TSTP Solution File: SEV176^5 by cocATP---0.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SEV176^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n186.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 13:33:50 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 : SEV176^5 : TPTP v6.1.0. Released v4.0.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n186.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 08:21:16 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 0xd45b48>, <kernel.DependentProduct object at 0xd45ab8>) of role type named cR
% Using role type
% Declaring cR:(fofType->(fofType->Prop))
% FOF formula (((ex fofType) (fun (Y:fofType)=> (forall (X:fofType), ((iff ((cR X) Y)) (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)))))->False) of role conjecture named cTHM25
% Conjecture to prove = (((ex fofType) (fun (Y:fofType)=> (forall (X:fofType), ((iff ((cR X) Y)) (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)))))->False):Prop
% Parameter fofType_DUMMY:fofType.
% We need to prove ['(((ex fofType) (fun (Y:fofType)=> (forall (X:fofType), ((iff ((cR X) Y)) (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)))))->False)']
% Parameter fofType:Type.
% Parameter cR:(fofType->(fofType->Prop)).
% Trying to prove (((ex fofType) (fun (Y:fofType)=> (forall (X:fofType), ((iff ((cR X) Y)) (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)))))->False)
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found x4:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x4 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x4:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x4 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x31:((cR X) x0)
% Found x31 as proof of ((cR X) x0)
% Found x20:=(x2 x30):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x20 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x31:((cR X) x0)
% Found x31 as proof of ((cR X) x0)
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found x20:=(x2 x30):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x20 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x20:=(x2 x30):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found x4:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x4 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found x20:=(x2 x30):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x50:((cR X0) x0)
% Found x50 as proof of ((cR X0) x0)
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x4:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x4 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x4:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x4 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found x50:((cR X0) x0)
% Found x50 as proof of ((cR X0) x0)
% Found x50:=(x5 x40):((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Instantiate: X0:=X:fofType
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x5:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x5 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x5:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x5 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x40:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Instantiate: X:=X0:fofType
% Found x40 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x20:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Instantiate: X0:=X:fofType
% Found x20 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x30:=(x3 x20):((cR X) x0)
% Instantiate: X0:=X:fofType
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x50:=(x5 x40):((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found x50:=(x5 x40):((cR X0) x0)
% Found (x5 x40) as proof of ((cR X0) x0)
% Found (x5 x40) as proof of ((cR X0) x0)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x30:=(x3 x20):((cR X) x0)
% Instantiate: X0:=X:fofType
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found x20:=(x2 x31):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x31) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x31) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found x32:((cR X) x0)
% Found x32 as proof of ((cR X) x0)
% Found x20:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Instantiate: X0:=X:fofType
% Found x20 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x5 x20) as proof of ((cR X0) x0)
% Found (x5 x20) as proof of ((cR X0) x0)
% Found x40:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Instantiate: X:=X0:fofType
% Found x40 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x3 x40) as proof of ((cR X) x0)
% Found (x3 x40) as proof of ((cR X) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x50:=(x5 x40):((cR X0) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found x50:=(x5 x40):((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Instantiate: X0:=X:fofType
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x40:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Instantiate: X:=X0:fofType
% Found x40 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x20:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Instantiate: X0:=X:fofType
% Found x20 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x30:=(x3 x20):((cR X) x0)
% Instantiate: X0:=X:fofType
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x4:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x4 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found x50:=(x5 x40):((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found x50:=(x5 x40):((cR X0) x0)
% Found (x5 x40) as proof of ((cR X0) x0)
% Found (x5 x40) as proof of ((cR X0) x0)
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Instantiate: X0:=X:fofType
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x40:=(x4 x50):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Instantiate: X:=X0:fofType
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x5:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x5 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x20:=(x2 x31):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x31) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x31) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x20 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x4:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x4 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x20:=(x2 x31):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x20 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x30:=(x3 x20):((cR X) x0)
% Instantiate: X0:=X:fofType
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found x32:((cR X) x0)
% Found x32 as proof of ((cR X) x0)
% Found x30:((cR X) x0)
% Found (fun (x5:((((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)->((cR X0) x0)))=> x30) as proof of ((cR X) x0)
% Found (fun (x5:((((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)->((cR X0) x0)))=> x30) as proof of (((((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)->((cR X0) x0))->((cR X) x0))
% Found x20:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x20 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x40:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x40 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found x40:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Instantiate: X:=X0:fofType
% Found x40 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x3 x40) as proof of ((cR X) x0)
% Found (x3 x40) as proof of ((cR X) x0)
% Found x20:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Instantiate: X0:=X:fofType
% Found x20 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x5 x20) as proof of ((cR X0) x0)
% Found (x5 x20) as proof of ((cR X0) x0)
% Found x20:=(x2 x31):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x31) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x31) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x20:=(x2 x31):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x31) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x31) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x50:=(x5 x40):((cR X0) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found x30:((cR X) x0)
% Found (fun (x5:((((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)->((cR X0) x0)))=> x30) as proof of ((cR X) x0)
% Found (fun (x4:(((cR X0) x0)->(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False))) (x5:((((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)->((cR X0) x0)))=> x30) as proof of (((((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)->((cR X0) x0))->((cR X) x0))
% Found (fun (x4:(((cR X0) x0)->(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False))) (x5:((((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)->((cR X0) x0)))=> x30) as proof of ((((cR X0) x0)->(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False))->(((((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)->((cR X0) x0))->((cR X) x0)))
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x30:=(x3 x21):((cR X) x0)
% Found (x3 x21) as proof of ((cR X) x0)
% Found (x3 x21) as proof of ((cR X) x0)
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x40:=(x4 x50):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x20:=(x2 x30):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x20 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x20:=(x2 x31):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x20 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x40:=(x4 x50):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Instantiate: X:=X0:fofType
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x20:=(x2 x30):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Instantiate: X0:=X:fofType
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x30:((cR X) x0)
% Instantiate: X:=x0:fofType;x4:=X:fofType
% Found x30 as proof of ((cR x4) X)
% Found x30:((cR X) x0)
% Instantiate: x4:=x0:fofType
% Found x30 as proof of ((cR X) x4)
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x4)
% Found ((conj00 x30) x30) as proof of ((and ((cR X) x4)) ((cR x4) X))
% Found (((conj0 ((cR x4) X)) x30) x30) as proof of ((and ((cR X) x4)) ((cR x4) X))
% Found ((((conj ((cR X) x4)) ((cR x4) X)) x30) x30) as proof of ((and ((cR X) x4)) ((cR x4) X))
% Found ((((conj ((cR X) x4)) ((cR x4) X)) x30) x30) as proof of ((and ((cR X) x4)) ((cR x4) X))
% Found (ex_intro000 ((((conj ((cR X) x4)) ((cR x4) X)) x30) x30)) as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found ((ex_intro00 X) ((((conj ((cR X) X)) ((cR X) X)) x30) x30)) as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found (((ex_intro0 (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))) X) ((((conj ((cR X) X)) ((cR X) X)) x30) x30)) as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found ((((ex_intro fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))) X) ((((conj ((cR X) X)) ((cR X) X)) x30) x30)) as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found ((((ex_intro fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))) X) ((((conj ((cR X) X)) ((cR X) X)) x30) x30)) as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found ((x2 x30) ((((ex_intro fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))) X) ((((conj ((cR X) X)) ((cR X) X)) x30) x30))) as proof of False
% Found ((x2 x30) ((((ex_intro fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))) X) ((((conj ((cR X) X)) ((cR X) X)) x30) x30))) as proof of False
% Found x50:=(x5 x40):((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x30:((cR X) x0)
% Found (fun (x5:((not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))->((cR X0) x0)))=> x30) as proof of ((cR X) x0)
% Found (fun (x5:((not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))->((cR X0) x0)))=> x30) as proof of (((not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))->((cR X0) x0))->((cR X) x0))
% Found x40:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Instantiate: X:=X0:fofType
% Found x40 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x20:=(x2 x31):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x31) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x31) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x20:=(x2 x31):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x31) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x31) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x50:=(x5 x40):((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found (x5 x40) as proof of ((cR X) x0)
% Found (fun (x5:((((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)->((cR X0) x0)))=> (x5 x40)) as proof of ((cR X) x0)
% Found (fun (x5:((((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)->((cR X0) x0)))=> (x5 x40)) as proof of (((((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)->((cR X0) x0))->((cR X) x0))
% Found x30:=(x3 x20):((cR X) x0)
% Instantiate: X0:=X:fofType
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found x40:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x40 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found x20:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x20 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x30:((cR X) x0)
% Found (fun (x5:((not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))->((cR X0) x0)))=> x30) as proof of ((cR X) x0)
% Found (fun (x4:(((cR X0) x0)->(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))))) (x5:((not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))->((cR X0) x0)))=> x30) as proof of (((not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))->((cR X0) x0))->((cR X) x0))
% Found (fun (x4:(((cR X0) x0)->(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))))) (x5:((not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))->((cR X0) x0)))=> x30) as proof of ((((cR X0) x0)->(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))))->(((not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))->((cR X0) x0))->((cR X) x0)))
% Found x000:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x000 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x000:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x000 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x30:=(x3 x21):((cR X) x0)
% Found (x3 x21) as proof of ((cR X) x0)
% Found (x3 x21) as proof of ((cR X) x0)
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x4:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x4 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x4:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x4 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x50:((cR X0) x0)
% Found x50 as proof of ((cR X0) x0)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x30:((cR X) x0)
% Instantiate: X:=x0:fofType;x4:=X:fofType
% Found x30 as proof of ((cR x4) X)
% Found x30:((cR X) x0)
% Instantiate: x4:=x0:fofType
% Found x30 as proof of ((cR X) x4)
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x4)
% Found ((conj00 x30) x30) as proof of ((and ((cR X) x4)) ((cR x4) X))
% Found (((conj0 ((cR x4) X)) x30) x30) as proof of ((and ((cR X) x4)) ((cR x4) X))
% Found ((((conj ((cR X) x4)) ((cR x4) X)) x30) x30) as proof of ((and ((cR X) x4)) ((cR x4) X))
% Found ((((conj ((cR X) x4)) ((cR x4) X)) x30) x30) as proof of ((and ((cR X) x4)) ((cR x4) X))
% Found (ex_intro000 ((((conj ((cR X) x4)) ((cR x4) X)) x30) x30)) as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found ((ex_intro00 X) ((((conj ((cR X) X)) ((cR X) X)) x30) x30)) as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found (((ex_intro0 (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))) X) ((((conj ((cR X) X)) ((cR X) X)) x30) x30)) as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found ((((ex_intro fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))) X) ((((conj ((cR X) X)) ((cR X) X)) x30) x30)) as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found ((((ex_intro fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))) X) ((((conj ((cR X) X)) ((cR X) X)) x30) x30)) as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found (x20 ((((ex_intro fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))) X) ((((conj ((cR X) X)) ((cR X) X)) x30) x30))) as proof of False
% Found ((x2 x30) ((((ex_intro fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))) X) ((((conj ((cR X) X)) ((cR X) X)) x30) x30))) as proof of False
% Found ((x2 x30) ((((ex_intro fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))) X) ((((conj ((cR X) X)) ((cR X) X)) x30) x30))) as proof of False
% Found x40:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Instantiate: X:=X0:fofType
% Found x40 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x3 x40) as proof of ((cR X) x0)
% Found (x3 x40) as proof of ((cR X) x0)
% Found x30:((cR X) x0)
% Instantiate: X:=x0:fofType;x4:=X:fofType
% Found x30 as proof of ((cR x4) X)
% Found x30:((cR X) x0)
% Instantiate: x4:=x0:fofType
% Found x30 as proof of ((cR X) x4)
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x4)
% Found ((conj00 x30) x30) as proof of ((and ((cR X) x4)) ((cR x4) X))
% Found (((conj0 ((cR x4) X)) x30) x30) as proof of ((and ((cR X) x4)) ((cR x4) X))
% Found ((((conj ((cR X) x4)) ((cR x4) X)) x30) x30) as proof of ((and ((cR X) x4)) ((cR x4) X))
% Found ((((conj ((cR X) x4)) ((cR x4) X)) x30) x30) as proof of ((and ((cR X) x4)) ((cR x4) X))
% Found (ex_intro000 ((((conj ((cR X) x4)) ((cR x4) X)) x30) x30)) as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found ((ex_intro00 X) ((((conj ((cR X) X)) ((cR X) X)) x30) x30)) as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found (((ex_intro0 (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))) X) ((((conj ((cR X) X)) ((cR X) X)) x30) x30)) as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found ((((ex_intro fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))) X) ((((conj ((cR X) X)) ((cR X) X)) x30) x30)) as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found ((((ex_intro fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))) X) ((((conj ((cR X) X)) ((cR X) X)) x30) x30)) as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found ((x2 x30) ((((ex_intro fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))) X) ((((conj ((cR X) X)) ((cR X) X)) x30) x30))) as proof of False
% Found ((x2 x30) ((((ex_intro fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))) X) ((((conj ((cR X) X)) ((cR X) X)) x30) x30))) as proof of False
% Found x40:=(x4 x50):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x20:=(x2 x30):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x40:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Instantiate: X:=X0:fofType
% Found x40 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x40:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Instantiate: X:=X0:fofType
% Found x40 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x50:=(x5 x40):((cR X0) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found x50:=(x5 x40):((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x50:((cR X0) x0)
% Found x50 as proof of ((cR X0) x0)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found ((x4 x50) x00) as proof of False
% Found ((x4 x50) x00) as proof of False
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found ((x2 x30) x00) as proof of False
% Found ((x2 x30) x00) as proof of False
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x40:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Instantiate: X:=X0:fofType
% Found x40 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x3 x40) as proof of ((cR X) x0)
% Found (fun (x5:((((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)->((cR X0) x0)))=> (x3 x40)) as proof of ((cR X) x0)
% Found (fun (x5:((((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)->((cR X0) x0)))=> (x3 x40)) as proof of (((((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)->((cR X0) x0))->((cR X) x0))
% Found x5:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x5 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x40:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Instantiate: X:=X0:fofType
% Found x40 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x50:=(x5 x40):((cR X0) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (fun (x5:((((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)->((cR X0) x0)))=> (x5 x40)) as proof of ((cR X) x0)
% Found (fun (x5:((((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)->((cR X0) x0)))=> (x5 x40)) as proof of (((((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)->((cR X0) x0))->((cR X) x0))
% Found x50:=(x5 x40):((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found (x5 x40) as proof of ((cR X) x0)
% Found (fun (x5:((not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))->((cR X0) x0)))=> (x5 x40)) as proof of ((cR X) x0)
% Found (fun (x5:((not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))->((cR X0) x0)))=> (x5 x40)) as proof of (((not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))->((cR X0) x0))->((cR X) x0))
% Found x40:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Instantiate: X:=X0:fofType
% Found x40 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x20:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Instantiate: X0:=X:fofType
% Found x20 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x30:=(x3 x20):((cR X) x0)
% Instantiate: X0:=X:fofType
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found x30:((cR X) x0)
% Instantiate: x4:=x0:fofType
% Found x30 as proof of ((cR X) x4)
% Found x40:=(x4 x50):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Instantiate: X:=X0:fofType
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x30:((cR X) x0)
% Instantiate: X:=x0:fofType;x4:=X:fofType
% Found x30 as proof of ((cR x4) X)
% Found x40:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Instantiate: X:=X0:fofType
% Found x40 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x50:((cR X0) x0)
% Found x50 as proof of ((cR X0) x0)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found ((x4 x50) x00) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))=> ((x4 x50) x00)) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))=> ((x4 x50) x00)) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x30:=(x3 x20):((cR X) x0)
% Instantiate: x4:=x0:fofType
% Found (x3 x20) as proof of ((cR X) x4)
% Found (x3 x20) as proof of ((cR X) x4)
% Found x30:=(x3 x20):((cR X) x0)
% Instantiate: X:=x0:fofType;x4:=X:fofType
% Found (x3 x20) as proof of ((cR x4) X)
% Found (x3 x20) as proof of ((cR x4) X)
% Found x30:=(x3 x20):((cR X) x0)
% Instantiate: X:=x0:fofType
% Found (x3 x20) as proof of ((cR x4) X)
% Found (x3 x20) as proof of ((cR x4) X)
% Found ((conj00 (x3 x20)) (x3 x20)) as proof of ((and ((cR X) x4)) ((cR x4) X))
% Found (((conj0 ((cR x4) X)) (x3 x20)) (x3 x20)) as proof of ((and ((cR X) x4)) ((cR x4) X))
% Found ((((conj ((cR X) x4)) ((cR x4) X)) (x3 x20)) (x3 x20)) as proof of ((and ((cR X) x4)) ((cR x4) X))
% Found ((((conj ((cR X) x4)) ((cR x4) X)) (x3 x20)) (x3 x20)) as proof of ((and ((cR X) x4)) ((cR x4) X))
% Found (ex_intro000 ((((conj ((cR X) x4)) ((cR x4) X)) (x3 x20)) (x3 x20))) as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found ((ex_intro00 x0) ((((conj ((cR X) x0)) ((cR x0) X)) (x3 x20)) (x3 x20))) as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found (((ex_intro0 (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))) x0) ((((conj ((cR X) x0)) ((cR x0) X)) (x3 x20)) (x3 x20))) as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found ((((ex_intro fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))) x0) ((((conj ((cR X) x0)) ((cR x0) X)) (x3 x20)) (x3 x20))) as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found ((((ex_intro fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))) x0) ((((conj ((cR X) x0)) ((cR x0) X)) (x3 x20)) (x3 x20))) as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found ((x2 (x3 x20)) ((((ex_intro fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))) x0) ((((conj ((cR X) x0)) ((cR x0) X)) (x3 x20)) (x3 x20)))) as proof of False
