0:fofType)=> (cQ Xx0))) Xx) x3) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found (x5 ((((ex_intro fofType) (fun (Xx0:fofType)=> (cQ Xx0))) Xx) x3)) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x5 ((((ex_intro fofType) (fun (Xx0:fofType)=> (cQ Xx0))) Xx) x3)) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found ex_intro0000:=(ex_intro000 x1):((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found (ex_intro000 x1) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found ((ex_intro00 Xx) x1) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found (((ex_intro0 (fun (Xx0:fofType)=> (cQ Xx0))) Xx) x1) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found ((((ex_intro fofType) (fun (Xx0:fofType)=> (cQ Xx0))) Xx) x1) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found ((((ex_intro fofType) (fun (Xx0:fofType)=> (cQ Xx0))) Xx) x1) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found ex_intro0000:=(ex_intro000 x00):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (ex_intro000 x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ((ex_intro00 Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (((ex_intro0 (fun (Xx0:fofType)=> (cP Xx0))) Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ((((ex_intro fofType) (fun (Xx0:fofType)=> (cP Xx0))) Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ((((ex_intro fofType) (fun (Xx0:fofType)=> (cP Xx0))) Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x40:=(x4 x50):((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found (x4 x50) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found (x4 x50) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found x50:=(x5 x40):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x5 x40) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x5 x40) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x50:=(x5 x40):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x5 x40) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x5 x40) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x50:=(x5 x40):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x5 x40) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x5 x40) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found ex_intro0000:=(ex_intro000 x00):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (ex_intro000 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found ((ex_intro00 Xx) x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (((ex_intro0 (fun (Xx:fofType)=> (cP Xx))) Xx) x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found ((((ex_intro fofType) (fun (Xx:fofType)=> (cP Xx))) Xx) x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found ((((ex_intro fofType) (fun (Xx:fofType)=> (cP Xx))) Xx) x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x2 ((((ex_intro fofType) (fun (Xx:fofType)=> (cP Xx))) Xx) x00)) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 ((((ex_intro fofType) (fun (Xx:fofType)=> (cP Xx))) Xx) x00)) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found ex_intro0000:=(ex_intro000 x00):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (ex_intro000 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found ((ex_intro00 Xx) x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (((ex_intro0 (fun (Xx:fofType)=> (cQ Xx))) Xx) x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found ((((ex_intro fofType) (fun (Xx:fofType)=> (cQ Xx))) Xx) x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found ((((ex_intro fofType) (fun (Xx:fofType)=> (cQ Xx))) Xx) x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x3 ((((ex_intro fofType) (fun (Xx:fofType)=> (cQ Xx))) Xx) x00)) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 ((((ex_intro fofType) (fun (Xx:fofType)=> (cQ Xx))) Xx) x00)) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x40:=(x4 x30):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x4 x30) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x4 x30) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x30:=(x3 x40):((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found (x3 x40) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found (x3 x40) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found ex_intro0000:=(ex_intro000 x00):((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found (ex_intro000 x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found ((ex_intro00 Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found (((ex_intro0 (fun (Xx0:fofType)=> (cQ Xx0))) Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found ((((ex_intro fofType) (fun (Xx0:fofType)=> (cQ Xx0))) Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found ((((ex_intro fofType) (fun (Xx0:fofType)=> (cQ Xx0))) Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found ex_intro0000:=(ex_intro000 x00):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (ex_intro000 x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ((ex_intro00 Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (((ex_intro0 (fun (Xx0:fofType)=> (cP Xx0))) Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ((((ex_intro fofType) (fun (Xx0:fofType)=> (cP Xx0))) Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ((((ex_intro fofType) (fun (Xx0:fofType)=> (cP Xx0))) Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ex_intro0000:=(ex_intro000 x00):((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found (ex_intro000 x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found ((ex_intro00 Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found (((ex_intro0 (fun (Xx0:fofType)=> (cQ Xx0))) Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found ((((ex_intro fofType) (fun (Xx0:fofType)=> (cQ Xx0))) Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found ((((ex_intro fofType) (fun (Xx0:fofType)=> (cQ Xx0))) Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found (x4 ((((ex_intro fofType) (fun (Xx0:fofType)=> (cQ Xx0))) Xx) x00)) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x4 ((((ex_intro fofType) (fun (Xx0:fofType)=> (cQ Xx0))) Xx) x00)) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ex_intro0000:=(ex_intro000 x00):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (ex_intro000 x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ((ex_intro00 Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (((ex_intro0 (fun (Xx0:fofType)=> (cP Xx0))) Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ((((ex_intro fofType) (fun (Xx0:fofType)=> (cP Xx0))) Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ((((ex_intro fofType) (fun (Xx0:fofType)=> (cP Xx0))) Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x3 ((((ex_intro fofType) (fun (Xx0:fofType)=> (cP Xx0))) Xx) x00)) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found (x3 ((((ex_intro fofType) (fun (Xx0:fofType)=> (cP Xx0))) Xx) x00)) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found ex_intro0000:=(ex_intro000 x00):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (ex_intro000 x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ((ex_intro00 Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (((ex_intro0 (fun (Xx0:fofType)=> (cP Xx0))) Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ((((ex_intro fofType) (fun (Xx0:fofType)=> (cP Xx0))) Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ((((ex_intro fofType) (fun (Xx0:fofType)=> (cP Xx0))) Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ex_intro0000:=(ex_intro000 x00):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (ex_intro000 x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ((ex_intro00 Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (((ex_intro0 (fun (Xx0:fofType)=> (cP Xx0))) Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ((((ex_intro fofType) (fun (Xx0:fofType)=> (cP Xx0))) Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ((((ex_intro fofType) (fun (Xx0:fofType)=> (cP Xx0))) Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ex_intro0000:=(ex_intro000 x00):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (ex_intro000 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found ((ex_intro00 Xx) x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (((ex_intro0 (fun (Xx:fofType)=> (cQ Xx))) Xx) x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found ((((ex_intro fofType) (fun (Xx:fofType)=> (cQ Xx))) Xx) x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found ((((ex_intro fofType) (fun (Xx:fofType)=> (cQ Xx))) Xx) x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x3 ((((ex_intro fofType) (fun (Xx:fofType)=> (cQ Xx))) Xx) x00)) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 ((((ex_intro fofType) (fun (Xx:fofType)=> (cQ Xx))) Xx) x00)) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found ex_intro0000:=(ex_intro000 x00):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (ex_intro000 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found ((ex_intro00 Xx) x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (((ex_intro0 (fun (Xx:fofType)=> (cP Xx))) Xx) x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found ((((ex_intro fofType) (fun (Xx:fofType)=> (cP Xx))) Xx) x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found ((((ex_intro fofType) (fun (Xx:fofType)=> (cP Xx))) Xx) x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x2 ((((ex_intro fofType) (fun (Xx:fofType)=> (cP Xx))) Xx) x00)) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 ((((ex_intro fofType) (fun (Xx:fofType)=> (cP Xx))) Xx) x00)) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found ex_intro0000:=(ex_intro000 x00):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (ex_intro000 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found ((ex_intro00 Xx) x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (((ex_intro0 (fun (Xx:fofType)=> (cQ Xx))) Xx) x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found ((((ex_intro fofType) (fun (Xx:fofType)=> (cQ Xx))) Xx) x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found ((((ex_intro fofType) (fun (Xx:fofType)=> (cQ Xx))) Xx) x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x3 ((((ex_intro fofType) (fun (Xx:fofType)=> (cQ Xx))) Xx) x00)) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 ((((ex_intro fofType) (fun (Xx:fofType)=> (cQ Xx))) Xx) x00)) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x40):((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found (x3 x40) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found (x3 x40) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found x40:=(x4 x30):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x4 x30) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x4 x30) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x40:=(x4 x30):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x4 x30) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x4 x30) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ex_intro0000:=(ex_intro000 x00):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (ex_intro000 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found ((ex_intro00 Xx) x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (((ex_intro0 (fun (Xx:fofType)=> (cP Xx))) Xx) x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found ((((ex_intro fofType) (fun (Xx:fofType)=> (cP Xx))) Xx) x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found ((((ex_intro fofType) (fun (Xx:fofType)=> (cP Xx))) Xx) x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x2 ((((ex_intro fofType) (fun (Xx:fofType)=> (cP Xx))) Xx) x00)) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 ((((ex_intro fofType) (fun (Xx:fofType)=> (cP Xx))) Xx) x00)) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x40:=(x4 x30):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x4 x30) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x4 x30) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found ex_intro0000:=(ex_intro000 x00):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (ex_intro000 x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ((ex_intro00 Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (((ex_intro0 (fun (Xx0:fofType)=> (cP Xx0))) Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ((((ex_intro fofType) (fun (Xx0:fofType)=> (cP Xx0))) Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ((((ex_intro fofType) (fun (Xx0:fofType)=> (cP Xx0))) Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ex_intro0000:=(ex_intro000 x00):((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found (ex_intro000 x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found ((ex_intro00 Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found (((ex_intro0 (fun (Xx0:fofType)=> (cQ Xx0))) Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found ((((ex_intro fofType) (fun (Xx0:fofType)=> (cQ Xx0))) Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found ((((ex_intro fofType) (fun (Xx0:fofType)=> (cQ Xx0))) Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found ex_intro0000:=(ex_intro000 x00):((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found (ex_intro000 x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found ((ex_intro00 Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found (((ex_intro0 (fun (Xx0:fofType)=> (cQ Xx0))) Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found ((((ex_intro fofType) (fun (Xx0:fofType)=> (cQ Xx0))) Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found ((((ex_intro fofType) (fun (Xx0:fofType)=> (cQ Xx0))) Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found ex_intro0000:=(ex_intro000 x00):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (ex_intro000 x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ((ex_intro00 Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (((ex_intro0 (fun (Xx0:fofType)=> (cP Xx0))) Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ((((ex_intro fofType) (fun (Xx0:fofType)=> (cP Xx0))) Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ((((ex_intro fofType) (fun (Xx0:fofType)=> (cP Xx0))) Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x30:=(x3 x40):((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found (x3 x40) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found (x3 x40) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found x40:=(x4 x30):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x4 x30) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x4 x30) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x40:=(x4 x30):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x4 x30) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x4 x30) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x30:=(x3 x40):((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found (x3 x40) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found (x3 x40) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found x40:=(x4 x30):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x4 x30) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x4 x30) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x40:=(x4 x30):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x4 x30) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x4 x30) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x50:=(x5 