% Found (fun (x3:((((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)->((cR X) x0)))=> ((x2 (x3 x20)) ((((ex_intro fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))) x0) ((((conj ((cR X) x0)) ((cR x0) X)) (x3 x20)) (x3 x20))))) as proof of False
% Found (fun (x3:((((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)->((cR X) x0)))=> ((x2 (x3 x20)) ((((ex_intro fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))) x0) ((((conj ((cR X) x0)) ((cR x0) X)) (x3 x20)) (x3 x20))))) as proof of (((((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)->((cR X) x0))->False)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found ((x2 x30) x00) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x2 x30) x00)) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x2 x30) x00)) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x4:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x4 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found (x20 x00) as proof of False
% Found ((x2 x30) x00) as proof of False
% Found ((x2 x30) x00) as proof of False
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found (x40 x00) as proof of False
% Found ((x4 x50) x00) as proof of False
% Found ((x4 x50) x00) as proof of False
% Found x20:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Instantiate: X0:=X:fofType
% Found x20 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x40:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Instantiate: X:=X0:fofType
% Found x40 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x40:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Instantiate: X:=X0:fofType
% Found (fun (x5:((not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))->((cR X0) x0)))=> x40) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (fun (x5:((not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))->((cR X0) x0)))=> x40) as proof of (((not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))->((cR X0) x0))->(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))))
% Found x30:((cR X) x0)
% Instantiate: x4:=x0:fofType
% Found x30 as proof of ((cR X) x4)
% Found x30:((cR X) x0)
% Instantiate: X:=x0:fofType;x4:=X:fofType
% Found x30 as proof of ((cR x4) X)
% Found x30:((cR X) x0)
% Instantiate: X:=x0:fofType
% Found x30 as proof of ((cR x4) X)
% Found ((conj00 x30) x30) as proof of ((and ((cR X) x4)) ((cR x4) X))
% Found (((conj0 ((cR x4) X)) x30) x30) as proof of ((and ((cR X) x4)) ((cR x4) X))
% Found ((((conj ((cR X) x4)) ((cR x4) X)) x30) x30) as proof of ((and ((cR X) x4)) ((cR x4) X))
% Found ((((conj ((cR X) x4)) ((cR x4) X)) x30) x30) as proof of ((and ((cR X) x4)) ((cR x4) X))
% Found (ex_intro000 ((((conj ((cR X) x4)) ((cR x4) X)) x30) x30)) as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found ((ex_intro00 x0) ((((conj ((cR X) x0)) ((cR x0) X)) x30) x30)) as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found (((ex_intro0 (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))) x0) ((((conj ((cR X) x0)) ((cR x0) X)) x30) x30)) as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found ((((ex_intro fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))) x0) ((((conj ((cR X) x0)) ((cR x0) X)) x30) x30)) as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found ((((ex_intro fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))) x0) ((((conj ((cR X) x0)) ((cR x0) X)) x30) x30)) as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found (x20 ((((ex_intro fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))) x0) ((((conj ((cR X) x0)) ((cR x0) X)) x30) x30))) as proof of False
% Found ((x2 x30) ((((ex_intro fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))) x0) ((((conj ((cR X) x0)) ((cR x0) X)) x30) x30))) as proof of False
% Found ((x2 x30) ((((ex_intro fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))) x0) ((((conj ((cR X) x0)) ((cR x0) X)) x30) x30))) as proof of False
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x30:=(x3 x21):((cR X) x0)
% Found (x3 x21) as proof of ((cR X) x0)
% Found (x3 x21) as proof of ((cR X) x0)
% Found x20:=(x2 x31):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x31) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x31) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found x50:((cR X0) x0)
% Found x50 as proof of ((cR X0) x0)
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x40:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x40 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found x40:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Instantiate: X:=X0:fofType
% Found x40 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x3 x40) as proof of ((cR X) x0)
% Found (x3 x40) as proof of ((cR X) x0)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x20:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Instantiate: X0:=X:fofType
% Found x20 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x40:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Instantiate: X:=X0:fofType
% Found x40 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found (x20 x00) as proof of False
% Found ((x2 x30) x00) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x2 x30) x00)) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x2 x30) x00)) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found (x40 x00) as proof of False
% Found ((x4 x50) x00) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))=> ((x4 x50) x00)) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))=> ((x4 x50) x00)) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x40:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Instantiate: X:=X0:fofType
% Found x40 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x50:=(x5 x40):((cR X0) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found x30:((cR X) x0)
% Instantiate: X:=x0:fofType;x4:=X:fofType
% Found x30 as proof of ((cR x4) X)
% Found x30:((cR X) x0)
% Instantiate: x4:=x0:fofType
% Found x30 as proof of ((cR X) x4)
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x4)
% Found ((conj00 x30) x30) as proof of ((and ((cR X) x4)) ((cR x4) X))
% Found (((conj0 ((cR x4) X)) x30) x30) as proof of ((and ((cR X) x4)) ((cR x4) X))
% Found ((((conj ((cR X) x4)) ((cR x4) X)) x30) x30) as proof of ((and ((cR X) x4)) ((cR x4) X))
% Found ((((conj ((cR X) x4)) ((cR x4) X)) x30) x30) as proof of ((and ((cR X) x4)) ((cR x4) X))
% Found x5:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x5 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x5:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x5 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Instantiate: X0:=X:fofType
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x30:=(x3 x20):((cR X) x0)
% Instantiate: X0:=X:fofType
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x40:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x40 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (fun (x5:((((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)->((cR X0) x0)))=> (x5 x40)) as proof of ((cR X) x0)
% Found (fun (x5:((((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)->((cR X0) x0)))=> (x5 x40)) as proof of (((((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)->((cR X0) x0))->((cR X) x0))
% Found x000:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x000 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x000:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x000 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x40:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Instantiate: X:=X0:fofType
% Found x40 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x3 x40) as proof of ((cR X) x0)
% Found (fun (x5:((not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))->((cR X0) x0)))=> (x3 x40)) as proof of ((cR X) x0)
% Found (fun (x5:((not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))->((cR X0) x0)))=> (x3 x40)) as proof of (((not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))->((cR X0) x0))->((cR X) x0))
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found ((x2 x30) x6) as proof of False
% Found ((x2 x30) x6) as proof of False
% Found x50:((cR X0) x0)
% Found x50 as proof of ((cR X0) x0)
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found ((x4 x50) x6) as proof of False
% Found ((x4 x50) x6) as proof of False
% Found x30:((cR X) x0)
% Instantiate: x4:=x0:fofType
% Found x30 as proof of ((cR X) x4)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x30:((cR X) x0)
% Instantiate: X:=x0:fofType;x4:=X:fofType
% Found x30 as proof of ((cR x4) X)
% Found x40:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Instantiate: X:=X0:fofType
% Found x40 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x50:=(x5 x40):((cR X0) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (fun (x5:((not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))->((cR X0) x0)))=> (x5 x40)) as proof of ((cR X) x0)
% Found (fun (x5:((not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))->((cR X0) x0)))=> (x5 x40)) as proof of (((not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))->((cR X0) x0))->((cR X) x0))
% Found x9:((cR x6) X)
% Instantiate: X:=x0:fofType;X0:=x6:fofType
% Found (fun (x9:((cR x6) X))=> x9) as proof of ((cR X0) x0)
% Found (fun (x8:((cR X) x6)) (x9:((cR x6) X))=> x9) as proof of (((cR x6) X)->((cR X0) x0))
% Found (fun (x8:((cR X) x6)) (x9:((cR x6) X))=> x9) as proof of (((cR X) x6)->(((cR x6) X)->((cR X0) x0)))
% Found (and_rect20 (fun (x8:((cR X) x6)) (x9:((cR x6) X))=> x9)) as proof of ((cR X0) x0)
% Found ((and_rect2 ((cR X0) x0)) (fun (x8:((cR X) x6)) (x9:((cR x6) X))=> x9)) as proof of ((cR X0) x0)
% Found (((fun (P:Type) (x8:(((cR X) x6)->(((cR x6) X)->P)))=> (((((and_rect ((cR X) x6)) ((cR x6) X)) P) x8) x7)) ((cR X0) x0)) (fun (x8:((cR X) x6)) (x9:((cR x6) X))=> x9)) as proof of ((cR X0) x0)
% Found (fun (x7:((and ((cR X) x6)) ((cR x6) X)))=> (((fun (P:Type) (x8:(((cR X) x6)->(((cR x6) X)->P)))=> (((((and_rect ((cR X) x6)) ((cR x6) X)) P) x8) x7)) ((cR X0) x0)) (fun (x8:((cR X) x6)) (x9:((cR x6) X))=> x9))) as proof of ((cR X0) x0)
% Found x9:((cR x6) X0)
% Instantiate: X:=x6:fofType;X0:=x0:fofType
% Found (fun (x9:((cR x6) X0))=> x9) as proof of ((cR X) x0)
% Found (fun (x8:((cR X0) x6)) (x9:((cR x6) X0))=> x9) as proof of (((cR x6) X0)->((cR X) x0))
% Found (fun (x8:((cR X0) x6)) (x9:((cR x6) X0))=> x9) as proof of (((cR X0) x6)->(((cR x6) X0)->((cR X) x0)))
% Found (and_rect20 (fun (x8:((cR X0) x6)) (x9:((cR x6) X0))=> x9)) as proof of ((cR X) x0)
% Found ((and_rect2 ((cR X) x0)) (fun (x8:((cR X0) x6)) (x9:((cR x6) X0))=> x9)) as proof of ((cR X) x0)
% Found (((fun (P:Type) (x8:(((cR X0) x6)->(((cR x6) X0)->P)))=> (((((and_rect ((cR X0) x6)) ((cR x6) X0)) P) x8) x7)) ((cR X) x0)) (fun (x8:((cR X0) x6)) (x9:((cR x6) X0))=> x9)) as proof of ((cR X) x0)
% Found (fun (x7:((and ((cR X0) x6)) ((cR x6) X0)))=> (((fun (P:Type) (x8:(((cR X0) x6)->(((cR x6) X0)->P)))=> (((((and_rect ((cR X0) x6)) ((cR x6) X0)) P) x8) x7)) ((cR X) x0)) (fun (x8:((cR X0) x6)) (x9:((cR x6) X0))=> x9))) as proof of ((cR X) x0)
% Found x40:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Instantiate: X:=X0:fofType
% Found x40 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x20:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Instantiate: X0:=X:fofType
% Found x20 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x9:((cR x6) X)
% Instantiate: X:=x0:fofType;X0:=x6:fofType
% Found (fun (x9:((cR x6) X))=> x9) as proof of ((cR X0) x0)
% Found (fun (x8:((cR X) x6)) (x9:((cR x6) X))=> x9) as proof of (((cR x6) X)->((cR X0) x0))
% Found (fun (x8:((cR X) x6)) (x9:((cR x6) X))=> x9) as proof of (((cR X) x6)->(((cR x6) X)->((cR X0) x0)))
% Found (and_rect20 (fun (x8:((cR X) x6)) (x9:((cR x6) X))=> x9)) as proof of ((cR X0) x0)
% Found ((and_rect2 ((cR X0) x0)) (fun (x8:((cR X) x6)) (x9:((cR x6) X))=> x9)) as proof of ((cR X0) x0)
% Found (((fun (P:Type) (x8:(((cR X) x6)->(((cR x6) X)->P)))=> (((((and_rect ((cR X) x6)) ((cR x6) X)) P) x8) x7)) ((cR X0) x0)) (fun (x8:((cR X) x6)) (x9:((cR x6) X))=> x9)) as proof of ((cR X0) x0)
% Found (((fun (P:Type) (x8:(((cR X) x6)->(((cR x6) X)->P)))=> (((((and_rect ((cR X) x6)) ((cR x6) X)) P) x8) x7)) ((cR X0) x0)) (fun (x8:((cR X) x6)) (x9:((cR x6) X))=> x9)) as proof of ((cR X0) x0)
% Found x4:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x4 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x9:((cR x6) X0)
% Instantiate: X:=x6:fofType;X0:=x0:fofType
% Found (fun (x9:((cR x6) X0))=> x9) as proof of ((cR X) x0)
% Found (fun (x8:((cR X0) x6)) (x9:((cR x6) X0))=> x9) as proof of (((cR x6) X0)->((cR X) x0))
% Found (fun (x8:((cR X0) x6)) (x9:((cR x6) X0))=> x9) as proof of (((cR X0) x6)->(((cR x6) X0)->((cR X) x0)))
% Found (and_rect20 (fun (x8:((cR X0) x6)) (x9:((cR x6) X0))=> x9)) as proof of ((cR X) x0)
% Found ((and_rect2 ((cR X) x0)) (fun (x8:((cR X0) x6)) (x9:((cR x6) X0))=> x9)) as proof of ((cR X) x0)
% Found (((fun (P:Type) (x8:(((cR X0) x6)->(((cR x6) X0)->P)))=> (((((and_rect ((cR X0) x6)) ((cR x6) X0)) P) x8) x7)) ((cR X) x0)) (fun (x8:((cR X0) x6)) (x9:((cR x6) X0))=> x9)) as proof of ((cR X) x0)
% Found (((fun (P:Type) (x8:(((cR X0) x6)->(((cR x6) X0)->P)))=> (((((and_rect ((cR X0) x6)) ((cR x6) X0)) P) x8) x7)) ((cR X) x0)) (fun (x8:((cR X0) x6)) (x9:((cR x6) X0))=> x9)) as proof of ((cR X) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Instantiate: x4:=x0:fofType
% Found (x3 x20) as proof of ((cR X) x4)
% Found (x3 x20) as proof of ((cR X) x4)
% Found x30:=(x3 x20):((cR X) x0)
% Instantiate: X:=x0:fofType;x4:=X:fofType
% Found (x3 x20) as proof of ((cR x4) X)
% Found (x3 x20) as proof of ((cR x4) X)
% Found x30:=(x3 x20):((cR X) x0)
% Instantiate: X:=x0:fofType
% Found (x3 x20) as proof of ((cR x4) X)
% Found (x3 x20) as proof of ((cR x4) X)
% Found ((conj00 (x3 x20)) (x3 x20)) as proof of ((and ((cR X) x4)) ((cR x4) X))
% Found (((conj0 ((cR x4) X)) (x3 x20)) (x3 x20)) as proof of ((and ((cR X) x4)) ((cR x4) X))
% Found ((((conj ((cR X) x4)) ((cR x4) X)) (x3 x20)) (x3 x20)) as proof of ((and ((cR X) x4)) ((cR x4) X))
% Found ((((conj ((cR X) x4)) ((cR x4) X)) (x3 x20)) (x3 x20)) as proof of ((and ((cR X) x4)) ((cR x4) X))
% Found (ex_intro000 ((((conj ((cR X) x4)) ((cR x4) X)) (x3 x20)) (x3 x20))) as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found ((ex_intro00 x0) ((((conj ((cR X) x0)) ((cR x0) X)) (x3 x20)) (x3 x20))) as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found (((ex_intro0 (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))) x0) ((((conj ((cR X) x0)) ((cR x0) X)) (x3 x20)) (x3 x20))) as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found ((((ex_intro fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))) x0) ((((conj ((cR X) x0)) ((cR x0) X)) (x3 x20)) (x3 x20))) as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found ((((ex_intro fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))) x0) ((((conj ((cR X) x0)) ((cR x0) X)) (x3 x20)) (x3 x20))) as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found ((x2 (x3 x20)) ((((ex_intro fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))) x0) ((((conj ((cR X) x0)) ((cR x0) X)) (x3 x20)) (x3 x20)))) as proof of False
% Found (fun (x3:((not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))->((cR X) x0)))=> ((x2 (x3 x20)) ((((ex_intro fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))) x0) ((((conj ((cR X) x0)) ((cR x0) X)) (x3 x20)) (x3 x20))))) as proof of False
% Found (fun (x3:((not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))->((cR X) x0)))=> ((x2 (x3 x20)) ((((ex_intro fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))) x0) ((((conj ((cR X) x0)) ((cR x0) X)) (x3 x20)) (x3 x20))))) as proof of (((not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))->((cR X) x0))->False)
% Found x30:((cR X) x0)
% Instantiate: X:=x0:fofType
% Found x30 as proof of ((cR x4) X)
% Found x40:=(x4 x50):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found x40:=(x4 x50):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Instantiate: X:=X0:fofType
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x30:=(x3 x20):((cR X) x0)
% Instantiate: X0:=X:fofType
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Instantiate: X0:=X:fofType
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x40:=(x4 x50):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Instantiate: X:=X0:fofType
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x40:=(x4 x50):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Instantiate: X:=X0:fofType
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Instantiate: X0:=X:fofType
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x40:=(x4 x50):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x4:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x4 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found ((x2 x30) x6) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x2 x30) x6)) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x2 x30) x6)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x50:((cR X0) x0)
% Found x50 as proof of ((cR X0) x0)
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found ((x4 x50) x6) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))=> ((x4 x50) x6)) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))=> ((x4 x50) x6)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x30:=(x3 x21):((cR X) x0)
% Found (x3 x21) as proof of ((cR X) x0)
% Found (x3 x21) as proof of ((cR X) x0)
% Found x40:=(x4 x50):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Instantiate: X:=X0:fofType
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x20:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Instantiate: X0:=X:fofType
% Found x20 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x20:=(x2 x31):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x31) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x31) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x40:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Instantiate: X:=X0:fofType
% Found x40 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found (x40 x6) as proof of False
% Found ((x4 x50) x6) as proof of False
% Found ((x4 x50) x6) as proof of False
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found (x20 x6) as proof of False
% Found ((x2 x30) x6) as proof of False
% Found ((x2 x30) x6) as proof of False
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x51:((cR X0) x0)
% Found x51 as proof of ((cR X0) x0)
% Found x51:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x51 as proof of ((cR X) x0)
% Found x31:((cR X) x0)
% Found x31 as proof of ((cR X) x0)
% Found x31:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x31 as proof of ((cR X0) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found x20:=(x2 x30):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x9:((cR x6) X)
% Instantiate: X:=x0:fofType;X0:=x6:fofType
% Found x9 as proof of ((cR X0) x0)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x9:((cR x6) X0)
% Instantiate: X:=x6:fofType;X0:=x0:fofType
% Found x9 as proof of ((cR X) x0)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x4:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x4 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Instantiate: X0:=X:fofType
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x40:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x40 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Instantiate: x4:=x0:fofType
% Found (x3 x20) as proof of ((cR X) x4)
% Found (x3 x20) as proof of ((cR X) x4)
% Found x30:=(x3 x20):((cR X) x0)
% Instantiate: X:=x0:fofType;x4:=X:fofType
% Found (x3 x20) as proof of ((cR x4) X)
% Found (x3 x20) as proof of ((cR x4) X)
% Found x30:((cR X) x0)
% Instantiate: X:=x0:fofType;x4:=X:fofType
% Found x30 as proof of ((cR x4) X)
% Found x30:((cR X) x0)
% Instantiate: x4:=x0:fofType
% Found x30 as proof of ((cR X) x4)
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x4)
% Found ((conj00 x30) x30) as proof of ((and ((cR X) x4)) ((cR x4) X))
% Found (((conj0 ((cR x4) X)) x30) x30) as proof of ((and ((cR X) x4)) ((cR x4) X))
% Found ((((conj ((cR X) x4)) ((cR x4) X)) x30) x30) as proof of ((and ((cR X) x4)) ((cR x4) X))
% Found ((((conj ((cR X) x4)) ((cR x4) X)) x30) x30) as proof of ((and ((cR X) x4)) ((cR x4) X))
% Found x20:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Instantiate: X0:=X:fofType
% Found x20 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x5:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x5 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x40:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Instantiate: X:=X0:fofType
% Found x40 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x3 x40) as proof of ((cR X) x0)
% Found (x3 x40) as proof of ((cR X) x0)
% Found x40:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Instantiate: X:=X0:fofType
% Found x40 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x3 x40) as proof of ((cR X) x0)
% Found (x3 x40) as proof of ((cR X) x0)
% Found x20:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Instantiate: X0:=X:fofType
% Found x20 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x31:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x31 as proof of ((cR X0) x0)
% Found x31:((cR X) x0)
% Found x31 as proof of ((cR X) x0)
% Found x20:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Instantiate: X0:=X:fofType
% Found x20 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x40:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Instantiate: X:=X0:fofType
% Found x40 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x40:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Instantiate: X:=X0:fofType
% Found x40 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x31:((cR X) x0)
% Found x31 as proof of ((cR X) x0)
% Found x31:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x31 as proof of ((cR X0) x0)
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found (x20 x6) as proof of False
% Found ((x2 x30) x6) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x2 x30) x6)) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x2 x30) x6)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found (x40 x6) as proof of False
% Found ((x4 x50) x6) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))=> ((x4 x50) x6)) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))=> ((x4 x50) x6)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found x4:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x4 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x000:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x000 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x30:=(x3 x20):((cR X) x0)
% Instantiate: X0:=X:fofType
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x30:=(x3 x40):((cR X) x0)
% Found (x3 x40) as proof of ((cR X0) x0)
% Found (x3 x40) as proof of ((cR X0) x0)
% Found (x3 x40) as proof of ((cR X0) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Instantiate: X0:=X:fofType
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Instantiate: X0:=X:fofType
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x20:=(x2 x30):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x40:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x40 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (fun (x5:((not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))->((cR X0) x0)))=> (x5 x40)) as proof of ((cR X) x0)
% Found (fun (x5:((not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))->((cR X0) x0)))=> (x5 x40)) as proof of (((not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))->((cR X0) x0))->((cR X) x0))
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found x50:((cR X0) x0)
% Found x50 as proof of ((cR X0) x0)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x30:((cR X) x0)
% Instantiate: X:=x0:fofType
% Found x30 as proof of ((cR x4) X)
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x31:((cR X) x0)
% Found x31 as proof of ((cR X) x0)
% Found x31:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x31 as proof of ((cR X0) x0)
% Found x31:((cR X) x0)
% Found x31 as proof of ((cR X) x0)
% Found x31:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x31 as proof of ((cR X0) x0)
% Found x20:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Instantiate: X0:=X:fofType
% Found x20 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x40:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Instantiate: X:=X0:fofType
% Found x40 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x20:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Instantiate: X0:=X:fofType
% Found x20 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x31:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x31 as proof of ((cR X0) x0)
% Found x31:((cR X) x0)
% Found x31 as proof of ((cR X) x0)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found (x4 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x4 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found (x2 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found (x4 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x4 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found (x2 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x40:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x40 as proof of ((cR X) x0)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Instantiate: X0:=X:fofType
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found x40:=(x4 x50):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x20:=(x2 x30):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x5:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x5 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x40:=(x4 x50):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x12:((cR x7) X0)
% Instantiate: X:=x7:fofType;X0:=x0:fofType
% Found (fun (x12:((cR x7) X0))=> x12) as proof of ((cR X) x0)
% Found (fun (x9:((cR X0) x7)) (x12:((cR x7) X0))=> x12) as proof of (((cR x7) X0)->((cR X) x0))
% Found (fun (x9:((cR X0) x7)) (x12:((cR x7) X0))=> x12) as proof of (((cR X0) x7)->(((cR x7) X0)->((cR X) x0)))
% Found (and_rect20 (fun (x9:((cR X0) x7)) (x12:((cR x7) X0))=> x12)) as proof of ((cR X) x0)
% Found ((and_rect2 ((cR X) x0)) (fun (x9:((cR X0) x7)) (x12:((cR x7) X0))=> x12)) as proof of ((cR X) x0)
% Found (((fun (P:Type) (x9:(((cR X0) x7)->(((cR x7) X0)->P)))=> (((((and_rect ((cR X0) x7)) ((cR x7) X0)) P) x9) x8)) ((cR X) x0)) (fun (x9:((cR X0) x7)) (x12:((cR x7) X0))=> x12)) as proof of ((cR X) x0)
% Found (fun (x8:((and ((cR X0) x7)) ((cR x7) X0)))=> (((fun (P:Type) (x9:(((cR X0) x7)->(((cR x7) X0)->P)))=> (((((and_rect ((cR X0) x7)) ((cR x7) X0)) P) x9) x8)) ((cR X) x0)) (fun (x9:((cR X0) x7)) (x12:((cR x7) X0))=> x12))) as proof of ((cR X) x0)
% Found x12:((cR x7) X)
% Instantiate: X:=x0:fofType;X0:=x7:fofType
% Found (fun (x12:((cR x7) X))=> x12) as proof of ((cR X0) x0)
% Found (fun (x9:((cR X) x7)) (x12:((cR x7) X))=> x12) as proof of (((cR x7) X)->((cR X0) x0))
% Found (fun (x9:((cR X) x7)) (x12:((cR x7) X))=> x12) as proof of (((cR X) x7)->(((cR x7) X)->((cR X0) x0)))
% Found (and_rect20 (fun (x9:((cR X) x7)) (x12:((cR x7) X))=> x12)) as proof of ((cR X0) x0)
% Found ((and_rect2 ((cR X0) x0)) (fun (x9:((cR X) x7)) (x12:((cR x7) X))=> x12)) as proof of ((cR X0) x0)
% Found (((fun (P:Type) (x9:(((cR X) x7)->(((cR x7) X)->P)))=> (((((and_rect ((cR X) x7)) ((cR x7) X)) P) x9) x8)) ((cR X0) x0)) (fun (x9:((cR X) x7)) (x12:((cR x7) X))=> x12)) as proof of ((cR X0) x0)
% Found (fun (x8:((and ((cR X) x7)) ((cR x7) X)))=> (((fun (P:Type) (x9:(((cR X) x7)->(((cR x7) X)->P)))=> (((((and_rect ((cR X) x7)) ((cR x7) X)) P) x9) x8)) ((cR X0) x0)) (fun (x9:((cR X) x7)) (x12:((cR x7) X))=> x12))) as proof of ((cR X0) x0)
% Found x40:=(x4 x50):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x40:=(x4 x50):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Instantiate: X:=X0:fofType
% Found x40 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Instantiate: X0:=X:fofType
% Found x20 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x20 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x40:=(x4 x50):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x40 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x30:=(x3 x20):((cR X) x0)
% Instantiate: x4:=x0:fofType
% Found (x3 x20) as proof of ((cR X) x4)
% Found (x3 x20) as proof of ((cR X) x4)
% Found x30:=(x3 x20):((cR X) x0)
% Instantiate: X:=x0:fofType;x4:=X:fofType
% Found (x3 x20) as proof of ((cR x4) X)
% Found (x3 x20) as proof of ((cR x4) X)
% Found x30:=(x3 x20):((cR X) x0)
% Instantiate: X:=x0:fofType
% Found (x3 x20) as proof of ((cR x4) X)
% Found (x3 x20) as proof of ((cR x4) X)
% Found ((conj00 (x3 x20)) (x3 x20)) as proof of ((and ((cR X) x4)) ((cR x4) X))
% Found (((conj0 ((cR x4) X)) (x3 x20)) (x3 x20)) as proof of ((and ((cR X) x4)) ((cR x4) X))
% Found ((((conj ((cR X) x4)) ((cR x4) X)) (x3 x20)) (x3 x20)) as proof of ((and ((cR X) x4)) ((cR x4) X))
% Found ((((conj ((cR X) x4)) ((cR x4) X)) (x3 x20)) (x3 x20)) as proof of ((and ((cR X) x4)) ((cR x4) X))
% Found x12:((cR x7) X0)
% Instantiate: X:=x7:fofType;X0:=x0:fofType
% Found (fun (x12:((cR x7) X0))=> x12) as proof of ((cR X) x0)
% Found (fun (x9:((cR X0) x7)) (x12:((cR x7) X0))=> x12) as proof of (((cR x7) X0)->((cR X) x0))
% Found (fun (x9:((cR X0) x7)) (x12:((cR x7) X0))=> x12) as proof of (((cR X0) x7)->(((cR x7) X0)->((cR X) x0)))
% Found (and_rect20 (fun (x9:((cR X0) x7)) (x12:((cR x7) X0))=> x12)) as proof of ((cR X) x0)
% Found ((and_rect2 ((cR X) x0)) (fun (x9:((cR X0) x7)) (x12:((cR x7) X0))=> x12)) as proof of ((cR X) x0)
% Found (((fun (P:Type) (x9:(((cR X0) x7)->(((cR x7) X0)->P)))=> (((((and_rect ((cR X0) x7)) ((cR x7) X0)) P) x9) x8)) ((cR X) x0)) (fun (x9:((cR X0) x7)) (x12:((cR x7) X0))=> x12)) as proof of ((cR X) x0)
% Found (((fun (P:Type) (x9:(((cR X0) x7)->(((cR x7) X0)->P)))=> (((((and_rect ((cR X0) x7)) ((cR x7) X0)) P) x9) x8)) ((cR X) x0)) (fun (x9:((cR X0) x7)) (x12:((cR x7) X0))=> x12)) as proof of ((cR X) x0)
% Found x12:((cR x7) X)
% Instantiate: X:=x0:fofType;X0:=x7:fofType
% Found (fun (x12:((cR x7) X))=> x12) as proof of ((cR X0) x0)
% Found (fun (x9:((cR X) x7)) (x12:((cR x7) X))=> x12) as proof of (((cR x7) X)->((cR X0) x0))
% Found (fun (x9:((cR X) x7)) (x12:((cR x7) X))=> x12) as proof of (((cR X) x7)->(((cR x7) X)->((cR X0) x0)))
% Found (and_rect20 (fun (x9:((cR X) x7)) (x12:((cR x7) X))=> x12)) as proof of ((cR X0) x0)
% Found ((and_rect2 ((cR X0) x0)) (fun (x9:((cR X) x7)) (x12:((cR x7) X))=> x12)) as proof of ((cR X0) x0)
% Found (((fun (P:Type) (x9:(((cR X) x7)->(((cR x7) X)->P)))=> (((((and_rect ((cR X) x7)) ((cR x7) X)) P) x9) x8)) ((cR X0) x0)) (fun (x9:((cR X) x7)) (x12:((cR x7) X))=> x12)) as proof of ((cR X0) x0)
% Found (((fun (P:Type) (x9:(((cR X) x7)->(((cR x7) X)->P)))=> (((((and_rect ((cR X) x7)) ((cR x7) X)) P) x9) x8)) ((cR X0) x0)) (fun (x9:((cR X) x7)) (x12:((cR x7) X))=> x12)) as proof of ((cR X0) x0)
% Found x20:=(x2 x30):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Instantiate: X0:=X:fofType
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x40:=(x4 x50):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Instantiate: X:=X0:fofType
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x20:=(x2 x30):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Instantiate: X0:=X:fofType
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x40:=(x4 x50):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Instantiate: X:=X0:fofType
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x20:=(x2 x30):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x40:=(x4 x50):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x40:=(x4 x50):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x50:((cR X0) x0)
% Found x50 as proof of ((cR X0) x0)
% Found ((x4 x50) x00) as proof of False
% Found ((x4 x50) x00) as proof of False
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x30:((cR X) x0)
% Instantiate: X:=x0:fofType;x4:=X:fofType
% Found x30 as proof of ((cR x4) X)
% Found x30:((cR X) x0)
% Instantiate: x4:=x0:fofType
% Found x30 as proof of ((cR X) x4)
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x4)
% Found ((conj00 x30) x30) as proof of ((and ((cR X) x4)) ((cR x4) X))
% Found (((conj0 ((cR x4) X)) x30) x30) as proof of ((and ((cR X) x4)) ((cR x4) X))
% Found ((((conj ((cR X) x4)) ((cR x4) X)) x30) x30) as proof of ((and ((cR X) x4)) ((cR x4) X))
% Found ((((conj ((cR X) x4)) ((cR x4) X)) x30) x30) as proof of ((and ((cR X) x4)) ((cR x4) X))
% Found (ex_intro000 ((((conj ((cR X) x4)) ((cR x4) X)) x30) x30)) as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found ((ex_intro00 X) ((((conj ((cR X) X)) ((cR X) X)) x30) x30)) as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found (((ex_intro0 (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))) X) ((((conj ((cR X) X)) ((cR X) X)) x30) x30)) as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found ((((ex_intro fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))) X) ((((conj ((cR X) X)) ((cR X) X)) x30) x30)) as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found ((((ex_intro fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))) X) ((((conj ((cR X) X)) ((cR X) X)) x30) x30)) as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found (x4 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x4 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found x51:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x51 as proof of ((cR X) x0)
% Found x51:((cR X0) x0)
% Found x51 as proof of ((cR X0) x0)
% Found x31:((cR X) x0)
% Found x31 as proof of ((cR X) x0)
% Found x31:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x31 as proof of ((cR X0) x0)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR x4) X)
% Found x30 as proof of ((cR x4) X)
% Found x30:=(x3 x20):((cR X) x0)
% Instantiate: x4:=x0:fofType
% Found (x3 x20) as proof of ((cR X) x4)
% Found (x3 x20) as proof of ((cR X) x4)
% Found x30:=(x3 x20):((cR X) x0)
% Instantiate: X:=x0:fofType;x4:=X:fofType
% Found (x3 x20) as proof of ((cR x4) X)
% Found (x3 x20) as proof of ((cR x4) X)
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Instantiate: X0:=X:fofType
% Found x20 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x20 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x20:=(x2 x30):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Instantiate: X0:=X:fofType
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x20:=(x2 x30):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x50:=(x5 x40):((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Instantiate: X0:=X:fofType
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x50:((cR X0) x0)
% Found x50 as proof of ((cR X0) x0)
% Found ((x4 x50) x00) as proof of False
% Found ((x4 x50) x00) as proof of False
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Instantiate: X0:=X:fofType
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x40:=(x4 x50):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Instantiate: X:=X0:fofType
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Instantiate: X0:=X:fofType
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x40:=(x4 x50):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Instantiate: X:=X0:fofType
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x40:=(x4 x50):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x40:=(x4 x50):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x40:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Instantiate: X:=X0:fofType
% Found x40 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x3 x40) as proof of ((cR X) x0)
% Found (x3 x40) as proof of ((cR X) x0)
% Found x40:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Instantiate: X:=X0:fofType
% Found x40 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x3 x40) as proof of ((cR X) x0)
% Found (x3 x40) as proof of ((cR X) x0)
% Found x20:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x20 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x40:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x40 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x3 x40) as proof of ((cR X0) x0)
% Found (x3 x40) as proof of ((cR X0) x0)
% Found (x3 x40) as proof of ((cR X0) x0)
% Found x20:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x20 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x50:((cR X0) x0)
% Found x50 as proof of ((cR X0) x0)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found ((x4 x50) x00) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))=> ((x4 x50) x00)) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))=> ((x4 x50) x00)) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found x12:((cR x7) X)
% Instantiate: X:=x0:fofType;X0:=x7:fofType
% Found x12 as proof of ((cR X0) x0)
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x12:((cR x7) X0)
% Instantiate: X:=x7:fofType;X0:=x0:fofType
% Found x12 as proof of ((cR X) x0)
% Found x31:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x31 as proof of ((cR X0) x0)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found (x4 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x4 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x31:((cR X) x0)
% Found x31 as proof of ((cR X) x0)
% Found x20:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Instantiate: X0:=X:fofType
% Found x20 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x20:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Instantiate: X0:=X:fofType
% Found x20 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x40:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Instantiate: X:=X0:fofType
% Found x40 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x40:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Instantiate: X:=X0:fofType
% Found x40 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x31:((cR X) x0)
% Found x31 as proof of ((cR X) x0)
% Found x31:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x31 as proof of ((cR X0) x0)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x40:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Instantiate: X:=X0:fofType
% Found x40 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x40:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Instantiate: X:=X0:fofType
% Found x40 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x20:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Instantiate: X0:=X:fofType
% Found x20 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found x40:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Instantiate: X:=X0:fofType
% Found x40 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x40:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Instantiate: X:=X0:fofType
% Found x40 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x20:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Instantiate: X0:=X:fofType
% Found x20 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found x20:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Instantiate: X0:=X:fofType
% Found x20 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x20:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Instantiate: X0:=X:fofType
% Found x20 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x20:=(x2 x50):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x30:=(x3 x40):((cR X) x0)
% Found (x3 x40) as proof of ((cR X0) x0)
% Found (x3 x40) as proof of ((cR X0) x0)
% Found (x3 x40) as proof of ((cR X0) x0)
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x20:=(x2 x50):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x20 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Instantiate: X0:=X:fofType
% Found x20 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found (x40 x00) as proof of False
% Found ((x4 x50) x00) as proof of False
% Found ((x4 x50) x00) as proof of False
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x20:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Instantiate: X0:=X:fofType
% Found x20 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x20:=(x2 x30):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Instantiate: X0:=X:fofType
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x30:=(x3 x20):((cR X) x0)
% Instantiate: X0:=X:fofType
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x20:=(x2 x30):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Instantiate: X0:=X:fofType
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x50:=(x5 x40):((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Instantiate: X0:=X:fofType
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found x4:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x4 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x50:=(x5 x40):((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Instantiate: X0:=X:fofType
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x50:=(x5 x40):((cR X0) x0)
% Found (x5 x40) as proof of ((cR X0) x0)
% Found (x5 x40) as proof of ((cR X0) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x50:=(x5 x40):((cR X0) x0)
% Found (x5 x40) as proof of ((cR X0) x0)
% Found (x5 x40) as proof of ((cR X0) x0)
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Instantiate: X0:=X:fofType
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x4)
% Found (x3 x20) as proof of ((cR X) x4)
% Found (x3 x20) as proof of ((cR X) x4)
% Found x30:=(x3 x20):((cR X) x0)
% Instantiate: X:=x0:fofType
% Found (x3 x20) as proof of ((cR x4) X)
% Found (x3 x20) as proof of ((cR x4) X)
% Found (x3 x20) as proof of ((cR x4) X)
% Found x20:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x20 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x31:((cR X) x0)
% Found x31 as proof of ((cR X) x0)
% Found x31:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x31 as proof of ((cR X0) x0)
% Found x20:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Instantiate: X0:=X:fofType
% Found x20 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x31:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x31 as proof of ((cR X0) x0)
% Found x31:((cR X) x0)
% Found x31 as proof of ((cR X) x0)
% Found x20:=(x2 x30):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x20:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Instantiate: X0:=X:fofType
% Found x20 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x31:((cR X) x0)
% Found x31 as proof of ((cR X) x0)
% Found x31:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x31 as proof of ((cR X0) x0)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x50:((cR X0) x0)
% Found x50 as proof of ((cR X0) x0)
% Found x50:((cR X0) x0)
% Found x50 as proof of ((cR X0) x0)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found x40:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x40 as proof of ((cR X) x0)
% Found x50:((cR X0) x0)
% Found x50 as proof of ((cR X0) x0)
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found x50:((cR X0) x0)
% Found x50 as proof of ((cR X0) x0)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found (x40 x00) as proof of False
% Found ((x4 x50) x00) as proof of False
% Found ((x4 x50) x00) as proof of False
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found (x4 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x4 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found (x2 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found x50:=(x5 x20):((cR X0) x0)
% Found (x5 x20) as proof of ((cR X0) x0)
% Found (x5 x20) as proof of ((cR X0) x0)
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found (x2 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x20:=(x2 x32):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x32) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x32) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found (x4 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x4 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x30:=(x3 x40):((cR X) x0)
% Found (x3 x40) as proof of ((cR X) x0)
% Found (x3 x40) as proof of ((cR X) x0)
% Found x30:=(x3 x40):((cR X) x0)
% Found (x3 x40) as proof of ((cR X0) x0)
% Found (x3 x40) as proof of ((cR X0) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x31:((cR X) x0)
% Found x31 as proof of ((cR X) x0)
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Instantiate: x4:=x0:fofType
% Found (x3 x20) as proof of ((cR X) x4)
% Found (x3 x20) as proof of ((cR X) x4)
% Found x30:=(x3 x20):((cR X) x0)
% Instantiate: X:=x0:fofType;x4:=X:fofType
% Found (x3 x20) as proof of ((cR x4) X)
% Found (x3 x20) as proof of ((cR x4) X)
% Found x30:=(x3 x20):((cR X) x0)
% Instantiate: X:=x0:fofType
% Found (x3 x20) as proof of ((cR x4) X)
% Found (x3 x20) as proof of ((cR x4) X)
% Found ((conj00 (x3 x20)) (x3 x20)) as proof of ((and ((cR X) x4)) ((cR x4) X))
% Found (((conj0 ((cR x4) X)) (x3 x20)) (x3 x20)) as proof of ((and ((cR X) x4)) ((cR x4) X))
% Found ((((conj ((cR X) x4)) ((cR x4) X)) (x3 x20)) (x3 x20)) as proof of ((and ((cR X) x4)) ((cR x4) X))
% Found ((((conj ((cR X) x4)) ((cR x4) X)) (x3 x20)) (x3 x20)) as proof of ((and ((cR X) x4)) ((cR x4) X))
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found (x40 x00) as proof of False
% Found ((x4 x50) x00) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))=> ((x4 x50) x00)) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))=> ((x4 x50) x00)) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x30:=(x3 x20):((cR X) x0)
% Instantiate: X0:=X:fofType
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x40:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Instantiate: X:=X0:fofType
% Found x40 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x30:=(x3 x20):((cR X) x0)
% Instantiate: X0:=X:fofType
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Instantiate: X0:=X:fofType
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Instantiate: X0:=X:fofType
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Instantiate: X0:=X:fofType
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x20:=(x2 x30):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Instantiate: X0:=X:fofType
% Found x20 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x40:=(x4 x50):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x40 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x20:=(x2 x30):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x20 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found x40:=(x4 x50):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Instantiate: X:=X0:fofType
% Found x40 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x40:=(x4 x50):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x40:=(x4 x30):((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found (x4 x30) as proof of ((cR X) x0)
% Found (x4 x30) as proof of ((cR X) x0)
% Found x20:=(x2 x30):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x50:((cR X0) x0)
% Found x50 as proof of ((cR X0) x0)
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Instantiate: X0:=X:fofType
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x40:=(x4 x50):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x20:=(x2 x30):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x4:(((cR X0) x0)->(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))))
% Instantiate: X:=x0:fofType;X0:=x7:fofType
% Found (fun (x9:((cR X) x7))=> x4) as proof of (((cR x7) X)->(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))))
% Found (fun (x9:((cR X) x7))=> x4) as proof of (((cR X) x7)->(((cR x7) X)->(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))))