x40):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x5 x40) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x5 x40) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x40:=(x4 x50):((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found (x4 x50) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found (x4 x50) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found ex_intro0000:=(ex_intro000 x1):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (ex_intro000 x1) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ((ex_intro00 Xx) x1) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (((ex_intro0 (fun (Xx0:fofType)=> (cP Xx0))) Xx) x1) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ((((ex_intro fofType) (fun (Xx0:fofType)=> (cP Xx0))) Xx) x1) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ((((ex_intro fofType) (fun (Xx0:fofType)=> (cP Xx0))) Xx) x1) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x4 ((((ex_intro fofType) (fun (Xx0:fofType)=> (cP Xx0))) Xx) x1)) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found (x4 ((((ex_intro fofType) (fun (Xx0:fofType)=> (cP Xx0))) Xx) x1)) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found ex_intro0000:=(ex_intro000 x1):((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found (ex_intro000 x1) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found ((ex_intro00 Xx) x1) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found (((ex_intro0 (fun (Xx0:fofType)=> (cQ Xx0))) Xx) x1) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found ((((ex_intro fofType) (fun (Xx0:fofType)=> (cQ Xx0))) Xx) x1) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found ((((ex_intro fofType) (fun (Xx0:fofType)=> (cQ Xx0))) Xx) x1) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found (x5 ((((ex_intro fofType) (fun (Xx0:fofType)=> (cQ Xx0))) Xx) x1)) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x5 ((((ex_intro fofType) (fun (Xx0:fofType)=> (cQ Xx0))) Xx) x1)) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x50:=(x5 x40):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x5 x40) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x5 x40) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x40):((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found (x3 x40) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found (x3 x40) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found x40:=(x4 x30):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x4 x30) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x4 x30) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found ex_intro0000:=(ex_intro000 x00):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (ex_intro000 x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ((ex_intro00 Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (((ex_intro0 (fun (Xx0:fofType)=> (cP Xx0))) Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ((((ex_intro fofType) (fun (Xx0:fofType)=> (cP Xx0))) Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ((((ex_intro fofType) (fun (Xx0:fofType)=> (cP Xx0))) Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x3 ((((ex_intro fofType) (fun (Xx0:fofType)=> (cP Xx0))) Xx) x00)) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found (x3 ((((ex_intro fofType) (fun (Xx0:fofType)=> (cP Xx0))) Xx) x00)) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found ex_intro0000:=(ex_intro000 x00):((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found (ex_intro000 x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found ((ex_intro00 Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found (((ex_intro0 (fun (Xx0:fofType)=> (cQ Xx0))) Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found ((((ex_intro fofType) (fun (Xx0:fofType)=> (cQ Xx0))) Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found ((((ex_intro fofType) (fun (Xx0:fofType)=> (cQ Xx0))) Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found (x4 ((((ex_intro fofType) (fun (Xx0:fofType)=> (cQ Xx0))) Xx) x00)) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x4 ((((ex_intro fofType) (fun (Xx0:fofType)=> (cQ Xx0))) Xx) x00)) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found ex_intro0000:=(ex_intro000 x00):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (ex_intro000 x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ((ex_intro00 Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (((ex_intro0 (fun (Xx0:fofType)=> (cP Xx0))) Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ((((ex_intro fofType) (fun (Xx0:fofType)=> (cP Xx0))) Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ((((ex_intro fofType) (fun (Xx0:fofType)=> (cP Xx0))) Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x40:=(x4 x30):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x4 x30) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x4 x30) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x50:=(x5 x40):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x50 as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x40:=(x4 x50):((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found x40 as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found x50:=(x5 x40):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x50 as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x50:=(x5 x40):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x50 as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x40:=(x4 x50):((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found x40 as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x40:=(x4 x30):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x4 x30) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x4 x30) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x30:=(x3 x22):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x22) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x22) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x40):((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found (x3 x40) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found (x3 x40) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found x30:=(x3 x40):((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found (x3 x40) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found (x3 x40) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found x40:=(x4 x30):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x4 x30) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x4 x30) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x20:=(x2 x32):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x32) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x32) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found ex_intro0000:=(ex_intro000 x00):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (ex_intro000 x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ((ex_intro00 Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (((ex_intro0 (fun (Xx0:fofType)=> (cP Xx0))) Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ((((ex_intro fofType) (fun (Xx0:fofType)=> (cP Xx0))) Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ((((ex_intro fofType) (fun (Xx0:fofType)=> (cP Xx0))) Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found ex_intro0000:=(ex_intro000 x00):((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found (ex_intro000 x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found ((ex_intro00 Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found (((ex_intro0 (fun (Xx0:fofType)=> (cQ Xx0))) Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found ((((ex_intro fofType) (fun (Xx0:fofType)=> (cQ Xx0))) Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found ((((ex_intro fofType) (fun (Xx0:fofType)=> (cQ Xx0))) Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found ex_intro0000:=(ex_intro000 x3):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (ex_intro000 x3) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ((ex_intro00 Xx) x3) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (((ex_intro0 (fun (Xx0:fofType)=> (cP Xx0))) Xx) x3) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ((((ex_intro fofType) (fun (Xx0:fofType)=> (cP Xx0))) Xx) x3) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ((((ex_intro fofType) (fun (Xx0:fofType)=> (cP Xx0))) Xx) x3) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ex_intro0000:=(ex_intro000 x00):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (ex_intro000 x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ((ex_intro00 Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (((ex_intro0 (fun (Xx0:fofType)=> (cP Xx0))) Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ((((ex_intro fofType) (fun (Xx0:fofType)=> (cP Xx0))) Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ((((ex_intro fofType) (fun (Xx0:fofType)=> (cP Xx0))) Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x3 ((((ex_intro fofType) (fun (Xx0:fofType)=> (cP Xx0))) Xx) x00)) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found (x3 ((((ex_intro fofType) (fun (Xx0:fofType)=> (cP Xx0))) Xx) x00)) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found ex_intro0000:=(ex_intro000 x00):((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found (ex_intro000 x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found ((ex_intro00 Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found (((ex_intro0 (fun (Xx0:fofType)=> (cQ Xx0))) Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found ((((ex_intro fofType) (fun (Xx0:fofType)=> (cQ Xx0))) Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found ((((ex_intro fofType) (fun (Xx0:fofType)=> (cQ Xx0))) Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found (x4 ((((ex_intro fofType) (fun (Xx0:fofType)=> (cQ Xx0))) Xx) x00)) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x4 ((((ex_intro fofType) (fun (Xx0:fofType)=> (cQ Xx0))) Xx) x00)) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found ex_intro0000:=(ex_intro000 x00):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (ex_intro000 x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ((ex_intro00 Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (((ex_intro0 (fun (Xx0:fofType)=> (cP Xx0))) Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ((((ex_intro fofType) (fun (Xx0:fofType)=> (cP Xx0))) Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ((((ex_intro fofType) (fun (Xx0:fofType)=> (cP Xx0))) Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x3 ((((ex_intro fofType) (fun (Xx0:fofType)=> (cP Xx0))) Xx) x00)) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found (x3 ((((ex_intro fofType) (fun (Xx0:fofType)=> (cP Xx0))) Xx) x00)) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found ex_intro0000:=(ex_intro000 x00):((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found (ex_intro000 x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found ((ex_intro00 Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found (((ex_intro0 (fun (Xx0:fofType)=> (cQ Xx0))) Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found ((((ex_intro fofType) (fun (Xx0:fofType)=> (cQ Xx0))) Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found ((((ex_intro fofType) (fun (Xx0:fofType)=> (cQ Xx0))) Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found (x4 ((((ex_intro fofType) (fun (Xx0:fofType)=> (cQ Xx0))) Xx) x00)) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x4 ((((ex_intro fofType) (fun (Xx0:fofType)=> (cQ Xx0))) Xx) x00)) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x40:=(x4 x30):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x4 x30) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x4 x30) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x40:=(x4 x30):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x4 x30) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x4 x30) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x30:=(x3 x40):((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found (x3 x40) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found (x3 x40) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x40:=(x4 x30):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x4 x30) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x4 x30) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x40:=(x4 x30):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x4 x30) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x4 x30) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x50:=(x5 x40):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x50 as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x50:=(x5 x40):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x50 as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x40:=(x4 x50):((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found x40 as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x50:=(x5 x40):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x50 as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x40:=(x4 x50):((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found x40 as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x40:=(x4 x30):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x40 as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x30:=(x3 x40):((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found x30 as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found x40:=(x4 x30):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x40 as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x30:=(x3 x40):((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found x30 as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found x40:=(x4 x30):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x40 as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x32):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x32) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x32) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x22):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x22) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x22) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found ex_intro0000:=(ex_intro000 x00):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (ex_intro000 x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ((ex_intro00 Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (((ex_intro0 (fun (Xx0:fofType)=> (cP Xx0))) Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ((((ex_intro fofType) (fun (Xx0:fofType)=> (cP Xx0))) Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ((((ex_intro fofType) (fun (Xx0:fofType)=> (cP Xx0))) Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x50:=(x5 x41):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x5 x41) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x5 x41) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x40:=(x4 x51):((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found (x4 x51) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found (x4 x51) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found x50:=(x5 x41):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x5 x41) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x5 x41) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x40:=(x4 x51):((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found (x4 x51) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found (x4 x51) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found x50:=(x5 x41):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x5 x41) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x5 x41) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x50:=(x5 x41):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x5 x41) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x5 x41) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x40:=(x4 x50):((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found x40 as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found x50:=(x5 x40):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x50 as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x40:=(x4 x50):((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found x40 as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found x50:=(x5 x40):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x50 as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x50:=(x5 x40):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x50 as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x40):((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found x30 as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found x40:=(x4 x30):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x40 as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x30:=(x3 x40):((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found x30 as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found x40:=(x4 x30):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x40 as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x40:=(x4 x30):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x40 as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x40:=(x4 x50):((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found x40 as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found x50:=(x5 x40):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x50 as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x50:=(x5 x40):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x50 as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x50:=(x5 x40):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x50 as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x40:=(x4 x50):((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found x40 as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x40:=(x4 x31):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x4 x31) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x4 x31) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x40:=(x4 x31):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x4 x31) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x4 x31) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x30:=(x3 x41):((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found (x3 x41) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found (x3 x41) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found x30:=(x3 x41):((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found (x3 x41) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found (x3 x41) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found x40:=(x4 x31):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x4 x31) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x4 x31) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x40:=(x4 x31):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x4 x31) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x4 x31) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x40:=(x4 x30):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x4 x30) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x4 x30) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x30:=(x3 x40):((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found (x3 x40) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found (x3 x40) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x40:=(x4 x30):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x40 as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x30:=(x3 x40):((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found x30 as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x40:=(x4 x30):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x40 as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x40:=(x4 x30):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x40 as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x30:=(x3 x40):((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found x30 as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found ex_intro0000:=(ex_intro000 x1):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (ex_intro000 x1) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ((ex_intro00 Xx) x1) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (((ex_intro0 (fun (Xx0:fofType)=> (cP Xx0))) Xx) x1) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ((((ex_intro fofType) (fun (Xx0:fofType)=> (cP Xx0))) Xx) x1) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ((((ex_intro fofType) (fun (Xx0:fofType)=> (cP Xx0))) Xx) x1) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found ex_intro0000:=(ex_intro000 x00):((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found (ex_intro000 x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found ((ex_intro00 Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found (((ex_intro0 (fun (Xx0:fofType)=> (cQ Xx0))) Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found ((((ex_intro fofType) (fun (Xx0:fofType)=> (cQ Xx0))) Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found ((((ex_intro fofType) (fun (Xx0:fofType)=> (cQ Xx0))) Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found (x4 ((((ex_intro fofType) (fun (Xx0:fofType)=> (cQ Xx0))) Xx) x00)) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x4 ((((ex_intro fofType) (fun (Xx0:fofType)=> (cQ Xx0))) Xx) x00)) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ex_intro0000:=(ex_intro000 x00):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (ex_intro000 x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ((ex_intro00 Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (((ex_intro0 (fun (Xx0:fofType)=> (cP Xx0))) Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ((((ex_intro fofType) (fun (Xx0:fofType)=> (cP Xx0))) Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ((((ex_intro fofType) (fun (Xx0:fofType)=> (cP Xx0))) Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x3 ((((ex_intro fofType) (fun (Xx0:fofType)=> (cP Xx0))) Xx) x00)) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found (x3 ((((ex_intro fofType) (fun (Xx0:fofType)=> (cP Xx0))) Xx) x00)) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x40:=(x4 x30):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x4 x30) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x4 x30) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x50:=(x5 x40):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x50 as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x50:=(x5 x40):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x50 as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x40:=(x4 x50):((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found x40 as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found x40:=(x4 x50):((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found x40 as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x50:=(x5 x40):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x50 