% Found (and_rect20 (fun (x9:((cR X) x7))=> x4)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found ((and_rect2 (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))) (fun (x9:((cR X) x7))=> x4)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (((fun (P:Type) (x9:(((cR X) x7)->(((cR x7) X)->P)))=> (((((and_rect ((cR X) x7)) ((cR x7) X)) P) x9) x8)) (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))) (fun (x9:((cR X) x7))=> x4)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (fun (x8:((and ((cR X) x7)) ((cR x7) X)))=> (((fun (P:Type) (x9:(((cR X) x7)->(((cR x7) X)->P)))=> (((((and_rect ((cR X) x7)) ((cR x7) X)) P) x9) x8)) (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))) (fun (x9:((cR X) x7))=> x4))) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x2:(((cR X) x0)->(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))))
% Instantiate: X:=x7:fofType;X0:=x0:fofType
% Found (fun (x9:((cR X0) x7))=> x2) as proof of (((cR x7) X0)->(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))))
% Found (fun (x9:((cR X0) x7))=> x2) as proof of (((cR X0) x7)->(((cR x7) X0)->(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))))
% Found (and_rect20 (fun (x9:((cR X0) x7))=> x2)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found ((and_rect2 (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))) (fun (x9:((cR X0) x7))=> x2)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (((fun (P:Type) (x9:(((cR X0) x7)->(((cR x7) X0)->P)))=> (((((and_rect ((cR X0) x7)) ((cR x7) X0)) P) x9) x8)) (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))) (fun (x9:((cR X0) x7))=> x2)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (((fun (P:Type) (x9:(((cR X0) x7)->(((cR x7) X0)->P)))=> (((((and_rect ((cR X0) x7)) ((cR x7) X0)) P) x9) x8)) (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))) (fun (x9:((cR X0) x7))=> x2)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x3 (((fun (P:Type) (x9:(((cR X0) x7)->(((cR x7) X0)->P)))=> (((((and_rect ((cR X0) x7)) ((cR x7) X0)) P) x9) x8)) (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))) (fun (x9:((cR X0) x7))=> x2))) as proof of ((cR X) x0)
% Found (fun (x8:((and ((cR X0) x7)) ((cR x7) X0)))=> (x3 (((fun (P:Type) (x9:(((cR X0) x7)->(((cR x7) X0)->P)))=> (((((and_rect ((cR X0) x7)) ((cR x7) X0)) P) x9) x8)) (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))) (fun (x9:((cR X0) x7))=> x2)))) as proof of ((cR X) x0)
% Found x4:(((cR X0) x0)->(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))))
% Instantiate: X:=x0:fofType;X0:=x7:fofType
% Found (fun (x9:((cR X) x7))=> x4) as proof of (((cR x7) X)->(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))))
% Found (fun (x9:((cR X) x7))=> x4) as proof of (((cR X) x7)->(((cR x7) X)->(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))))
% Found (and_rect20 (fun (x9:((cR X) x7))=> x4)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found ((and_rect2 (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))) (fun (x9:((cR X) x7))=> x4)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (((fun (P:Type) (x9:(((cR X) x7)->(((cR x7) X)->P)))=> (((((and_rect ((cR X) x7)) ((cR x7) X)) P) x9) x8)) (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))) (fun (x9:((cR X) x7))=> x4)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (((fun (P:Type) (x9:(((cR X) x7)->(((cR x7) X)->P)))=> (((((and_rect ((cR X) x7)) ((cR x7) X)) P) x9) x8)) (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))) (fun (x9:((cR X) x7))=> x4)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x5 (((fun (P:Type) (x9:(((cR X) x7)->(((cR x7) X)->P)))=> (((((and_rect ((cR X) x7)) ((cR x7) X)) P) x9) x8)) (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))) (fun (x9:((cR X) x7))=> x4))) as proof of ((cR X0) x0)
% Found (fun (x8:((and ((cR X) x7)) ((cR x7) X)))=> (x5 (((fun (P:Type) (x9:(((cR X) x7)->(((cR x7) X)->P)))=> (((((and_rect ((cR X) x7)) ((cR x7) X)) P) x9) x8)) (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))) (fun (x9:((cR X) x7))=> x4)))) as proof of ((cR X0) x0)
% Found x2:(((cR X) x0)->(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))))
% Instantiate: X:=x7:fofType;X0:=x0:fofType
% Found (fun (x9:((cR X0) x7))=> x2) as proof of (((cR x7) X0)->(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))))
% Found (fun (x9:((cR X0) x7))=> x2) as proof of (((cR X0) x7)->(((cR x7) X0)->(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))))
% Found (and_rect20 (fun (x9:((cR X0) x7))=> x2)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found ((and_rect2 (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))) (fun (x9:((cR X0) x7))=> x2)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (((fun (P:Type) (x9:(((cR X0) x7)->(((cR x7) X0)->P)))=> (((((and_rect ((cR X0) x7)) ((cR x7) X0)) P) x9) x8)) (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))) (fun (x9:((cR X0) x7))=> x2)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (fun (x8:((and ((cR X0) x7)) ((cR x7) X0)))=> (((fun (P:Type) (x9:(((cR X0) x7)->(((cR x7) X0)->P)))=> (((((and_rect ((cR X0) x7)) ((cR x7) X0)) P) x9) x8)) (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))) (fun (x9:((cR X0) x7))=> x2))) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x31:((cR X) x0)
% Found x31 as proof of ((cR X) x0)
% Found x30:((cR X) x0)
% Instantiate: X:=x0:fofType;x4:=X:fofType
% Found x30 as proof of ((cR x4) X)
% Found x30:((cR X) x0)
% Instantiate: x4:=x0:fofType
% Found x30 as proof of ((cR X) x4)
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x4)
% Found ((conj00 x30) x30) as proof of ((and ((cR X) x4)) ((cR x4) X))
% Found (((conj0 ((cR x4) X)) x30) x30) as proof of ((and ((cR X) x4)) ((cR x4) X))
% Found ((((conj ((cR X) x4)) ((cR x4) X)) x30) x30) as proof of ((and ((cR X) x4)) ((cR x4) X))
% Found ((((conj ((cR X) x4)) ((cR x4) X)) x30) x30) as proof of ((and ((cR X) x4)) ((cR x4) X))
% Found (ex_intro000 ((((conj ((cR X) x4)) ((cR x4) X)) x30) x30)) as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found ((ex_intro00 X) ((((conj ((cR X) X)) ((cR X) X)) x30) x30)) as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found (((ex_intro0 (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))) X) ((((conj ((cR X) X)) ((cR X) X)) x30) x30)) as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found ((((ex_intro fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))) X) ((((conj ((cR X) X)) ((cR X) X)) x30) x30)) as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found ((((ex_intro fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))) X) ((((conj ((cR X) X)) ((cR X) X)) x30) x30)) as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x30:=(x3 x20):((cR X) x0)
% Instantiate: X0:=X:fofType
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x50:=(x5 x40):((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Instantiate: X0:=X:fofType
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x50:((cR X0) x0)
% Found x50 as proof of ((cR X0) x0)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found x20:=(x2 x30):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR x4) X)
% Found x30 as proof of ((cR x4) X)
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x000:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x000 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found (x4 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x4 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x50:((cR X0) x0)
% Found x50 as proof of ((cR X0) x0)
% Found ((x4 x50) x6) as proof of False
% Found ((x4 x50) x6) as proof of False
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x20:=(fun (x9:((cR X) x0))=> ((x2 x9) x00)):(((cR X) x0)->False)
% Instantiate: X:=x6:fofType;X0:=x0:fofType
% Found (fun (x9:((cR X) x0))=> ((x2 x9) x00)) as proof of (((cR x6) X0)->False)
% Found (fun (x8:((cR X0) x6)) (x9:((cR X) x0))=> ((x2 x9) x00)) as proof of (((cR x6) X0)->False)
% Found (fun (x8:((cR X0) x6)) (x9:((cR X) x0))=> ((x2 x9) x00)) as proof of (((cR X0) x6)->(((cR x6) X0)->False))
% Found (and_rect20 (fun (x8:((cR X0) x6)) (x9:((cR X) x0))=> ((x2 x9) x00))) as proof of False
% Found ((and_rect2 False) (fun (x8:((cR X0) x6)) (x9:((cR X) x0))=> ((x2 x9) x00))) as proof of False
% Found (((fun (P:Type) (x8:(((cR X0) x6)->(((cR x6) X0)->P)))=> (((((and_rect ((cR X0) x6)) ((cR x6) X0)) P) x8) x7)) False) (fun (x8:((cR X0) x6)) (x9:((cR X) x0))=> ((x2 x9) x00))) as proof of False
% Found (fun (x7:((and ((cR X0) x6)) ((cR x6) X0)))=> (((fun (P:Type) (x8:(((cR X0) x6)->(((cR x6) X0)->P)))=> (((((and_rect ((cR X0) x6)) ((cR x6) X0)) P) x8) x7)) False) (fun (x8:((cR X0) x6)) (x9:((cR X) x0))=> ((x2 x9) x00)))) as proof of False
% Found x40:=(fun (x9:((cR X0) x0))=> ((x4 x9) x00)):(((cR X0) x0)->False)
% Instantiate: X:=x0:fofType;X0:=x6:fofType
% Found (fun (x9:((cR X0) x0))=> ((x4 x9) x00)) as proof of (((cR x6) X)->False)
% Found (fun (x8:((cR X) x6)) (x9:((cR X0) x0))=> ((x4 x9) x00)) as proof of (((cR x6) X)->False)
% Found (fun (x8:((cR X) x6)) (x9:((cR X0) x0))=> ((x4 x9) x00)) as proof of (((cR X) x6)->(((cR x6) X)->False))
% Found (and_rect20 (fun (x8:((cR X) x6)) (x9:((cR X0) x0))=> ((x4 x9) x00))) as proof of False
% Found ((and_rect2 False) (fun (x8:((cR X) x6)) (x9:((cR X0) x0))=> ((x4 x9) x00))) as proof of False
% Found (((fun (P:Type) (x8:(((cR X) x6)->(((cR x6) X)->P)))=> (((((and_rect ((cR X) x6)) ((cR x6) X)) P) x8) x7)) False) (fun (x8:((cR X) x6)) (x9:((cR X0) x0))=> ((x4 x9) x00))) as proof of False
% Found (fun (x7:((and ((cR X) x6)) ((cR x6) X)))=> (((fun (P:Type) (x8:(((cR X) x6)->(((cR x6) X)->P)))=> (((((and_rect ((cR X) x6)) ((cR x6) X)) P) x8) x7)) False) (fun (x8:((cR X) x6)) (x9:((cR X0) x0))=> ((x4 x9) x00)))) as proof of False
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found x50:=(x5 x20):((cR X0) x0)
% Found (x5 x20) as proof of ((cR X0) x0)
% Found (x5 x20) as proof of ((cR X0) x0)
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x50:=(x5 x40):((cR X0) x0)
% Found (x5 x40) as proof of ((cR X0) x0)
% Found (x5 x40) as proof of ((cR X0) x0)
% Found ((x4 (x5 x40)) x00) as proof of False
% Found (fun (x5:((((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)->((cR X0) x0)))=> ((x4 (x5 x40)) x00)) as proof of False
% Found (fun (x5:((((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)->((cR X0) x0)))=> ((x4 (x5 x40)) x00)) as proof of (((((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)->((cR X0) x0))->False)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found (x4 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x4 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found (x2 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found ((x2 x50) x00) as proof of False
% Found ((x2 x50) x00) as proof of False
% Found x50:((cR X0) x0)
% Found x50 as proof of ((cR X0) x0)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found ((x4 x50) x00) as proof of False
% Found ((x4 x50) x00) as proof of False
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found ((x4 x30) x00) as proof of False
% Found ((x4 x30) x00) as proof of False
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found ((x2 x30) x00) as proof of False
% Found ((x2 x30) x00) as proof of False
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found (x4 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x4 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found (x2 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x9:((cR x6) X)
% Instantiate: X:=x0:fofType;X0:=x6:fofType
% Found (fun (x9:((cR x6) X))=> x9) as proof of ((cR X0) x0)
% Found (fun (x8:((cR X) x6)) (x9:((cR x6) X))=> x9) as proof of (((cR x6) X)->((cR X0) x0))
% Found (fun (x8:((cR X) x6)) (x9:((cR x6) X))=> x9) as proof of (((cR X) x6)->(((cR x6) X)->((cR X0) x0)))
% Found (and_rect20 (fun (x8:((cR X) x6)) (x9:((cR x6) X))=> x9)) as proof of ((cR X0) x0)
% Found ((and_rect2 ((cR X0) x0)) (fun (x8:((cR X) x6)) (x9:((cR x6) X))=> x9)) as proof of ((cR X0) x0)
% Found (((fun (P:Type) (x8:(((cR X) x6)->(((cR x6) X)->P)))=> (((((and_rect ((cR X) x6)) ((cR x6) X)) P) x8) x7)) ((cR X0) x0)) (fun (x8:((cR X) x6)) (x9:((cR x6) X))=> x9)) as proof of ((cR X0) x0)
% Found (fun (x7:((and ((cR X) x6)) ((cR x6) X)))=> (((fun (P:Type) (x8:(((cR X) x6)->(((cR x6) X)->P)))=> (((((and_rect ((cR X) x6)) ((cR x6) X)) P) x8) x7)) ((cR X0) x0)) (fun (x8:((cR X) x6)) (x9:((cR x6) X))=> x9))) as proof of ((cR X0) x0)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x20:=(x2 x30):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x20 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x20:=(x2 x30):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x20:=(x2 x30):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Instantiate: X0:=X:fofType
% Found x20 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x40:=(x4 x30):((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found (x4 x30) as proof of ((cR X) x0)
% Found (fun (x4:((((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)->((cR X0) x0)))=> (x4 x30)) as proof of ((cR X) x0)
% Found (fun (x4:((((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)->((cR X0) x0)))=> (x4 x30)) as proof of (((((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)->((cR X0) x0))->((cR X) x0))
% Found x9:((cR x6) X)
% Instantiate: X:=x0:fofType;X0:=x6:fofType
% Found (fun (x9:((cR x6) X))=> x9) as proof of ((cR X0) x0)
% Found (fun (x8:((cR X) x6)) (x9:((cR x6) X))=> x9) as proof of (((cR x6) X)->((cR X0) x0))
% Found (fun (x8:((cR X) x6)) (x9:((cR x6) X))=> x9) as proof of (((cR X) x6)->(((cR x6) X)->((cR X0) x0)))
% Found (and_rect20 (fun (x8:((cR X) x6)) (x9:((cR x6) X))=> x9)) as proof of ((cR X0) x0)
% Found ((and_rect2 ((cR X0) x0)) (fun (x8:((cR X) x6)) (x9:((cR x6) X))=> x9)) as proof of ((cR X0) x0)
% Found (((fun (P:Type) (x8:(((cR X) x6)->(((cR x6) X)->P)))=> (((((and_rect ((cR X) x6)) ((cR x6) X)) P) x8) x7)) ((cR X0) x0)) (fun (x8:((cR X) x6)) (x9:((cR x6) X))=> x9)) as proof of ((cR X0) x0)
% Found (((fun (P:Type) (x8:(((cR X) x6)->(((cR x6) X)->P)))=> (((((and_rect ((cR X) x6)) ((cR x6) X)) P) x8) x7)) ((cR X0) x0)) (fun (x8:((cR X) x6)) (x9:((cR x6) X))=> x9)) as proof of ((cR X0) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x50:=(x5 x40):((cR X0) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found x40:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Instantiate: X:=X0:fofType
% Found x40 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x50:((cR X0) x0)
% Found x50 as proof of ((cR X0) x0)
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found ((x4 x50) x6) as proof of False
% Found ((x4 x50) x6) as proof of False
% Found x40:=(x4 x50):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x50:=(x5 x40):((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Instantiate: X0:=X:fofType
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x40:=(x4 x50):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x000:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x000 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x40:=(x4 x50):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Instantiate: X:=X0:fofType
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x20:=(x2 x30):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Instantiate: X0:=X:fofType
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x40:=(x4 x50):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Instantiate: X:=X0:fofType
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x20:=(x2 x30):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Instantiate: X0:=X:fofType
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x40:=(x4 x50):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x20:=(x2 x30):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x4:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x4 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x60:((cR X0) x0)
% Found x60 as proof of ((cR X0) x0)
% Found ((x5 x60) x4) as proof of False
% Found ((x5 x60) x4) as proof of False
% Found x40:=(x4 x50):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found x20:=(x2 x30):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x20:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x20 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x40:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x40 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x3 x40) as proof of ((cR X0) x0)
% Found (x3 x40) as proof of ((cR X0) x0)
% Found (x3 x40) as proof of ((cR X0) x0)
% Found x50:((cR X0) x0)
% Found (fun (x7:((and ((cR X) x6)) ((cR x6) X)))=> x50) as proof of ((cR X0) x0)
% Found (fun (x7:((and ((cR X) x6)) ((cR x6) X)))=> x50) as proof of (((and ((cR X) x6)) ((cR x6) X))->((cR X0) x0))
% Found x30:((cR X) x0)
% Found (fun (x7:((and ((cR X0) x6)) ((cR x6) X0)))=> x30) as proof of ((cR X) x0)
% Found (fun (x7:((and ((cR X0) x6)) ((cR x6) X0)))=> x30) as proof of (((and ((cR X0) x6)) ((cR x6) X0))->((cR X) x0))
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x5:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x5 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x20:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x20 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found (x4 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x4 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Instantiate: X0:=X:fofType
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x20:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Instantiate: X0:=X:fofType
% Found x20 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x5 x20) as proof of ((cR X0) x0)
% Found (x5 x20) as proof of ((cR X0) x0)
% Found x20:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Instantiate: X0:=X:fofType
% Found x20 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x40:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Instantiate: X:=X0:fofType
% Found x40 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x20:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Instantiate: X0:=X:fofType
% Found x20 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x40:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Instantiate: X:=X0:fofType
% Found x40 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x50:((cR X0) x0)
% Found x50 as proof of ((cR X0) x0)
% Found ((x4 x50) x6) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))=> ((x4 x50) x6)) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))=> ((x4 x50) x6)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x20:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Instantiate: X0:=X:fofType
% Found x20 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x5 x20) as proof of ((cR X0) x0)
% Found (x5 x20) as proof of ((cR X0) x0)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x40:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Instantiate: X:=X0:fofType
% Found x40 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x3 x40) as proof of ((cR X) x0)
% Found (x3 x40) as proof of ((cR X) x0)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found (x4 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x4 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x40:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Instantiate: X:=X0:fofType
% Found x40 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x40:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Instantiate: X:=X0:fofType
% Found x40 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x3 x40) as proof of ((cR X) x0)
% Found (x3 x40) as proof of ((cR X) x0)
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found x20:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Instantiate: X0:=X:fofType
% Found x20 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x20:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Instantiate: X0:=X:fofType
% Found x20 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x40:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Instantiate: X:=X0:fofType
% Found x40 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found ((x4 x30) x00) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x4 x30) x00)) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x4 x30) x00)) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found ((x2 x30) x00) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x2 x30) x00)) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x2 x30) x00)) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found ((x2 x50) x00) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))=> ((x2 x50) x00)) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))=> ((x2 x50) x00)) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x50:((cR X0) x0)
% Found x50 as proof of ((cR X0) x0)
% Found ((x4 x50) x00) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))=> ((x4 x50) x00)) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))=> ((x4 x50) x00)) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found (x4 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x4 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found ((x4 x30) x00) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x4 x30) x00)) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x4 x30) x00)) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found ((x2 x30) x00) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x2 x30) x00)) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x2 x30) x00)) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found ((x2 x50) x00) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))=> ((x2 x50) x00)) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))=> ((x2 x50) x00)) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x50:((cR X0) x0)
% Found x50 as proof of ((cR X0) x0)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found ((x4 x50) x00) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))=> ((x4 x50) x00)) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))=> ((x4 x50) x00)) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x20:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Instantiate: X0:=X:fofType
% Found x20 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x4)
% Found (x3 x20) as proof of ((cR X) x4)
% Found (x3 x20) as proof of ((cR X) x4)
% Found x20:=(x2 x30):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x20 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x20:=(x2 x30):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x40:=(x4 x50):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x40:=(x4 x50):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x20:=(x2 x30):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x20:=(x2 x30):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x20:=(x2 x30):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Instantiate: X0:=X:fofType
% Found x20 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x8:((cR x5) X)
% Instantiate: X:=x0:fofType;X0:=x5:fofType
% Found (fun (x8:((cR x5) X))=> x8) as proof of ((cR X0) x0)
% Found (fun (x7:((cR X) x5)) (x8:((cR x5) X))=> x8) as proof of (((cR x5) X)->((cR X0) x0))
% Found (fun (x7:((cR X) x5)) (x8:((cR x5) X))=> x8) as proof of (((cR X) x5)->(((cR x5) X)->((cR X0) x0)))
% Found (and_rect20 (fun (x7:((cR X) x5)) (x8:((cR x5) X))=> x8)) as proof of ((cR X0) x0)
% Found ((and_rect2 ((cR X0) x0)) (fun (x7:((cR X) x5)) (x8:((cR x5) X))=> x8)) as proof of ((cR X0) x0)
% Found (((fun (P:Type) (x7:(((cR X) x5)->(((cR x5) X)->P)))=> (((((and_rect ((cR X) x5)) ((cR x5) X)) P) x7) x6)) ((cR X0) x0)) (fun (x7:((cR X) x5)) (x8:((cR x5) X))=> x8)) as proof of ((cR X0) x0)
% Found (fun (x6:((and ((cR X) x5)) ((cR x5) X)))=> (((fun (P:Type) (x7:(((cR X) x5)->(((cR x5) X)->P)))=> (((((and_rect ((cR X) x5)) ((cR x5) X)) P) x7) x6)) ((cR X0) x0)) (fun (x7:((cR X) x5)) (x8:((cR x5) X))=> x8))) as proof of ((cR X0) x0)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x40:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Instantiate: X:=X0:fofType
% Found (fun (x5:((not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))->((cR X0) x0)))=> x40) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (fun (x5:((not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))->((cR X0) x0)))=> x40) as proof of (((not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))->((cR X0) x0))->(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))))
% Found x30:=(x3 x20):((cR X) x0)
% Instantiate: X:=x0:fofType
% Found (x3 x20) as proof of ((cR x4) X)
% Found (x3 x20) as proof of ((cR x4) X)
% Found (x3 x20) as proof of ((cR x4) X)
% Found x31:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x31 as proof of ((cR X0) x0)
% Found x31:((cR X) x0)
% Found x31 as proof of ((cR X) x0)
% Found x20:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (fun (x5:((not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))->((cR X0) x0)))=> x20) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (fun (x5:((not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))->((cR X0) x0)))=> x20) as proof of (((not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))->((cR X0) x0))->(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))))
% Found x20:=(x2 x30):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x20 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Instantiate: X0:=X:fofType
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x31:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x31 as proof of ((cR X0) x0)
% Found x31:((cR X) x0)
% Found x31 as proof of ((cR X) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found x50:=(x5 x40):((cR X0) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Instantiate: X0:=X:fofType
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Instantiate: x4:=x0:fofType
% Found (x3 x20) as proof of ((cR X) x4)
% Found (x3 x20) as proof of ((cR X) x4)
% Found x30:=(x3 x20):((cR X) x0)
% Instantiate: X:=x0:fofType;x4:=X:fofType
% Found (x3 x20) as proof of ((cR x4) X)
% Found (x3 x20) as proof of ((cR x4) X)
% Found x30:=(x3 x20):((cR X) x0)
% Instantiate: X:=x0:fofType
% Found (x3 x20) as proof of ((cR x4) X)
% Found (x3 x20) as proof of ((cR x4) X)
% Found ((conj00 (x3 x20)) (x3 x20)) as proof of ((and ((cR X) x4)) ((cR x4) X))
% Found (((conj0 ((cR x4) X)) (x3 x20)) (x3 x20)) as proof of ((and ((cR X) x4)) ((cR x4) X))
% Found ((((conj ((cR X) x4)) ((cR x4) X)) (x3 x20)) (x3 x20)) as proof of ((and ((cR X) x4)) ((cR x4) X))
% Found ((((conj ((cR X) x4)) ((cR x4) X)) (x3 x20)) (x3 x20)) as proof of ((and ((cR X) x4)) ((cR x4) X))
% Found (ex_intro000 ((((conj ((cR X) x4)) ((cR x4) X)) (x3 x20)) (x3 x20))) as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found ((ex_intro00 x0) ((((conj ((cR X) x0)) ((cR x0) X)) (x3 x20)) (x3 x20))) as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found (((ex_intro0 (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))) x0) ((((conj ((cR X) x0)) ((cR x0) X)) (x3 x20)) (x3 x20))) as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found ((((ex_intro fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))) x0) ((((conj ((cR X) x0)) ((cR x0) X)) (x3 x20)) (x3 x20))) as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found ((((ex_intro fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))) x0) ((((conj ((cR X) x0)) ((cR x0) X)) (x3 x20)) (x3 x20))) as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x30:((cR X) x0)
% Found (fun (x7:((and ((cR X0) x6)) ((cR x6) X0)))=> x30) as proof of ((cR X) x0)
% Found (fun (x7:((and ((cR X0) x6)) ((cR x6) X0)))=> x30) as proof of (((and ((cR X0) x6)) ((cR x6) X0))->((cR X) x0))
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x50:((cR X0) x0)
% Found (fun (x7:((and ((cR X) x6)) ((cR x6) X)))=> x50) as proof of ((cR X0) x0)
% Found (fun (x7:((and ((cR X) x6)) ((cR x6) X)))=> x50) as proof of (((and ((cR X) x6)) ((cR x6) X))->((cR X0) x0))
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x50:=(x5 x40):((cR X0) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x50:=(x5 x40):((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Instantiate: X0:=X:fofType
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found (x40 x6) as proof of False
% Found ((x4 x50) x6) as proof of False
% Found ((x4 x50) x6) as proof of False
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x8:((cR x5) X)
% Instantiate: X:=x0:fofType;X0:=x5:fofType
% Found (fun (x8:((cR x5) X))=> x8) as proof of ((cR X0) x0)
% Found (fun (x7:((cR X) x5)) (x8:((cR x5) X))=> x8) as proof of (((cR x5) X)->((cR X0) x0))
% Found (fun (x7:((cR X) x5)) (x8:((cR x5) X))=> x8) as proof of (((cR X) x5)->(((cR x5) X)->((cR X0) x0)))
% Found (and_rect20 (fun (x7:((cR X) x5)) (x8:((cR x5) X))=> x8)) as proof of ((cR X0) x0)
% Found ((and_rect2 ((cR X0) x0)) (fun (x7:((cR X) x5)) (x8:((cR x5) X))=> x8)) as proof of ((cR X0) x0)
% Found (((fun (P:Type) (x7:(((cR X) x5)->(((cR x5) X)->P)))=> (((((and_rect ((cR X) x5)) ((cR x5) X)) P) x7) x6)) ((cR X0) x0)) (fun (x7:((cR X) x5)) (x8:((cR x5) X))=> x8)) as proof of ((cR X0) x0)
% Found (((fun (P:Type) (x7:(((cR X) x5)->(((cR x5) X)->P)))=> (((((and_rect ((cR X) x5)) ((cR x5) X)) P) x7) x6)) ((cR X0) x0)) (fun (x7:((cR X) x5)) (x8:((cR x5) X))=> x8)) as proof of ((cR X0) x0)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x50:=(x5 x40):((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found x50:=(x5 x40):((cR X0) x0)
% Found (x5 x40) as proof of ((cR X0) x0)
% Found (x5 x40) as proof of ((cR X0) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x31:((cR X) x0)
% Found x31 as proof of ((cR X) x0)
% Found x31:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x31 as proof of ((cR X0) x0)
% Found x50:=(x5 x40):((cR X0) x0)
% Found (x5 x40) as proof of ((cR X0) x0)
% Found (x5 x40) as proof of ((cR X0) x0)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found (x20 x00) as proof of False
% Found ((x2 x30) x00) as proof of False
% Found ((x2 x30) x00) as proof of False
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found (x40 x30) as proof of False
% Found ((fun (x6:((cR X0) x0))=> ((x4 x6) x00)) x30) as proof of False
% Found ((fun (x6:((cR X0) x0))=> ((x4 x6) x00)) x30) as proof of False
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found (x40 x00) as proof of False
% Found ((x4 x50) x00) as proof of False
% Found ((x4 x50) x00) as proof of False
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found (x20 x50) as proof of False
% Found ((fun (x6:((cR X) x0))=> ((x2 x6) x00)) x50) as proof of False
% Found ((fun (x6:((cR X) x0))=> ((x2 x6) x00)) x50) as proof of False
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x50:((cR X0) x0)
% Found x50 as proof of ((cR X0) x0)
% Found ((x4 x50) x6) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))=> ((x4 x50) x6)) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))=> ((x4 x50) x6)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x4:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x4 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x20:=(x2 x30):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Instantiate: X0:=X:fofType
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x20:=(x2 x30):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x20:=(x2 x30):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Instantiate: X0:=X:fofType
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x20:=(x2 x30):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x40:=(fun (x9:((cR X0) x0))=> ((x4 x9) x000)):(((cR X0) x0)->False)
% Instantiate: X:=x0:fofType;X0:=x6:fofType
% Found (fun (x9:((cR X0) x0))=> ((x4 x9) x000)) as proof of (((cR x6) X)->False)
% Found (fun (x8:((cR X) x6)) (x9:((cR X0) x0))=> ((x4 x9) x000)) as proof of (((cR x6) X)->False)
% Found (fun (x8:((cR X) x6)) (x9:((cR X0) x0))=> ((x4 x9) x000)) as proof of (((cR X) x6)->(((cR x6) X)->False))
% Found (and_rect20 (fun (x8:((cR X) x6)) (x9:((cR X0) x0))=> ((x4 x9) x000))) as proof of False
% Found ((and_rect2 False) (fun (x8:((cR X) x6)) (x9:((cR X0) x0))=> ((x4 x9) x000))) as proof of False
% Found (((fun (P:Type) (x8:(((cR X) x6)->(((cR x6) X)->P)))=> (((((and_rect ((cR X) x6)) ((cR x6) X)) P) x8) x7)) False) (fun (x8:((cR X) x6)) (x9:((cR X0) x0))=> ((x4 x9) x000))) as proof of False
% Found (fun (x7:((and ((cR X) x6)) ((cR x6) X)))=> (((fun (P:Type) (x8:(((cR X) x6)->(((cR x6) X)->P)))=> (((((and_rect ((cR X) x6)) ((cR x6) X)) P) x8) x7)) False) (fun (x8:((cR X) x6)) (x9:((cR X0) x0))=> ((x4 x9) x000)))) as proof of False
% Found x20:=(fun (x9:((cR X) x0))=> ((x2 x9) x000)):(((cR X) x0)->False)
% Instantiate: X:=x6:fofType;X0:=x0:fofType
% Found (fun (x9:((cR X) x0))=> ((x2 x9) x000)) as proof of (((cR x6) X0)->False)
% Found (fun (x8:((cR X0) x6)) (x9:((cR X) x0))=> ((x2 x9) x000)) as proof of (((cR x6) X0)->False)
% Found (fun (x8:((cR X0) x6)) (x9:((cR X) x0))=> ((x2 x9) x000)) as proof of (((cR X0) x6)->(((cR x6) X0)->False))
% Found (and_rect20 (fun (x8:((cR X0) x6)) (x9:((cR X) x0))=> ((x2 x9) x000))) as proof of False
% Found ((and_rect2 False) (fun (x8:((cR X0) x6)) (x9:((cR X) x0))=> ((x2 x9) x000))) as proof of False
% Found (((fun (P:Type) (x8:(((cR X0) x6)->(((cR x6) X0)->P)))=> (((((and_rect ((cR X0) x6)) ((cR x6) X0)) P) x8) x7)) False) (fun (x8:((cR X0) x6)) (x9:((cR X) x0))=> ((x2 x9) x000))) as proof of False
% Found (fun (x7:((and ((cR X0) x6)) ((cR x6) X0)))=> (((fun (P:Type) (x8:(((cR X0) x6)->(((cR x6) X0)->P)))=> (((((and_rect ((cR X0) x6)) ((cR x6) X0)) P) x8) x7)) False) (fun (x8:((cR X0) x6)) (x9:((cR X) x0))=> ((x2 x9) x000)))) as proof of False
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x20:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x20 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x20:=(x2 x32):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x32) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x32) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x40:=(fun (x9:((cR X0) x0))=> ((x4 x9) x000)):(((cR X0) x0)->False)
% Instantiate: X:=x0:fofType;X0:=x6:fofType
% Found (fun (x9:((cR X0) x0))=> ((x4 x9) x000)) as proof of (((cR x6) X)->False)
% Found (fun (x8:((cR X) x6)) (x9:((cR X0) x0))=> ((x4 x9) x000)) as proof of (((cR x6) X)->False)
% Found (fun (x8:((cR X) x6)) (x9:((cR X0) x0))=> ((x4 x9) x000)) as proof of (((cR X) x6)->(((cR x6) X)->False))
% Found (and_rect20 (fun (x8:((cR X) x6)) (x9:((cR X0) x0))=> ((x4 x9) x000))) as proof of False
% Found ((and_rect2 False) (fun (x8:((cR X) x6)) (x9:((cR X0) x0))=> ((x4 x9) x000))) as proof of False
% Found (((fun (P:Type) (x8:(((cR X) x6)->(((cR x6) X)->P)))=> (((((and_rect ((cR X) x6)) ((cR x6) X)) P) x8) x7)) False) (fun (x8:((cR X) x6)) (x9:((cR X0) x0))=> ((x4 x9) x000))) as proof of False
% Found (fun (x000:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> (((fun (P:Type) (x8:(((cR X) x6)->(((cR x6) X)->P)))=> (((((and_rect ((cR X) x6)) ((cR x6) X)) P) x8) x7)) False) (fun (x8:((cR X) x6)) (x9:((cR X0) x0))=> ((x4 x9) x000)))) as proof of False
% Found (fun (x000:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> (((fun (P:Type) (x8:(((cR X) x6)->(((cR x6) X)->P)))=> (((((and_rect ((cR X) x6)) ((cR x6) X)) P) x8) x7)) False) (fun (x8:((cR X) x6)) (x9:((cR X0) x0))=> ((x4 x9) x000)))) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x5 (fun (x000:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> (((fun (P:Type) (x8:(((cR X) x6)->(((cR x6) X)->P)))=> (((((and_rect ((cR X) x6)) ((cR x6) X)) P) x8) x7)) False) (fun (x8:((cR X) x6)) (x9:((cR X0) x0))=> ((x4 x9) x000))))) as proof of ((cR X0) x0)
% Found (fun (x7:((and ((cR X) x6)) ((cR x6) X)))=> (x5 (fun (x000:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> (((fun (P:Type) (x8:(((cR X) x6)->(((cR x6) X)->P)))=> (((((and_rect ((cR X) x6)) ((cR x6) X)) P) x8) x7)) False) (fun (x8:((cR X) x6)) (x9:((cR X0) x0))=> ((x4 x9) x000)))))) as proof of ((cR X0) x0)
% Found x20:=(fun (x9:((cR X) x0))=> ((x2 x9) x000)):(((cR X) x0)->False)
% Instantiate: X:=x6:fofType;X0:=x0:fofType
% Found (fun (x9:((cR X) x0))=> ((x2 x9) x000)) as proof of (((cR x6) X0)->False)
% Found (fun (x8:((cR X0) x6)) (x9:((cR X) x0))=> ((x2 x9) x000)) as proof of (((cR x6) X0)->False)
% Found (fun (x8:((cR X0) x6)) (x9:((cR X) x0))=> ((x2 x9) x000)) as proof of (((cR X0) x6)->(((cR x6) X0)->False))
% Found (and_rect20 (fun (x8:((cR X0) x6)) (x9:((cR X) x0))=> ((x2 x9) x000))) as proof of False
% Found ((and_rect2 False) (fun (x8:((cR X0) x6)) (x9:((cR X) x0))=> ((x2 x9) x000))) as proof of False
% Found (((fun (P:Type) (x8:(((cR X0) x6)->(((cR x6) X0)->P)))=> (((((and_rect ((cR X0) x6)) ((cR x6) X0)) P) x8) x7)) False) (fun (x8:((cR X0) x6)) (x9:((cR X) x0))=> ((x2 x9) x000))) as proof of False
% Found (fun (x000:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))=> (((fun (P:Type) (x8:(((cR X0) x6)->(((cR x6) X0)->P)))=> (((((and_rect ((cR X0) x6)) ((cR x6) X0)) P) x8) x7)) False) (fun (x8:((cR X0) x6)) (x9:((cR X) x0))=> ((x2 x9) x000)))) as proof of False
% Found (fun (x000:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))=> (((fun (P:Type) (x8:(((cR X0) x6)->(((cR x6) X0)->P)))=> (((((and_rect ((cR X0) x6)) ((cR x6) X0)) P) x8) x7)) False) (fun (x8:((cR X0) x6)) (x9:((cR X) x0))=> ((x2 x9) x000)))) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x3 (fun (x000:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))=> (((fun (P:Type) (x8:(((cR X0) x6)->(((cR x6) X0)->P)))=> (((((and_rect ((cR X0) x6)) ((cR x6) X0)) P) x8) x7)) False) (fun (x8:((cR X0) x6)) (x9:((cR X) x0))=> ((x2 x9) x000))))) as proof of ((cR X) x0)
% Found (fun (x7:((and ((cR X0) x6)) ((cR x6) X0)))=> (x3 (fun (x000:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))=> (((fun (P:Type) (x8:(((cR X0) x6)->(((cR x6) X0)->P)))=> (((((and_rect ((cR X0) x6)) ((cR x6) X0)) P) x8) x7)) False) (fun (x8:((cR X0) x6)) (x9:((cR X) x0))=> ((x2 x9) x000)))))) as proof of ((cR X) x0)
% Found x50:((cR X0) x0)
% Found (fun (x7:((and ((cR X) x6)) ((cR x6) X)))=> x50) as proof of ((cR X0) x0)
% Found (fun (x6:fofType) (x7:((and ((cR X) x6)) ((cR x6) X)))=> x50) as proof of (((and ((cR X) x6)) ((cR x6) X))->((cR X0) x0))
% Found (fun (x6:fofType) (x7:((and ((cR X) x6)) ((cR x6) X)))=> x50) as proof of (forall (x:fofType), (((and ((cR X) x)) ((cR x) X))->((cR X0) x0)))
% Found x30:((cR X) x0)
% Found (fun (x7:((and ((cR X0) x6)) ((cR x6) X0)))=> x30) as proof of ((cR X) x0)
% Found (fun (x6:fofType) (x7:((and ((cR X0) x6)) ((cR x6) X0)))=> x30) as proof of (((and ((cR X0) x6)) ((cR x6) X0))->((cR X) x0))
% Found (fun (x6:fofType) (x7:((and ((cR X0) x6)) ((cR x6) X0)))=> x30) as proof of (forall (x:fofType), (((and ((cR X0) x)) ((cR x) X0))->((cR X) x0)))
% Found x20:=(x2 x31):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x20 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x000:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x000 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x9:((cR x6) X)
% Instantiate: X:=x0:fofType;X0:=x6:fofType
% Found x9 as proof of ((cR X0) x0)
% Found x000:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x000 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x20:=(x2 x32):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x20 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x20:=(x2 x30):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found x50:((cR X0) x0)
% Found x50 as proof of ((cR X0) x0)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found x20:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Instantiate: X0:=X:fofType
% Found x20 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x5 x20) as proof of ((cR X0) x0)
% Found (x5 x20) as proof of ((cR X0) x0)
% Found x20:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Instantiate: X0:=X:fofType
% Found x20 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x5 x20) as proof of ((cR X0) x0)
% Found (x5 x20) as proof of ((cR X0) x0)
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found (x40 x6) as proof of False
% Found ((x4 x50) x6) as proof of False
% Found ((x4 x50) x6) as proof of False
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found (x4 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x4 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found (x4 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x4 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x50:((cR X0) x0)
% Found x50 as proof of ((cR X0) x0)
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found ((x4 x30) x00) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x4 x30) x00)) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x4 x30) x00)) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found ((x2 x30) x00) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x2 x30) x00)) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x2 x30) x00)) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x50:((cR X0) x0)
% Found x50 as proof of ((cR X0) x0)
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x31:((cR X) x0)
% Found x31 as proof of ((cR X) x0)
% Found x31:((cR X) x0)
% Found x31 as proof of ((cR X) x0)
% Found x31:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x31 as proof of ((cR X0) x0)
% Found x50:=(x5 x40):((cR X0) x0)
% Found (x5 x40) as proof of ((cR X0) x0)
% Found (x5 x40) as proof of ((cR X0) x0)
% Found x30:=(x3 x40):((cR X) x0)
% Found (x3 x40) as proof of ((cR X) x0)
% Found (x3 x40) as proof of ((cR X) x0)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x30:=(x3 x20):((cR X) x0)
% Instantiate: X0:=X:fofType
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x50:=(x5 x40):((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found x20:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x20 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x3 x20) as proof of ((cR X) x4)
% Found (x3 x20) as proof of ((cR X) x4)
% Found (x3 x20) as proof of ((cR X) x4)
% Found x4:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x4 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found (x50 x4) as proof of False
% Found ((x5 x60) x4) as proof of False
% Found ((x5 x60) x4) as proof of False
% Found x40:=(x4 x30):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x4 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x4 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x40:=(x4 x30):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x4 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x4 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x30:=(x3 x20):((cR X) x0)
% Instantiate: X0:=X:fofType
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Instantiate: X0:=X:fofType
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x40:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Instantiate: X:=X0:fofType
% Found x40 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found x20:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (fun (x5:((not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))->((cR X0) x0)))=> x20) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (fun (x4:(((cR X0) x0)->(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))))) (x5:((not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))->((cR X0) x0)))=> x20) as proof of (((not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))->((cR X0) x0))->(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))))
% Found (fun (x4:(((cR X0) x0)->(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))))) (x5:((not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))->((cR X0) x0)))=> x20) as proof of ((((cR X0) x0)->(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))))->(((not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))->((cR X0) x0))->(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))))
% Found x30:=(x3 x20):((cR X) x0)
% Instantiate: X0:=X:fofType
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x20:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Instantiate: X0:=X:fofType
% Found x20 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found x40:=(x4 x30):((cR X0) x0)
% Found (x4 x30) as proof of ((cR X) x0)
% Found (x4 x30) as proof of ((cR X) x0)
% Found (x4 x30) as proof of ((cR X) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x40:=(x4 x30):((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found (x4 x30) as proof of ((cR X) x0)
% Found (x4 x30) as proof of ((cR X) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Instantiate: X0:=X:fofType
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found x20:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Instantiate: X0:=X:fofType
% Found x20 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Instantiate: X0:=X:fofType
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x40:=(x4 x50):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Instantiate: X:=X0:fofType
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found (x40 x00) as proof of False
% Found ((x4 x50) x00) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))=> ((x4 x50) x00)) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))=> ((x4 x50) x00)) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found (x20 x50) as proof of False
% Found ((fun (x6:((cR X) x0))=> ((x2 x6) x00)) x50) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))=> ((fun (x6:((cR X) x0))=> ((x2 x6) x00)) x50)) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))=> ((fun (x6:((cR X) x0))=> ((x2 x6) x00)) x50)) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found (x40 x30) as proof of False
% Found ((fun (x6:((cR X0) x0))=> ((x4 x6) x00)) x30) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((fun (x6:((cR X0) x0))=> ((x4 x6) x00)) x30)) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((fun (x6:((cR X0) x0))=> ((x4 x6) x00)) x30)) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found (x20 x00) as proof of False
% Found ((x2 x30) x00) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x2 x30) x00)) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x2 x30) x00)) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x30:=(x3 x21):((cR X) x0)
% Instantiate: X0:=X:fofType
% Found (x3 x21) as proof of ((cR X0) x0)
% Found (x3 x21) as proof of ((cR X0) x0)
% Found x50:=(x5 x40):((cR X0) x0)
% Found (x5 x40) as proof of ((cR X0) x0)
% Found (x5 x40) as proof of ((cR X0) x0)
% Found x50:=(x5 x41):((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found (x5 x41) as proof of ((cR X) x0)
% Found (x5 x41) as proof of ((cR X) x0)
% Found x41:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Instantiate: X:=X0:fofType
% Found x41 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x3 x41) as proof of ((cR X) x0)
% Found (x3 x41) as proof of ((cR X) x0)
% Found x50:=(x5 x41):((cR X0) x0)
% Found (x5 x41) as proof of ((cR X) x0)
% Found (x5 x41) as proof of ((cR X) x0)
% Found (x5 x41) as proof of ((cR X) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found x20:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Instantiate: X0:=X:fofType
% Found x20 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x5 x20) as proof of ((cR X0) x0)
% Found (x5 x20) as proof of ((cR X0) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found (x40 x30) as proof of False
% Found ((fun (x6:((cR X0) x0))=> ((x4 x6) x00)) x30) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((fun (x6:((cR X0) x0))=> ((x4 x6) x00)) x30)) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((fun (x6:((cR X0) x0))=> ((x4 x6) x00)) x30)) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found (x20 x00) as proof of False
% Found ((x2 x30) x00) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x2 x30) x00)) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x2 x30) x00)) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x20:=(x2 x30):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Instantiate: X0:=X:fofType
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found (x20 x50) as proof of False