as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x40:=(x4 x30):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x40 as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x30:=(x3 x40):((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found x30 as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found x40:=(x4 x30):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x40 as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x30:=(x3 x40):((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found x30 as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found x40:=(x4 x30):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x40 as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x22):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x22) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x22) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found ex_intro0000:=(ex_intro000 x00):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (ex_intro000 x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ((ex_intro00 Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (((ex_intro0 (fun (Xx0:fofType)=> (cP Xx0))) Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ((((ex_intro fofType) (fun (Xx0:fofType)=> (cP Xx0))) Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ((((ex_intro fofType) (fun (Xx0:fofType)=> (cP Xx0))) Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x20:=(x2 x32):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x32) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x32) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x40:=(x4 x51):((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found (x4 x51) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found (x4 x51) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found x50:=(x5 x41):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x5 x41) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x5 x41) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x50:=(x5 x41):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x5 x41) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x5 x41) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x50:=(x5 x41):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x5 x41) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x5 x41) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x40:=(x4 x51):((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found (x4 x51) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found (x4 x51) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found x50:=(x5 x41):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x5 x41) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x5 x41) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x50:=(x5 x40):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x50 as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x40:=(x4 x50):((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found x40 as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found x50:=(x5 x40):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x50 as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x40:=(x4 x50):((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found x40 as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found x50:=(x5 x40):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x50 as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x40:=(x4 x30):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x40 as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x40:=(x4 x30):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x40 as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x30:=(x3 x40):((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found x30 as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found x40:=(x4 x30):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x40 as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x30:=(x3 x40):((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found x30 as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x32):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x32) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x32) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x22):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x22) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x22) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x32):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x32) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x32) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x22):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x22) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x22) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found ex_intro0000:=(ex_intro000 x00):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (ex_intro000 x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ((ex_intro00 Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (((ex_intro0 (fun (Xx0:fofType)=> (cP Xx0))) Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ((((ex_intro fofType) (fun (Xx0:fofType)=> (cP Xx0))) Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ((((ex_intro fofType) (fun (Xx0:fofType)=> (cP Xx0))) Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ex_intro0000:=(ex_intro000 x00):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (ex_intro000 x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ((ex_intro00 Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (((ex_intro0 (fun (Xx0:fofType)=> (cP Xx0))) Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ((((ex_intro fofType) (fun (Xx0:fofType)=> (cP Xx0))) Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found ((((ex_intro fofType) (fun (Xx0:fofType)=> (cP Xx0))) Xx) x00) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x40:=(x4 x31):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x4 x31) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x4 x31) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x40:=(x4 x31):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x4 x31) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x4 x31) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x40:=(x4 x31):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x4 x31) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x4 x31) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x40:=(x4 x31):((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x4 x31) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found (x4 x31) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cP Xx0)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x41):((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found (x3 x41) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found (x3 x41) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x41):((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found (x3 x41) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found (x3 x41) as proof of ((ex fofType) (fun (Xx0:fofType)=> (cQ Xx0)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x30) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20 as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x20):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x20:=(x2 x31):((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found (x2 x31) as proof of ((ex fofType) (fun (Xx:fofType)=> (cQ Xx)))
% Found x30:=(x3 x21):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x3 x21) as proof of ((ex fofType) (fun (Xx:
% EOF
%------------------------------------------------------------------------------