% Found ((fun (x6:((cR X) x0))=> ((x2 x6) x00)) x50) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))=> ((fun (x6:((cR X) x0))=> ((x2 x6) x00)) x50)) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))=> ((fun (x6:((cR X) x0))=> ((x2 x6) x00)) x50)) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found (x40 x00) as proof of False
% Found ((x4 x50) x00) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))=> ((x4 x50) x00)) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))=> ((x4 x50) x00)) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x50:((cR X0) x0)
% Found (fun (x7:((and ((cR X) x6)) ((cR x6) X)))=> x50) as proof of ((cR X0) x0)
% Found (fun (x6:fofType) (x7:((and ((cR X) x6)) ((cR x6) X)))=> x50) as proof of (((and ((cR X) x6)) ((cR x6) X))->((cR X0) x0))
% Found (fun (x6:fofType) (x7:((and ((cR X) x6)) ((cR x6) X)))=> x50) as proof of (forall (x:fofType), (((and ((cR X) x)) ((cR x) X))->((cR X0) x0)))
% Found x30:((cR X) x0)
% Found (fun (x7:((and ((cR X0) x6)) ((cR x6) X0)))=> x30) as proof of ((cR X) x0)
% Found (fun (x6:fofType) (x7:((and ((cR X0) x6)) ((cR x6) X0)))=> x30) as proof of (((and ((cR X0) x6)) ((cR x6) X0))->((cR X) x0))
% Found (fun (x6:fofType) (x7:((and ((cR X0) x6)) ((cR x6) X0)))=> x30) as proof of (forall (x:fofType), (((and ((cR X0) x)) ((cR x) X0))->((cR X) x0)))
% Found x20:=(x2 x30):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x20:=(x2 x30):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x20:=(x2 x30):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Instantiate: X0:=X:fofType
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found (x40 x6) as proof of False
% Found ((x4 x50) x6) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))=> ((x4 x50) x6)) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))=> ((x4 x50) x6)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x30:=(x3 x20):((cR X) x0)
% Instantiate: X0:=X:fofType
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Instantiate: X0:=X:fofType
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x50:=(x5 x40):((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Instantiate: X0:=X:fofType
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x30:=(x3 x20):((cR X) x0)
% Instantiate: X0:=X:fofType
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x50:=(x5 x40):((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Instantiate: X0:=X:fofType
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x40:=(x4 x50):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Instantiate: X:=X0:fofType
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x40:=(x4 x50):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Instantiate: X:=X0:fofType
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Instantiate: X0:=X:fofType
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x40:=(x4 x50):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Instantiate: X:=X0:fofType
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Instantiate: X0:=X:fofType
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x50:=(x5 x40):((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found x50:=(x5 x40):((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found x40:=(x4 x50):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Instantiate: X:=X0:fofType
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Instantiate: X0:=X:fofType
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x20:=(x2 x30):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found x40:=(x4 x50):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found x50:=(x5 x40):((cR X0) x0)
% Found (x5 x40) as proof of ((cR X0) x0)
% Found (x5 x40) as proof of ((cR X0) x0)
% Found x40:=(x4 x50):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x50:=(x5 x40):((cR X0) x0)
% Found (x5 x40) as proof of ((cR X0) x0)
% Found (x5 x40) as proof of ((cR X0) x0)
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR x4) X)
% Found (x3 x20) as proof of ((cR x4) X)
% Found (x3 x20) as proof of ((cR x4) X)
% Found (x3 x20) as proof of ((cR x4) X)
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR x4) X)
% Found (x3 x20) as proof of ((cR x4) X)
% Found (x3 x20) as proof of ((cR x4) X)
% Found (x3 x20) as proof of ((cR x4) X)
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Instantiate: X0:=X:fofType
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x50:=(x5 x40):((cR X0) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x50:((cR X0) x0)
% Found x50 as proof of ((cR X0) x0)
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x50:=(x5 x40):((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Instantiate: X0:=X:fofType
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x5:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x5 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x20:=(x2 x32):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x32) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x32) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x5:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x5 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x8:((cR x5) X)
% Instantiate: X:=x0:fofType;X0:=x5:fofType
% Found x8 as proof of ((cR X0) x0)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x20:=(x2 x32):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x32) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x32) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x9:((cR x6) X)
% Instantiate: X:=x0:fofType;X0:=x6:fofType
% Found (fun (x9:((cR x6) X))=> x9) as proof of ((cR X0) x0)
% Found (fun (x8:((cR X) x6)) (x9:((cR x6) X))=> x9) as proof of (((cR x6) X)->((cR X0) x0))
% Found (fun (x8:((cR X) x6)) (x9:((cR x6) X))=> x9) as proof of (((cR X) x6)->(((cR x6) X)->((cR X0) x0)))
% Found (and_rect20 (fun (x8:((cR X) x6)) (x9:((cR x6) X))=> x9)) as proof of ((cR X0) x0)
% Found ((and_rect2 ((cR X0) x0)) (fun (x8:((cR X) x6)) (x9:((cR x6) X))=> x9)) as proof of ((cR X0) x0)
% Found (((fun (P:Type) (x8:(((cR X) x6)->(((cR x6) X)->P)))=> (((((and_rect ((cR X) x6)) ((cR x6) X)) P) x8) x7)) ((cR X0) x0)) (fun (x8:((cR X) x6)) (x9:((cR x6) X))=> x9)) as proof of ((cR X0) x0)
% Found (fun (x7:((and ((cR X) x6)) ((cR x6) X)))=> (((fun (P:Type) (x8:(((cR X) x6)->(((cR x6) X)->P)))=> (((((and_rect ((cR X) x6)) ((cR x6) X)) P) x8) x7)) ((cR X0) x0)) (fun (x8:((cR X) x6)) (x9:((cR x6) X))=> x9))) as proof of ((cR X0) x0)
% Found x9:((cR x6) X0)
% Instantiate: X:=x6:fofType;X0:=x0:fofType
% Found (fun (x9:((cR x6) X0))=> x9) as proof of ((cR X) x0)
% Found (fun (x8:((cR X0) x6)) (x9:((cR x6) X0))=> x9) as proof of (((cR x6) X0)->((cR X) x0))
% Found (fun (x8:((cR X0) x6)) (x9:((cR x6) X0))=> x9) as proof of (((cR X0) x6)->(((cR x6) X0)->((cR X) x0)))
% Found (and_rect20 (fun (x8:((cR X0) x6)) (x9:((cR x6) X0))=> x9)) as proof of ((cR X) x0)
% Found ((and_rect2 ((cR X) x0)) (fun (x8:((cR X0) x6)) (x9:((cR x6) X0))=> x9)) as proof of ((cR X) x0)
% Found (((fun (P:Type) (x8:(((cR X0) x6)->(((cR x6) X0)->P)))=> (((((and_rect ((cR X0) x6)) ((cR x6) X0)) P) x8) x7)) ((cR X) x0)) (fun (x8:((cR X0) x6)) (x9:((cR x6) X0))=> x9)) as proof of ((cR X) x0)
% Found (fun (x7:((and ((cR X0) x6)) ((cR x6) X0)))=> (((fun (P:Type) (x8:(((cR X0) x6)->(((cR x6) X0)->P)))=> (((((and_rect ((cR X0) x6)) ((cR x6) X0)) P) x8) x7)) ((cR X) x0)) (fun (x8:((cR X0) x6)) (x9:((cR x6) X0))=> x9))) as proof of ((cR X) x0)
% Found x4:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x4 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found ((x4 x30) x00) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x4 x30) x00)) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x4 x30) x00)) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found ((x2 x30) x00) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x2 x30) x00)) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x2 x30) x00)) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x4:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x4 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found (x40 x6) as proof of False
% Found ((x4 x50) x6) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))=> ((x4 x50) x6)) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))=> ((x4 x50) x6)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x40:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x40 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found x20:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x20 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x50:((cR X0) x0)
% Found x50 as proof of ((cR X0) x0)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x9:((cR x6) X0)
% Instantiate: X:=x6:fofType;X0:=x0:fofType
% Found (fun (x9:((cR x6) X0))=> x9) as proof of ((cR X) x0)
% Found (fun (x8:((cR X0) x6)) (x9:((cR x6) X0))=> x9) as proof of (((cR x6) X0)->((cR X) x0))
% Found (fun (x8:((cR X0) x6)) (x9:((cR x6) X0))=> x9) as proof of (((cR X0) x6)->(((cR x6) X0)->((cR X) x0)))
% Found (and_rect20 (fun (x8:((cR X0) x6)) (x9:((cR x6) X0))=> x9)) as proof of ((cR X) x0)
% Found ((and_rect2 ((cR X) x0)) (fun (x8:((cR X0) x6)) (x9:((cR x6) X0))=> x9)) as proof of ((cR X) x0)
% Found (((fun (P:Type) (x8:(((cR X0) x6)->(((cR x6) X0)->P)))=> (((((and_rect ((cR X0) x6)) ((cR x6) X0)) P) x8) x7)) ((cR X) x0)) (fun (x8:((cR X0) x6)) (x9:((cR x6) X0))=> x9)) as proof of ((cR X) x0)
% Found (((fun (P:Type) (x8:(((cR X0) x6)->(((cR x6) X0)->P)))=> (((((and_rect ((cR X0) x6)) ((cR x6) X0)) P) x8) x7)) ((cR X) x0)) (fun (x8:((cR X0) x6)) (x9:((cR x6) X0))=> x9)) as proof of ((cR X) x0)
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x9:((cR x6) X)
% Instantiate: X:=x0:fofType;X0:=x6:fofType
% Found (fun (x9:((cR x6) X))=> x9) as proof of ((cR X0) x0)
% Found (fun (x8:((cR X) x6)) (x9:((cR x6) X))=> x9) as proof of (((cR x6) X)->((cR X0) x0))
% Found (fun (x8:((cR X) x6)) (x9:((cR x6) X))=> x9) as proof of (((cR X) x6)->(((cR x6) X)->((cR X0) x0)))
% Found (and_rect20 (fun (x8:((cR X) x6)) (x9:((cR x6) X))=> x9)) as proof of ((cR X0) x0)
% Found ((and_rect2 ((cR X0) x0)) (fun (x8:((cR X) x6)) (x9:((cR x6) X))=> x9)) as proof of ((cR X0) x0)
% Found (((fun (P:Type) (x8:(((cR X) x6)->(((cR x6) X)->P)))=> (((((and_rect ((cR X) x6)) ((cR x6) X)) P) x8) x7)) ((cR X0) x0)) (fun (x8:((cR X) x6)) (x9:((cR x6) X))=> x9)) as proof of ((cR X0) x0)
% Found (((fun (P:Type) (x8:(((cR X) x6)->(((cR x6) X)->P)))=> (((((and_rect ((cR X) x6)) ((cR x6) X)) P) x8) x7)) ((cR X0) x0)) (fun (x8:((cR X) x6)) (x9:((cR x6) X))=> x9)) as proof of ((cR X0) x0)
% Found x20:=(x2 x30):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x20:=(x2 x30):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x50:((cR X0) x0)
% Found x50 as proof of ((cR X0) x0)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x50:((cR X0) x0)
% Found x50 as proof of ((cR X0) x0)
% Found ((x4 x50) x00) as proof of False
% Found ((x4 x50) x00) as proof of False
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found ((x2 x30) x00) as proof of False
% Found ((x2 x30) x00) as proof of False
% Found x000:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x000 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x000:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x000 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x000:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x000 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x000:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x000 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found ((x4 x30) x6) as proof of False
% Found ((x4 x30) x6) as proof of False
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found ((x2 x30) x6) as proof of False
% Found ((x2 x30) x6) as proof of False
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found (x4 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x4 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found (x2 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found ((x2 x50) x6) as proof of False
% Found ((x2 x50) x6) as proof of False
% Found x50:((cR X0) x0)
% Found x50 as proof of ((cR X0) x0)
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found ((x4 x50) x6) as proof of False
% Found ((x4 x50) x6) as proof of False
% Found x60:=(x6 x50):((cR X0) x0)
% Found (x6 x50) as proof of ((cR X0) x0)
% Found (x6 x50) as proof of ((cR X0) x0)
% Found ((x5 (x6 x50)) x4) as proof of False
% Found (fun (x6:((not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))->((cR X0) x0)))=> ((x5 (x6 x50)) x4)) as proof of False
% Found (fun (x6:((not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))->((cR X0) x0)))=> ((x5 (x6 x50)) x4)) as proof of (((not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))->((cR X0) x0))->False)
% Found x40:=(x4 x30):((cR X0) x0)
% Found (x4 x30) as proof of ((cR X) x0)
% Found (x4 x30) as proof of ((cR X) x0)
% Found (fun (x4:((((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)->((cR X0) x0)))=> (x4 x30)) as proof of ((cR X) x0)
% Found (fun (x4:((((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)->((cR X0) x0)))=> (x4 x30)) as proof of (((((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)->((cR X0) x0))->((cR X) x0))
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found (x2 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found (x4 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x4 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x40:=(x4 x30):((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found (x4 x30) as proof of ((cR X) x0)
% Found (fun (x4:((not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))->((cR X0) x0)))=> (x4 x30)) as proof of ((cR X) x0)
% Found (fun (x4:((not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))->((cR X0) x0)))=> (x4 x30)) as proof of (((not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))->((cR X0) x0))->((cR X) x0))
% Found x40:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Instantiate: X:=X0:fofType
% Found x40 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found (x20 x00) as proof of False
% Found ((x2 x30) x00) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x2 x30) x00)) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x2 x30) x00)) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found (x40 x30) as proof of False
% Found ((fun (x6:((cR X0) x0))=> ((x4 x6) x00)) x30) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((fun (x6:((cR X0) x0))=> ((x4 x6) x00)) x30)) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((fun (x6:((cR X0) x0))=> ((x4 x6) x00)) x30)) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x9:((cR x6) X)
% Instantiate: X:=x0:fofType;X0:=x6:fofType
% Found (fun (x9:((cR x6) X))=> x9) as proof of ((cR X0) x0)
% Found (fun (x8:((cR X) x6)) (x9:((cR x6) X))=> x9) as proof of (((cR x6) X)->((cR X0) x0))
% Found (fun (x8:((cR X) x6)) (x9:((cR x6) X))=> x9) as proof of (((cR X) x6)->(((cR x6) X)->((cR X0) x0)))
% Found (and_rect20 (fun (x8:((cR X) x6)) (x9:((cR x6) X))=> x9)) as proof of ((cR X0) x0)
% Found ((and_rect2 ((cR X0) x0)) (fun (x8:((cR X) x6)) (x9:((cR x6) X))=> x9)) as proof of ((cR X0) x0)
% Found (((fun (P:Type) (x8:(((cR X) x6)->(((cR x6) X)->P)))=> (((((and_rect ((cR X) x6)) ((cR x6) X)) P) x8) x7)) ((cR X0) x0)) (fun (x8:((cR X) x6)) (x9:((cR x6) X))=> x9)) as proof of ((cR X0) x0)
% Found (fun (x7:((and ((cR X) x6)) ((cR x6) X)))=> (((fun (P:Type) (x8:(((cR X) x6)->(((cR x6) X)->P)))=> (((((and_rect ((cR X) x6)) ((cR x6) X)) P) x8) x7)) ((cR X0) x0)) (fun (x8:((cR X) x6)) (x9:((cR x6) X))=> x9))) as proof of ((cR X0) x0)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found (x4 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x4 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x40:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Instantiate: X:=X0:fofType
% Found x40 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x40:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Instantiate: X:=X0:fofType
% Found x40 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x9:((cR x6) X)
% Instantiate: X:=x0:fofType;X0:=x6:fofType
% Found (fun (x9:((cR x6) X))=> x9) as proof of ((cR X0) x0)
% Found (fun (x8:((cR X) x6)) (x9:((cR x6) X))=> x9) as proof of (((cR x6) X)->((cR X0) x0))
% Found (fun (x8:((cR X) x6)) (x9:((cR x6) X))=> x9) as proof of (((cR X) x6)->(((cR x6) X)->((cR X0) x0)))
% Found (and_rect20 (fun (x8:((cR X) x6)) (x9:((cR x6) X))=> x9)) as proof of ((cR X0) x0)
% Found ((and_rect2 ((cR X0) x0)) (fun (x8:((cR X) x6)) (x9:((cR x6) X))=> x9)) as proof of ((cR X0) x0)
% Found (((fun (P:Type) (x8:(((cR X) x6)->(((cR x6) X)->P)))=> (((((and_rect ((cR X) x6)) ((cR x6) X)) P) x8) x7)) ((cR X0) x0)) (fun (x8:((cR X) x6)) (x9:((cR x6) X))=> x9)) as proof of ((cR X0) x0)
% Found (((fun (P:Type) (x8:(((cR X) x6)->(((cR x6) X)->P)))=> (((((and_rect ((cR X) x6)) ((cR x6) X)) P) x8) x7)) ((cR X0) x0)) (fun (x8:((cR X) x6)) (x9:((cR x6) X))=> x9)) as proof of ((cR X0) x0)
% Found x4:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x4 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x4:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x4 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x50:=(x5 x40):((cR X0) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x40:=(x4 x50):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x20:=(x2 x30):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x40:=(fun (x13:((cR X0) x0))=> ((x4 x13) x6)):(((cR X0) x0)->False)
% Instantiate: X:=x0:fofType;X0:=x8:fofType
% Found (fun (x13:((cR X0) x0))=> ((x4 x13) x6)) as proof of (((cR x8) X)->False)
% Found (fun (x12:((cR X) x8)) (x13:((cR X0) x0))=> ((x4 x13) x6)) as proof of (((cR x8) X)->False)
% Found (fun (x12:((cR X) x8)) (x13:((cR X0) x0))=> ((x4 x13) x6)) as proof of (((cR X) x8)->(((cR x8) X)->False))
% Found (and_rect20 (fun (x12:((cR X) x8)) (x13:((cR X0) x0))=> ((x4 x13) x6))) as proof of False
% Found ((and_rect2 False) (fun (x12:((cR X) x8)) (x13:((cR X0) x0))=> ((x4 x13) x6))) as proof of False
% Found (((fun (P:Type) (x12:(((cR X) x8)->(((cR x8) X)->P)))=> (((((and_rect ((cR X) x8)) ((cR x8) X)) P) x12) x9)) False) (fun (x12:((cR X) x8)) (x13:((cR X0) x0))=> ((x4 x13) x6))) as proof of False
% Found (fun (x9:((and ((cR X) x8)) ((cR x8) X)))=> (((fun (P:Type) (x12:(((cR X) x8)->(((cR x8) X)->P)))=> (((((and_rect ((cR X) x8)) ((cR x8) X)) P) x12) x9)) False) (fun (x12:((cR X) x8)) (x13:((cR X0) x0))=> ((x4 x13) x6)))) as proof of False
% Found x20:=(fun (x13:((cR X) x0))=> ((x2 x13) x6)):(((cR X) x0)->False)
% Instantiate: X:=x8:fofType;X0:=x0:fofType
% Found (fun (x13:((cR X) x0))=> ((x2 x13) x6)) as proof of (((cR x8) X0)->False)
% Found (fun (x12:((cR X0) x8)) (x13:((cR X) x0))=> ((x2 x13) x6)) as proof of (((cR x8) X0)->False)
% Found (fun (x12:((cR X0) x8)) (x13:((cR X) x0))=> ((x2 x13) x6)) as proof of (((cR X0) x8)->(((cR x8) X0)->False))
% Found (and_rect20 (fun (x12:((cR X0) x8)) (x13:((cR X) x0))=> ((x2 x13) x6))) as proof of False
% Found ((and_rect2 False) (fun (x12:((cR X0) x8)) (x13:((cR X) x0))=> ((x2 x13) x6))) as proof of False
% Found (((fun (P:Type) (x12:(((cR X0) x8)->(((cR x8) X0)->P)))=> (((((and_rect ((cR X0) x8)) ((cR x8) X0)) P) x12) x9)) False) (fun (x12:((cR X0) x8)) (x13:((cR X) x0))=> ((x2 x13) x6))) as proof of False
% Found (fun (x9:((and ((cR X0) x8)) ((cR x8) X0)))=> (((fun (P:Type) (x12:(((cR X0) x8)->(((cR x8) X0)->P)))=> (((((and_rect ((cR X0) x8)) ((cR x8) X0)) P) x12) x9)) False) (fun (x12:((cR X0) x8)) (x13:((cR X) x0))=> ((x2 x13) x6)))) as proof of False
% Found x20:=(x2 x30):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x40:=(x4 x50):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x12:((cR x7) X)
% Instantiate: X:=x0:fofType;X0:=x7:fofType
% Found (fun (x12:((cR x7) X))=> x12) as proof of ((cR X0) x0)
% Found (fun (x9:((cR X) x7)) (x12:((cR x7) X))=> x12) as proof of (((cR x7) X)->((cR X0) x0))
% Found (fun (x9:((cR X) x7)) (x12:((cR x7) X))=> x12) as proof of (((cR X) x7)->(((cR x7) X)->((cR X0) x0)))
% Found (and_rect20 (fun (x9:((cR X) x7)) (x12:((cR x7) X))=> x12)) as proof of ((cR X0) x0)
% Found ((and_rect2 ((cR X0) x0)) (fun (x9:((cR X) x7)) (x12:((cR x7) X))=> x12)) as proof of ((cR X0) x0)
% Found (((fun (P:Type) (x9:(((cR X) x7)->(((cR x7) X)->P)))=> (((((and_rect ((cR X) x7)) ((cR x7) X)) P) x9) x8)) ((cR X0) x0)) (fun (x9:((cR X) x7)) (x12:((cR x7) X))=> x12)) as proof of ((cR X0) x0)
% Found (fun (x8:((and ((cR X) x7)) ((cR x7) X)))=> (((fun (P:Type) (x9:(((cR X) x7)->(((cR x7) X)->P)))=> (((((and_rect ((cR X) x7)) ((cR x7) X)) P) x9) x8)) ((cR X0) x0)) (fun (x9:((cR X) x7)) (x12:((cR x7) X))=> x12))) as proof of ((cR X0) x0)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Instantiate: X0:=X:fofType
% Found x20 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x20 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x4:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x4 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x12:((cR x7) X)
% Instantiate: X:=x0:fofType;X0:=x7:fofType
% Found (fun (x12:((cR x7) X))=> x12) as proof of ((cR X0) x0)
% Found (fun (x9:((cR X) x7)) (x12:((cR x7) X))=> x12) as proof of (((cR x7) X)->((cR X0) x0))
% Found (fun (x9:((cR X) x7)) (x12:((cR x7) X))=> x12) as proof of (((cR X) x7)->(((cR x7) X)->((cR X0) x0)))
% Found (and_rect20 (fun (x9:((cR X) x7)) (x12:((cR x7) X))=> x12)) as proof of ((cR X0) x0)
% Found ((and_rect2 ((cR X0) x0)) (fun (x9:((cR X) x7)) (x12:((cR x7) X))=> x12)) as proof of ((cR X0) x0)
% Found (((fun (P:Type) (x9:(((cR X) x7)->(((cR x7) X)->P)))=> (((((and_rect ((cR X) x7)) ((cR x7) X)) P) x9) x8)) ((cR X0) x0)) (fun (x9:((cR X) x7)) (x12:((cR x7) X))=> x12)) as proof of ((cR X0) x0)
% Found (((fun (P:Type) (x9:(((cR X) x7)->(((cR x7) X)->P)))=> (((((and_rect ((cR X) x7)) ((cR x7) X)) P) x9) x8)) ((cR X0) x0)) (fun (x9:((cR X) x7)) (x12:((cR x7) X))=> x12)) as proof of ((cR X0) x0)
% Found x20:=(x2 x30):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Instantiate: X0:=X:fofType
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x20:=(x2 x30):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x20:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x20 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x20:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Instantiate: X0:=X:fofType
% Found x20 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x5 x20) as proof of ((cR X0) x0)
% Found (x5 x20) as proof of ((cR X0) x0)
% Found x40:=(x4 x50):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Instantiate: X:=X0:fofType
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x40:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x40 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found x20:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x20 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x20:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Instantiate: X0:=X:fofType
% Found x20 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x5 x20) as proof of ((cR X0) x0)
% Found (x5 x20) as proof of ((cR X0) x0)
% Found x40:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x40 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found x40:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Instantiate: X:=X0:fofType
% Found x40 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x3 x40) as proof of ((cR X) x0)
% Found (x3 x40) as proof of ((cR X) x0)
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x20:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Instantiate: X0:=X:fofType
% Found x20 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x20:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Instantiate: X0:=X:fofType
% Found x20 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x000:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x000 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x40:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Instantiate: X:=X0:fofType
% Found x40 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x40:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Instantiate: X:=X0:fofType
% Found x40 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x3 x40) as proof of ((cR X) x0)
% Found (x3 x40) as proof of ((cR X) x0)
% Found x40:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Instantiate: X:=X0:fofType
% Found x40 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x30:((cR X) x0)
% Found (fun (x8:((and ((cR X0) x7)) ((cR x7) X0)))=> x30) as proof of ((cR X) x0)
% Found (fun (x8:((and ((cR X0) x7)) ((cR x7) X0)))=> x30) as proof of (((and ((cR X0) x7)) ((cR x7) X0))->((cR X) x0))
% Found x50:((cR X0) x0)
% Found (fun (x8:((and ((cR X) x7)) ((cR x7) X)))=> x50) as proof of ((cR X0) x0)
% Found (fun (x8:((and ((cR X) x7)) ((cR x7) X)))=> x50) as proof of (((and ((cR X) x7)) ((cR x7) X))->((cR X0) x0))
% Found x000:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x000 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x30:=(x3 x20):((cR X) x0)
% Instantiate: x4:=x0:fofType
% Found (x3 x20) as proof of ((cR X) x4)
% Found (x3 x20) as proof of ((cR X) x4)
% Found x30:=(x3 x20):((cR X) x0)
% Instantiate: X:=x0:fofType;x4:=X:fofType
% Found (x3 x20) as proof of ((cR x4) X)
% Found (x3 x20) as proof of ((cR x4) X)
% Found x30:=(x3 x20):((cR X) x0)
% Instantiate: X:=x0:fofType
% Found (x3 x20) as proof of ((cR x4) X)
% Found (x3 x20) as proof of ((cR x4) X)
% Found ((conj00 (x3 x20)) (x3 x20)) as proof of ((and ((cR X) x4)) ((cR x4) X))
% Found (((conj0 ((cR x4) X)) (x3 x20)) (x3 x20)) as proof of ((and ((cR X) x4)) ((cR x4) X))
% Found ((((conj ((cR X) x4)) ((cR x4) X)) (x3 x20)) (x3 x20)) as proof of ((and ((cR X) x4)) ((cR x4) X))
% Found ((((conj ((cR X) x4)) ((cR x4) X)) (x3 x20)) (x3 x20)) as proof of ((and ((cR X) x4)) ((cR x4) X))
% Found (ex_intro000 ((((conj ((cR X) x4)) ((cR x4) X)) (x3 x20)) (x3 x20))) as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found ((ex_intro00 x0) ((((conj ((cR X) x0)) ((cR x0) X)) (x3 x20)) (x3 x20))) as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found (((ex_intro0 (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))) x0) ((((conj ((cR X) x0)) ((cR x0) X)) (x3 x20)) (x3 x20))) as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found ((((ex_intro fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))) x0) ((((conj ((cR X) x0)) ((cR x0) X)) (x3 x20)) (x3 x20))) as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found ((((ex_intro fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))) x0) ((((conj ((cR X) x0)) ((cR x0) X)) (x3 x20)) (x3 x20))) as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x50:((cR X0) x0)
% Found x50 as proof of ((cR X0) x0)
% Found ((x4 x50) x00) as proof of False
% Found (fun (x7:((and ((cR X) x6)) ((cR x6) X)))=> ((x4 x50) x00)) as proof of False
% Found (fun (x7:((and ((cR X) x6)) ((cR x6) X)))=> ((x4 x50) x00)) as proof of (((and ((cR X) x6)) ((cR x6) X))->False)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found ((x2 x30) x00) as proof of False
% Found (fun (x7:((and ((cR X0) x6)) ((cR x6) X0)))=> ((x2 x30) x00)) as proof of False
% Found (fun (x7:((and ((cR X0) x6)) ((cR x6) X0)))=> ((x2 x30) x00)) as proof of (((and ((cR X0) x6)) ((cR x6) X0))->False)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found (x4 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x4 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found ((x2 x50) x6) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))=> ((x2 x50) x6)) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))=> ((x2 x50) x6)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x50:((cR X0) x0)
% Found x50 as proof of ((cR X0) x0)
% Found ((x4 x50) x6) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))=> ((x4 x50) x6)) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))=> ((x4 x50) x6)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found ((x4 x30) x6) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x4 x30) x6)) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x4 x30) x6)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found ((x2 x30) x6) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x2 x30) x6)) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x2 x30) x6)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found (x4 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x4 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found ((x2 x30) x6) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x2 x30) x6)) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x2 x30) x6)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found ((x4 x30) x6) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x4 x30) x6)) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x4 x30) x6)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x50:((cR X0) x0)
% Found x50 as proof of ((cR X0) x0)
% Found ((x4 x50) x6) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))=> ((x4 x50) x6)) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))=> ((x4 x50) x6)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found ((x2 x50) x6) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))=> ((x2 x50) x6)) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))=> ((x2 x50) x6)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found (x20 x00) as proof of False
% Found ((x2 x30) x00) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x2 x30) x00)) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x2 x30) x00)) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found (x40 x30) as proof of False
% Found ((fun (x6:((cR X0) x0))=> ((x4 x6) x00)) x30) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((fun (x6:((cR X0) x0))=> ((x4 x6) x00)) x30)) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((fun (x6:((cR X0) x0))=> ((x4 x6) x00)) x30)) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x31:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x31 as proof of ((cR X0) x0)
% Found x31:((cR X) x0)
% Found x31 as proof of ((cR X) x0)
% Found x20:=(x2 x31):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x20 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x31:((cR X) x0)
% Found x31 as proof of ((cR X) x0)
% Found x31:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x31 as proof of ((cR X0) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Instantiate: X0:=X:fofType
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Instantiate: X0:=X:fofType
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x20:=(x2 x32):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x20 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found x12:((cR x7) X)
% Instantiate: X:=x0:fofType;X0:=x7:fofType
% Found (fun (x12:((cR x7) X))=> x12) as proof of ((cR X0) x0)
% Found (fun (x9:((cR X) x7)) (x12:((cR x7) X))=> x12) as proof of (((cR x7) X)->((cR X0) x0))
% Found (fun (x9:((cR X) x7)) (x12:((cR x7) X))=> x12) as proof of (((cR X) x7)->(((cR x7) X)->((cR X0) x0)))
% Found (and_rect20 (fun (x9:((cR X) x7)) (x12:((cR x7) X))=> x12)) as proof of ((cR X0) x0)
% Found ((and_rect2 ((cR X0) x0)) (fun (x9:((cR X) x7)) (x12:((cR x7) X))=> x12)) as proof of ((cR X0) x0)
% Found (((fun (P:Type) (x9:(((cR X) x7)->(((cR x7) X)->P)))=> (((((and_rect ((cR X) x7)) ((cR x7) X)) P) x9) x8)) ((cR X0) x0)) (fun (x9:((cR X) x7)) (x12:((cR x7) X))=> x12)) as proof of ((cR X0) x0)
% Found (fun (x8:((and ((cR X) x7)) ((cR x7) X)))=> (((fun (P:Type) (x9:(((cR X) x7)->(((cR x7) X)->P)))=> (((((and_rect ((cR X) x7)) ((cR x7) X)) P) x9) x8)) ((cR X0) x0)) (fun (x9:((cR X) x7)) (x12:((cR x7) X))=> x12))) as proof of ((cR X0) x0)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x50:=(x5 x41):((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found (x5 x41) as proof of ((cR X) x0)
% Found (x5 x41) as proof of ((cR X) x0)
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x31:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x31 as proof of ((cR X0) x0)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x31:((cR X) x0)
% Found x31 as proof of ((cR X) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x50:=(x5 x40):((cR X0) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found x50:=(x5 x41):((cR X0) x0)
% Found (x5 x41) as proof of ((cR X0) x0)
% Found (x5 x41) as proof of ((cR X0) x0)
% Found x50:=(x5 x40):((cR X0) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found x4:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x4 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x12:((cR x7) X)
% Instantiate: X:=x0:fofType;X0:=x7:fofType
% Found (fun (x12:((cR x7) X))=> x12) as proof of ((cR X0) x0)
% Found (fun (x9:((cR X) x7)) (x12:((cR x7) X))=> x12) as proof of (((cR x7) X)->((cR X0) x0))
% Found (fun (x9:((cR X) x7)) (x12:((cR x7) X))=> x12) as proof of (((cR X) x7)->(((cR x7) X)->((cR X0) x0)))
% Found (and_rect20 (fun (x9:((cR X) x7)) (x12:((cR x7) X))=> x12)) as proof of ((cR X0) x0)
% Found ((and_rect2 ((cR X0) x0)) (fun (x9:((cR X) x7)) (x12:((cR x7) X))=> x12)) as proof of ((cR X0) x0)
% Found (((fun (P:Type) (x9:(((cR X) x7)->(((cR x7) X)->P)))=> (((((and_rect ((cR X) x7)) ((cR x7) X)) P) x9) x8)) ((cR X0) x0)) (fun (x9:((cR X) x7)) (x12:((cR x7) X))=> x12)) as proof of ((cR X0) x0)
% Found (((fun (P:Type) (x9:(((cR X) x7)->(((cR x7) X)->P)))=> (((((and_rect ((cR X) x7)) ((cR x7) X)) P) x9) x8)) ((cR X0) x0)) (fun (x9:((cR X) x7)) (x12:((cR x7) X))=> x12)) as proof of ((cR X0) x0)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x9:((cR x6) X)
% Instantiate: X:=x0:fofType;X0:=x6:fofType
% Found x9 as proof of ((cR X0) x0)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x20:=(x2 x30):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x9:((cR x6) X0)
% Instantiate: X:=x6:fofType;X0:=x0:fofType
% Found x9 as proof of ((cR X) x0)
% Found x4:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x4 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x20:=(x2 x30):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found (x40 x30) as proof of False
% Found ((fun (x7:((cR X0) x0))=> ((x4 x7) x6)) x30) as proof of False
% Found ((fun (x7:((cR X0) x0))=> ((x4 x7) x6)) x30) as proof of False
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found (x20 x6) as proof of False
% Found ((x2 x30) x6) as proof of False
% Found ((x2 x30) x6) as proof of False
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found (x40 x6) as proof of False
% Found ((x4 x50) x6) as proof of False
% Found ((x4 x50) x6) as proof of False
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found (x20 x50) as proof of False
% Found ((fun (x7:((cR X) x0))=> ((x2 x7) x6)) x50) as proof of False
% Found ((fun (x7:((cR X) x0))=> ((x2 x7) x6)) x50) as proof of False
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x9:((cR x6) X)
% Instantiate: X:=x0:fofType;X0:=x6:fofType
% Found (fun (x9:((cR x6) X))=> x9) as proof of ((cR X0) x0)
% Found (fun (x8:((cR X) x6)) (x9:((cR x6) X))=> x9) as proof of (((cR x6) X)->((cR X0) x0))
% Found (fun (x8:((cR X) x6)) (x9:((cR x6) X))=> x9) as proof of (((cR X) x6)->(((cR x6) X)->((cR X0) x0)))
% Found (and_rect20 (fun (x8:((cR X) x6)) (x9:((cR x6) X))=> x9)) as proof of ((cR X0) x0)
% Found ((and_rect2 ((cR X0) x0)) (fun (x8:((cR X) x6)) (x9:((cR x6) X))=> x9)) as proof of ((cR X0) x0)
% Found (((fun (P:Type) (x8:(((cR X) x6)->(((cR x6) X)->P)))=> (((((and_rect ((cR X) x6)) ((cR x6) X)) P) x8) x7)) ((cR X0) x0)) (fun (x8:((cR X) x6)) (x9:((cR x6) X))=> x9)) as proof of ((cR X0) x0)
% Found (fun (x7:((and ((cR X) x6)) ((cR x6) X)))=> (((fun (P:Type) (x8:(((cR X) x6)->(((cR x6) X)->P)))=> (((((and_rect ((cR X) x6)) ((cR x6) X)) P) x8) x7)) ((cR X0) x0)) (fun (x8:((cR X) x6)) (x9:((cR x6) X))=> x9))) as proof of ((cR X0) x0)
% Found x30:((cR X) x0)
% Found (fun (x8:((and ((cR X0) x7)) ((cR x7) X0)))=> x30) as proof of ((cR X) x0)
% Found (fun (x8:((and ((cR X0) x7)) ((cR x7) X0)))=> x30) as proof of (((and ((cR X0) x7)) ((cR x7) X0))->((cR X) x0))
% Found x50:((cR X0) x0)
% Found (fun (x8:((and ((cR X) x7)) ((cR x7) X)))=> x50) as proof of ((cR X0) x0)
% Found (fun (x8:((and ((cR X) x7)) ((cR x7) X)))=> x50) as proof of (((and ((cR X) x7)) ((cR x7) X))->((cR X0) x0))
% Found x31:((cR X) x0)
% Instantiate: X:=x0:fofType;x4:=X:fofType
% Found x31 as proof of ((cR x4) X)
% Found x31:((cR X) x0)
% Instantiate: x4:=x0:fofType
% Found x31 as proof of ((cR X) x4)
% Found x31:((cR X) x0)
% Found x31 as proof of ((cR X) x4)
% Found ((conj00 x31) x31) as proof of ((and ((cR X) x4)) ((cR x4) X))
% Found (((conj0 ((cR x4) X)) x31) x31) as proof of ((and ((cR X) x4)) ((cR x4) X))
% Found ((((conj ((cR X) x4)) ((cR x4) X)) x31) x31) as proof of ((and ((cR X) x4)) ((cR x4) X))
% Found ((((conj ((cR X) x4)) ((cR x4) X)) x31) x31) as proof of ((and ((cR X) x4)) ((cR x4) X))
% Found (ex_intro000 ((((conj ((cR X) x4)) ((cR x4) X)) x31) x31)) as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found ((ex_intro00 X) ((((conj ((cR X) X)) ((cR X) X)) x31) x31)) as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found (((ex_intro0 (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))) X) ((((conj ((cR X) X)) ((cR X) X)) x31) x31)) as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found ((((ex_intro fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))) X) ((((conj ((cR X) X)) ((cR X) X)) x31) x31)) as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found ((((ex_intro fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))) X) ((((conj ((cR X) X)) ((cR X) X)) x31) x31)) as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found ((x2 x31) ((((ex_intro fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))) X) ((((conj ((cR X) X)) ((cR X) X)) x31) x31))) as proof of False
% Found ((x2 x31) ((((ex_intro fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))) X) ((((conj ((cR X) X)) ((cR X) X)) x31) x31))) as proof of False
% Found x9:((cR x6) X)
% Instantiate: X:=x0:fofType;X0:=x6:fofType
% Found (fun (x9:((cR x6) X))=> x9) as proof of ((cR X0) x0)
% Found (fun (x8:((cR X) x6)) (x9:((cR x6) X))=> x9) as proof of (((cR x6) X)->((cR X0) x0))
% Found (fun (x8:((cR X) x6)) (x9:((cR x6) X))=> x9) as proof of (((cR X) x6)->(((cR x6) X)->((cR X0) x0)))
% Found (and_rect20 (fun (x8:((cR X) x6)) (x9:((cR x6) X))=> x9)) as proof of ((cR X0) x0)
% Found ((and_rect2 ((cR X0) x0)) (fun (x8:((cR X) x6)) (x9:((cR x6) X))=> x9)) as proof of ((cR X0) x0)
% Found (((fun (P:Type) (x8:(((cR X) x6)->(((cR x6) X)->P)))=> (((((and_rect ((cR X) x6)) ((cR x6) X)) P) x8) x7)) ((cR X0) x0)) (fun (x8:((cR X) x6)) (x9:((cR x6) X))=> x9)) as proof of ((cR X0) x0)
% Found (((fun (P:Type) (x8:(((cR X) x6)->(((cR x6) X)->P)))=> (((((and_rect ((cR X) x6)) ((cR x6) X)) P) x8) x7)) ((cR X0) x0)) (fun (x8:((cR X) x6)) (x9:((cR x6) X))=> x9)) as proof of ((cR X0) x0)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found (x40 x00) as proof of False
% Found ((x4 x50) x00) as proof of False
% Found ((x4 x50) x00) as proof of False
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x9:((cR x6) X)
% Instantiate: X:=x0:fofType;X0:=x6:fofType
% Found x9 as proof of ((cR X0) x0)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found (x20 x00) as proof of False
% Found ((x2 x30) x00) as proof of False
% Found ((x2 x30) x00) as proof of False
% Found x30:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x30 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x4 x30) as proof of ((cR X) x0)
% Found (x4 x30) as proof of ((cR X) x0)
% Found (x4 x30) as proof of ((cR X) x0)
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found x20:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x20 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x3 x20) as proof of ((cR X) x4)
% Found (x3 x20) as proof of ((cR X) x4)
% Found (x3 x20) as proof of ((cR X) x4)
% Found x7:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x7 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x7:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x7 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x20:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x20 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x20:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x20 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x20:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Instantiate: X0:=X:fofType
% Found x20 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x5 x20) as proof of ((cR X0) x0)
% Found (x5 x20) as proof of ((cR X0) x0)
% Found x20:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Instantiate: X0:=X:fofType
% Found x20 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x5 x20) as proof of ((cR X0) x0)
% Found (x5 x20) as proof of ((cR X0) x0)
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Instantiate: X0:=X:fofType
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Instantiate: X0:=X:fofType
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x41:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x41 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x5 x41) as proof of ((cR X) x0)
% Found (x5 x41) as proof of ((cR X) x0)
% Found (x5 x41) as proof of ((cR X) x0)
% Found x20:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x20 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x31:((cR X) x0)
% Found x31 as proof of ((cR X) x0)
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x31:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x31 as proof of ((cR X0) x0)
% Found x9:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x9 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found ((x2 x30) x00) as proof of False
% Found (fun (x7:((and ((cR X0) x6)) ((cR x6) X0)))=> ((x2 x30) x00)) as proof of False
% Found (fun (x6:fofType) (x7:((and ((cR X0) x6)) ((cR x6) X0)))=> ((x2 x30) x00)) as proof of (((and ((cR X0) x6)) ((cR x6) X0))->False)
% Found (fun (x6:fofType) (x7:((and ((cR X0) x6)) ((cR x6) X0)))=> ((x2 x30) x00)) as proof of (forall (x:fofType), (((and ((cR X0) x)) ((cR x) X0))->False))
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x50:((cR X0) x0)
% Found x50 as proof of ((cR X0) x0)
% Found ((x4 x50) x00) as proof of False
% Found (fun (x7:((and ((cR X) x6)) ((cR x6) X)))=> ((x4 x50) x00)) as proof of False
% Found (fun (x6:fofType) (x7:((and ((cR X) x6)) ((cR x6) X)))=> ((x4 x50) x00)) as proof of (((and ((cR X) x6)) ((cR x6) X))->False)
% Found (fun (x6:fofType) (x7:((and ((cR X) x6)) ((cR x6) X)))=> ((x4 x50) x00)) as proof of (forall (x:fofType), (((and ((cR X) x)) ((cR x) X))->False))
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found (x4 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x4 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x50:((cR X0) x0)
% Found (fun (x8:((and ((cR X) x7)) ((cR x7) X)))=> x50) as proof of ((cR X0) x0)
% Found (fun (x7:fofType) (x8:((and ((cR X) x7)) ((cR x7) X)))=> x50) as proof of (((and ((cR X) x7)) ((cR x7) X))->((cR X0) x0))
% Found (fun (x7:fofType) (x8:((and ((cR X) x7)) ((cR x7) X)))=> x50) as proof of (forall (x:fofType), (((and ((cR X) x)) ((cR x) X))->((cR X0) x0)))
% Found x30:((cR X) x0)
% Found (fun (x8:((and ((cR X0) x7)) ((cR x7) X0)))=> x30) as proof of ((cR X) x0)
% Found (fun (x7:fofType) (x8:((and ((cR X0) x7)) ((cR x7) X0)))=> x30) as proof of (((and ((cR X0) x7)) ((cR x7) X0))->((cR X) x0))
% Found (fun (x7:fofType) (x8:((and ((cR X0) x7)) ((cR x7) X0)))=> x30) as proof of (forall (x:fofType), (((and ((cR X0) x)) ((cR x) X0))->((cR X) x0)))
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x9:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x9 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found ((x4 x30) x6) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x4 x30) x6)) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x4 x30) x6)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found ((x2 x30) x6) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x2 x30) x6)) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x2 x30) x6)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found (x4 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x4 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x20:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x20 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found x50:=(x5 x40):((cR X0) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found ((x2 x50) x00) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))=> ((x2 x50) x00)) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))=> ((x2 x50) x00)) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found ((x4 x30) x00) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x4 x30) x00)) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x4 x30) x00)) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x40:=(x4 x30):((cR X0) x0)
% Found (x4 x30) as proof of ((cR X) x0)
% Found (x4 x30) as proof of ((cR X) x0)
% Found (x4 x30) as proof of ((cR X) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Instantiate: X0:=X:fofType
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x12:((cR x7) X)
% Instantiate: X:=x0:fofType;X0:=x7:fofType
% Found x12 as proof of ((cR X0) x0)
% Found x9:((cR x4) X)
% Instantiate: X:=x0:fofType;X0:=x4:fofType
% Found (fun (x9:((cR x4) X))=> x9) as proof of ((cR X0) x0)
% Found (fun (x8:((cR X) x4)) (x9:((cR x4) X))=> x9) as proof of (((cR x4) X)->((cR X0) x0))
% Found (fun (x8:((cR X) x4)) (x9:((cR x4) X))=> x9) as proof of (((cR X) x4)->(((cR x4) X)->((cR X0) x0)))
% Found (and_rect20 (fun (x8:((cR X) x4)) (x9:((cR x4) X))=> x9)) as proof of ((cR X0) x0)
% Found ((and_rect2 ((cR X0) x0)) (fun (x8:((cR X) x4)) (x9:((cR x4) X))=> x9)) as proof of ((cR X0) x0)
% Found (((fun (P:Type) (x8:(((cR X) x4)->(((cR x4) X)->P)))=> (((((and_rect ((cR X) x4)) ((cR x4) X)) P) x8) x5)) ((cR X0) x0)) (fun (x8:((cR X) x4)) (x9:((cR x4) X))=> x9)) as proof of ((cR X0) x0)
% Found (((fun (P:Type) (x8:(((cR X) x4)->(((cR x4) X)->P)))=> (((((and_rect ((cR X) x4)) ((cR x4) X)) P) x8) x5)) ((cR X0) x0)) (fun (x8:((cR X) x4)) (x9:((cR x4) X))=> x9)) as proof of ((cR X0) x0)
% Found x20:=(x2 x30):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x30:=(x3 x20):((cR X) x0)
% Instantiate: X0:=X:fofType
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x50:=(x5 x40):((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found x50:=(x5 x40):((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found x20:=(fun (x13:((cR X) x0))=> ((x2 x13) x7)):(((cR X) x0)->False)
% Instantiate: X:=x8:fofType;X0:=x0:fofType
% Found (fun (x13:((cR X) x0))=> ((x2 x13) x7)) as proof of (((cR x8) X0)->False)
% Found (fun (x12:((cR X0) x8)) (x13:((cR X) x0))=> ((x2 x13) x7)) as proof of (((cR x8) X0)->False)
% Found (fun (x12:((cR X0) x8)) (x13:((cR X) x0))=> ((x2 x13) x7)) as proof of (((cR X0) x8)->(((cR x8) X0)->False))
% Found (and_rect20 (fun (x12:((cR X0) x8)) (x13:((cR X) x0))=> ((x2 x13) x7))) as proof of False
% Found ((and_rect2 False) (fun (x12:((cR X0) x8)) (x13:((cR X) x0))=> ((x2 x13) x7))) as proof of False
% Found (((fun (P:Type) (x12:(((cR X0) x8)->(((cR x8) X0)->P)))=> (((((and_rect ((cR X0) x8)) ((cR x8) X0)) P) x12) x9)) False) (fun (x12:((cR X0) x8)) (x13:((cR X) x0))=> ((x2 x13) x7))) as proof of False
% Found (fun (x9:((and ((cR X0) x8)) ((cR x8) X0)))=> (((fun (P:Type) (x12:(((cR X0) x8)->(((cR x8) X0)->P)))=> (((((and_rect ((cR X0) x8)) ((cR x8) X0)) P) x12) x9)) False) (fun (x12:((cR X0) x8)) (x13:((cR X) x0))=> ((x2 x13) x7)))) as proof of False
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found ((x2 x30) x00) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x2 x30) x00)) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x2 x30) x00)) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x40:=(fun (x13:((cR X0) x0))=> ((x4 x13) x7)):(((cR X0) x0)->False)
% Instantiate: X:=x0:fofType;X0:=x8:fofType
% Found (fun (x13:((cR X0) x0))=> ((x4 x13) x7)) as proof of (((cR x8) X)->False)
% Found (fun (x12:((cR X) x8)) (x13:((cR X0) x0))=> ((x4 x13) x7)) as proof of (((cR x8) X)->False)
% Found (fun (x12:((cR X) x8)) (x13:((cR X0) x0))=> ((x4 x13) x7)) as proof of (((cR X) x8)->(((cR x8) X)->False))
% Found (and_rect20 (fun (x12:((cR X) x8)) (x13:((cR X0) x0))=> ((x4 x13) x7))) as proof of False
% Found ((and_rect2 False) (fun (x12:((cR X) x8)) (x13:((cR X0) x0))=> ((x4 x13) x7))) as proof of False
% Found (((fun (P:Type) (x12:(((cR X) x8)->(((cR x8) X)->P)))=> (((((and_rect ((cR X) x8)) ((cR x8) X)) P) x12) x9)) False) (fun (x12:((cR X) x8)) (x13:((cR X0) x0))=> ((x4 x13) x7))) as proof of False
% Found (fun (x9:((and ((cR X) x8)) ((cR x8) X)))=> (((fun (P:Type) (x12:(((cR X) x8)->(((cR x8) X)->P)))=> (((((and_rect ((cR X) x8)) ((cR x8) X)) P) x12) x9)) False) (fun (x12:((cR X) x8)) (x13:((cR X0) x0))=> ((x4 x13) x7)))) as proof of False
% Found x20:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Instantiate: X0:=X:fofType
% Found x20 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x50:((cR X0) x0)
% Found x50 as proof of ((cR X0) x0)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found ((x4 x50) x00) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))=> ((x4 x50) x00)) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))=> ((x4 x50) x00)) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x40:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x40 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found x50:=(x5 x40):((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found x20:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x20 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x20:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Instantiate: X0:=X:fofType
% Found x20 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR x4) X)
% Found (x3 x20) as proof of ((cR x4) X)
% Found (x3 x20) as proof of ((cR x4) X)
% Found (x3 x20) as proof of ((cR x4) X)
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR x4) X)
% Found (x3 x20) as proof of ((cR x4) X)
% Found (x3 x20) as proof of ((cR x4) X)
% Found (x3 x20) as proof of ((cR x4) X)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x20:=(fun (x13:((cR X) x0))=> ((x2 x13) x9)):(((cR X) x0)->False)
% Instantiate: X:=x7:fofType;X0:=x0:fofType
% Found (fun (x13:((cR X) x0))=> ((x2 x13) x9)) as proof of (((cR x7) X0)->False)
% Found (fun (x12:((cR X0) x7)) (x13:((cR X) x0))=> ((x2 x13) x9)) as proof of (((cR x7) X0)->False)
% Found (fun (x12:((cR X0) x7)) (x13:((cR X) x0))=> ((x2 x13) x9)) as proof of (((cR X0) x7)->(((cR x7) X0)->False))
% Found (and_rect20 (fun (x12:((cR X0) x7)) (x13:((cR X) x0))=> ((x2 x13) x9))) as proof of False
% Found ((and_rect2 False) (fun (x12:((cR X0) x7)) (x13:((cR X) x0))=> ((x2 x13) x9))) as proof of False
% Found (((fun (P:Type) (x12:(((cR X0) x7)->(((cR x7) X0)->P)))=> (((((and_rect ((cR X0) x7)) ((cR x7) X0)) P) x12) x8)) False) (fun (x12:((cR X0) x7)) (x13:((cR X) x0))=> ((x2 x13) x9))) as proof of False
% Found (fun (x9:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))=> (((fun (P:Type) (x12:(((cR X0) x7)->(((cR x7) X0)->P)))=> (((((and_rect ((cR X0) x7)) ((cR x7) X0)) P) x12) x8)) False) (fun (x12:((cR X0) x7)) (x13:((cR X) x0))=> ((x2 x13) x9)))) as proof of False
% Found (fun (x8:((and ((cR X0) x7)) ((cR x7) X0))) (x9:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))=> (((fun (P:Type) (x12:(((cR X0) x7)->(((cR x7) X0)->P)))=> (((((and_rect ((cR X0) x7)) ((cR x7) X0)) P) x12) x8)) False) (fun (x12:((cR X0) x7)) (x13:((cR X) x0))=> ((x2 x13) x9)))) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x40:=(fun (x13:((cR X0) x0))=> ((x4 x13) x9)):(((cR X0) x0)->False)
% Instantiate: X:=x0:fofType;X0:=x7:fofType
% Found (fun (x13:((cR X0) x0))=> ((x4 x13) x9)) as proof of (((cR x7) X)->False)
% Found (fun (x12:((cR X) x7)) (x13:((cR X0) x0))=> ((x4 x13) x9)) as proof of (((cR x7) X)->False)
% Found (fun (x12:((cR X) x7)) (x13:((cR X0) x0))=> ((x4 x13) x9)) as proof of (((cR X) x7)->(((cR x7) X)->False))
% Found (and_rect20 (fun (x12:((cR X) x7)) (x13:((cR X0) x0))=> ((x4 x13) x9))) as proof of False
% Found ((and_rect2 False) (fun (x12:((cR X) x7)) (x13:((cR X0) x0))=> ((x4 x13) x9))) as proof of False
% Found (((fun (P:Type) (x12:(((cR X) x7)->(((cR x7) X)->P)))=> (((((and_rect ((cR X) x7)) ((cR x7) X)) P) x12) x8)) False) (fun (x12:((cR X) x7)) (x13:((cR X0) x0))=> ((x4 x13) x9))) as proof of False
% Found (fun (x9:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> (((fun (P:Type) (x12:(((cR X) x7)->(((cR x7) X)->P)))=> (((((and_rect ((cR X) x7)) ((cR x7) X)) P) x12) x8)) False) (fun (x12:((cR X) x7)) (x13:((cR X0) x0))=> ((x4 x13) x9)))) as proof of False
% Found (fun (x8:((and ((cR X) x7)) ((cR x7) X))) (x9:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> (((fun (P:Type) (x12:(((cR X) x7)->(((cR x7) X)->P)))=> (((((and_rect ((cR X) x7)) ((cR x7) X)) P) x12) x8)) False) (fun (x12:((cR X) x7)) (x13:((cR X0) x0))=> ((x4 x13) x9)))) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x50:=(x5 x40):((cR X0) x0)
% Found (x5 x40) as proof of ((cR X0) x0)
% Found (x5 x40) as proof of ((cR X0) x0)
% Found x50:=(x5 x41):((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found (x5 x41) as proof of ((cR X) x0)
% Found (x5 x41) as proof of ((cR X) x0)
% Found x41:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Instantiate: X:=X0:fofType
% Found x41 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x3 x41) as proof of ((cR X) x0)
% Found (x3 x41) as proof of ((cR X) x0)
% Found x20:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Instantiate: X0:=X:fofType
% Found x20 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x20:=(x2 x32):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x32) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x32) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x20:=(x2 x30):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found x30:=(x3 x21):((cR X) x0)
% Instantiate: X0:=X:fofType
% Found (x3 x21) as proof of ((cR X0) x0)
% Found (x3 x21) as proof of ((cR X0) x0)
% Found x20:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Instantiate: X0:=X:fofType
% Found x20 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x5 x20) as proof of ((cR X0) x0)
% Found (x5 x20) as proof of ((cR X0) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x50:=(x5 x41):((cR X0) x0)
% Found (x5 x41) as proof of ((cR X) x0)
% Found (x5 x41) as proof of ((cR X) x0)
% Found (x5 x41) as proof of ((cR X) x0)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x20:=(x2 x32):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x32) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x32) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x20:=(x2 x30):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x50:=(x5 x40):((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Instantiate: X0:=X:fofType
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x50:=(x5 x40):((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found x50:=(x5 x40):((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Instantiate: X0:=X:fofType
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x50:=(x5 x40):((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Instantiate: X0:=X:fofType
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Instantiate: X0:=X:fofType
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found x40:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Instantiate: X:=X0:fofType
% Found x40 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x20:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Instantiate: X0:=X:fofType
% Found x20 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x20:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Instantiate: X0:=X:fofType
% Found x20 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x20:=(x2 x30):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Instantiate: X0:=X:fofType
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x40:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Instantiate: X:=X0:fofType
% Found x40 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x9:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x9 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found (x40 x30) as proof of False
% Found ((fun (x7:((cR X0) x0))=> ((x4 x7) x6)) x30) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((fun (x7:((cR X0) x0))=> ((x4 x7) x6)) x30)) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((fun (x7:((cR X0) x0))=> ((x4 x7) x6)) x30)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found (x20 x6) as proof of False
% Found ((x2 x30) x6) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x2 x30) x6)) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x2 x30) x6)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found (x40 x6) as proof of False
% Found ((x4 x50) x6) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))=> ((x4 x50) x6)) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))=> ((x4 x50) x6)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found (x20 x50) as proof of False
% Found ((fun (x7:((cR X) x0))=> ((x2 x7) x6)) x50) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))=> ((fun (x7:((cR X) x0))=> ((x2 x7) x6)) x50)) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))=> ((fun (x7:((cR X) x0))=> ((x2 x7) x6)) x50)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x50:=(x5 x40):((cR X0) x0)
% Found (x5 x40) as proof of ((cR X0) x0)
% Found (x5 x40) as proof of ((cR X0) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found x50:=(x5 x40):((cR X0) x0)
% Found (x5 x40) as proof of ((cR X0) x0)
% Found (x5 x40) as proof of ((cR X0) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found x40:=(x4 x50):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Instantiate: X:=X0:fofType
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x9:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x9 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found (x40 x30) as proof of False
% Found ((fun (x7:((cR X0) x0))=> ((x4 x7) x6)) x30) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((fun (x7:((cR X0) x0))=> ((x4 x7) x6)) x30)) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((fun (x7:((cR X0) x0))=> ((x4 x7) x6)) x30)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found (x20 x6) as proof of False
% Found ((x2 x30) x6) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x2 x30) x6)) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x2 x30) x6)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found (x20 x50) as proof of False
% Found ((fun (x7:((cR X) x0))=> ((x2 x7) x6)) x50) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))=> ((fun (x7:((cR X) x0))=> ((x2 x7) x6)) x50)) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))=> ((fun (x7:((cR X) x0))=> ((x2 x7) x6)) x50)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found (x40 x6) as proof of False
% Found ((x4 x50) x6) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))=> ((x4 x50) x6)) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))=> ((x4 x50) x6)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x20:=(x2 x30):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Instantiate: X0:=X:fofType
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x20:=(x2 x30):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Instantiate: X0:=X:fofType
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x40:=(x4 x50):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Instantiate: X:=X0:fofType
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x40:=(x4 x50):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Instantiate: X:=X0:fofType
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x40:=(x4 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x4 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x4 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x40:=(x4 x50):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x40:=(x4 x50):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x20:=(x2 x30):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x20:=(x2 x30):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x40:=(x4 x50):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Instantiate: X:=X0:fofType
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x40:=(x4 x50):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Instantiate: X:=X0:fofType
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x20:=(x2 x30):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Instantiate: X0:=X:fofType
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x20:=(x2 x30):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Instantiate: X0:=X:fofType
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x30:=(x3 x20):((cR X) x0)
% Instantiate: X0:=X:fofType
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found (x40 x00) as proof of False
% Found ((x4 x50) x00) as proof of False
% Found (fun (x7:((and ((cR X) x6)) ((cR x6) X)))=> ((x4 x50) x00)) as proof of False
% Found (fun (x7:((and ((cR X) x6)) ((cR x6) X)))=> ((x4 x50) x00)) as proof of (((and ((cR X) x6)) ((cR x6) X))->False)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found (x20 x00) as proof of False
% Found ((x2 x30) x00) as proof of False
% Found (fun (x7:((and ((cR X0) x6)) ((cR x6) X0)))=> ((x2 x30) x00)) as proof of False
% Found (fun (x7:((and ((cR X0) x6)) ((cR x6) X0)))=> ((x2 x30) x00)) as proof of (((and ((cR X0) x6)) ((cR x6) X0))->False)
% Found x30:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x30 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x4 x30) as proof of ((cR X) x0)
% Found (x4 x30) as proof of ((cR X) x0)
% Found (fun (x4:((((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)->((cR X0) x0)))=> (x4 x30)) as proof of ((cR X) x0)
% Found (fun (x4:((((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)->((cR X0) x0)))=> (x4 x30)) as proof of (((((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)->((cR X0) x0))->((cR X) x0))
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Instantiate: X0:=X:fofType
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found x50:((cR X0) x0)
% Found (fun (x8:((and ((cR X) x7)) ((cR x7) X)))=> x50) as proof of ((cR X0) x0)
% Found (fun (x7:fofType) (x8:((and ((cR X) x7)) ((cR x7) X)))=> x50) as proof of (((and ((cR X) x7)) ((cR x7) X))->((cR X0) x0))
% Found (fun (x7:fofType) (x8:((and ((cR X) x7)) ((cR x7) X)))=> x50) as proof of (forall (x:fofType), (((and ((cR X) x)) ((cR x) X))->((cR X0) x0)))
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x30:((cR X) x0)
% Found (fun (x8:((and ((cR X0) x7)) ((cR x7) X0)))=> x30) as proof of ((cR X) x0)
% Found (fun (x7:fofType) (x8:((and ((cR X0) x7)) ((cR x7) X0)))=> x30) as proof of (((and ((cR X0) x7)) ((cR x7) X0))->((cR X) x0))
% Found (fun (x7:fofType) (x8:((and ((cR X0) x7)) ((cR x7) X0)))=> x30) as proof of (forall (x:fofType), (((and ((cR X0) x)) ((cR x) X0))->((cR X) x0)))
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found x50:=(x5 x40):((cR X0) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x12:((cR x7) X)
% Instantiate: X:=x0:fofType;X0:=x7:fofType
% Found x12 as proof of ((cR X0) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Instantiate: X0:=X:fofType
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found x8:((cR x5) X)
% Instantiate: X:=x0:fofType;X0:=x5:fofType
% Found (fun (x8:((cR x5) X))=> x8) as proof of ((cR X0) x0)
% Found (fun (x7:((cR X) x5)) (x8:((cR x5) X))=> x8) as proof of (((cR x5) X)->((cR X0) x0))
% Found (fun (x7:((cR X) x5)) (x8:((cR x5) X))=> x8) as proof of (((cR X) x5)->(((cR x5) X)->((cR X0) x0)))
% Found (and_rect20 (fun (x7:((cR X) x5)) (x8:((cR x5) X))=> x8)) as proof of ((cR X0) x0)
% Found ((and_rect2 ((cR X0) x0)) (fun (x7:((cR X) x5)) (x8:((cR x5) X))=> x8)) as proof of ((cR X0) x0)
% Found (((fun (P:Type) (x7:(((cR X) x5)->(((cR x5) X)->P)))=> (((((and_rect ((cR X) x5)) ((cR x5) X)) P) x7) x6)) ((cR X0) x0)) (fun (x7:((cR X) x5)) (x8:((cR x5) X))=> x8)) as proof of ((cR X0) x0)
% Found (fun (x6:((and ((cR X) x5)) ((cR x5) X)))=> (((fun (P:Type) (x7:(((cR X) x5)->(((cR x5) X)->P)))=> (((((and_rect ((cR X) x5)) ((cR x5) X)) P) x7) x6)) ((cR X0) x0)) (fun (x7:((cR X) x5)) (x8:((cR x5) X))=> x8))) as proof of ((cR X0) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Instantiate: X0:=X:fofType
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found ((x2 (x3 x20)) x00) as proof of False
% Found (fun (x7:((and ((cR X0) x6)) ((cR x6) X0)))=> ((x2 (x3 x20)) x00)) as proof of False
% Found (fun (x7:((and ((cR X0) x6)) ((cR x6) X0)))=> ((x2 (x3 x20)) x00)) as proof of (((and ((cR X0) x6)) ((cR x6) X0))->False)
% Found x50:=(x5 x40):((cR X0) x0)
% Found (x5 x40) as proof of ((cR X0) x0)
% Found (x5 x40) as proof of ((cR X0) x0)
% Found ((x4 (x5 x40)) x00) as proof of False
% Found (fun (x7:((and ((cR X) x6)) ((cR x6) X)))=> ((x4 (x5 x40)) x00)) as proof of False
% Found (fun (x7:((and ((cR X) x6)) ((cR x6) X)))=> ((x4 (x5 x40)) x00)) as proof of (((and ((cR X) x6)) ((cR x6) X))->False)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found (x4 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x4 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x8:((cR x5) X)
% Instantiate: X:=x0:fofType;X0:=x5:fofType
% Found (fun (x8:((cR x5) X))=> x8) as proof of ((cR X0) x0)
% Found (fun (x7:((cR X) x5)) (x8:((cR x5) X))=> x8) as proof of (((cR x5) X)->((cR X0) x0))
% Found (fun (x7:((cR X) x5)) (x8:((cR x5) X))=> x8) as proof of (((cR X) x5)->(((cR x5) X)->((cR X0) x0)))
% Found (and_rect20 (fun (x7:((cR X) x5)) (x8:((cR x5) X))=> x8)) as proof of ((cR X0) x0)
% Found ((and_rect2 ((cR X0) x0)) (fun (x7:((cR X) x5)) (x8:((cR x5) X))=> x8)) as proof of ((cR X0) x0)
% Found (((fun (P:Type) (x7:(((cR X) x5)->(((cR x5) X)->P)))=> (((((and_rect ((cR X) x5)) ((cR x5) X)) P) x7) x6)) ((cR X0) x0)) (fun (x7:((cR X) x5)) (x8:((cR x5) X))=> x8)) as proof of ((cR X0) x0)
% Found (((fun (P:Type) (x7:(((cR X) x5)->(((cR x5) X)->P)))=> (((((and_rect ((cR X) x5)) ((cR x5) X)) P) x7) x6)) ((cR X0) x0)) (fun (x7:((cR X) x5)) (x8:((cR x5) X))=> x8)) as proof of ((cR X0) x0)
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found (x2 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found ((x2 x30) x6) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x2 x30) x6)) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x2 x30) x6)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found ((x4 x30) x6) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x4 x30) x6)) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x4 x30) x6)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x7:((cR x4) X)
% Instantiate: X:=x0:fofType;X0:=x4:fofType
% Found x7 as proof of ((cR X0) x0)
% Found x40:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Instantiate: X:=X0:fofType
% Found x40 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x3 x40) as proof of ((cR X) x0)
% Found (x3 x40) as proof of ((cR X) x0)
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found (x2 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found (x4 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x4 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found (x4 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x4 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x40:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Instantiate: X:=X0:fofType
% Found x40 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x3 x40) as proof of ((cR X) x0)
% Found (x3 x40) as proof of ((cR X) x0)
% Found x20:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Instantiate: X0:=X:fofType
% Found x20 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x5 x20) as proof of ((cR X0) x0)
% Found (x5 x20) as proof of ((cR X0) x0)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found (x4 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x4 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x40:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Instantiate: X:=X0:fofType
% Found x40 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x3 x40) as proof of ((cR X) x0)
% Found (x3 x40) as proof of ((cR X) x0)
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found (x2 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found (x2 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x20:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Instantiate: X0:=X:fofType
% Found x20 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x5 x20) as proof of ((cR X0) x0)
% Found (x5 x20) as proof of ((cR X0) x0)
% Found x20:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Instantiate: X0:=X:fofType
% Found x20 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x5 x20) as proof of ((cR X0) x0)
% Found (x5 x20) as proof of ((cR X0) x0)
% Found x20:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Instantiate: X0:=X:fofType
% Found x20 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x5 x20) as proof of ((cR X0) x0)
% Found (x5 x20) as proof of ((cR X0) x0)
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found (x2 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x40:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Instantiate: X:=X0:fofType
% Found x40 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x3 x40) as proof of ((cR X) x0)
% Found (x3 x40) as proof of ((cR X) x0)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found (x4 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x4 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found ((x4 x30) x00) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x4 x30) x00)) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x4 x30) x00)) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x20:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x20 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x40:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x40 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found x40:=(x4 x30):((cR X0) x0)
% Found (x4 x30) as proof of ((cR X) x0)
% Found (x4 x30) as proof of ((cR X) x0)
% Found (fun (x4:((not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))->((cR X0) x0)))=> (x4 x30)) as proof of ((cR X) x0)
% Found (fun (x4:((not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))->((cR X0) x0)))=> (x4 x30)) as proof of (((not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))->((cR X0) x0))->((cR X) x0))
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found x40:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Instantiate: X:=X0:fofType
% Found x40 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x20:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x20 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x3 x20) as proof of ((cR x4) X)
% Found (x3 x20) as proof of ((cR x4) X)
% Found (x3 x20) as proof of ((cR x4) X)
% Found (x3 x20) as proof of ((cR x4) X)
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found ((x2 x30) x00) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x2 x30) x00)) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x2 x30) x00)) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x5:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x5 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x9:((cR x6) X)
% Instantiate: X:=x0:fofType;X0:=x6:fofType
% Found x9 as proof of ((cR X0) x0)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x9:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x9 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x5:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x5 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x9:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x9 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x50:=(x5 x40):((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found (x5 x40) as proof of ((cR X) x0)
% Found (fun (x5:((((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)->((cR X0) x0)))=> (x5 x40)) as proof of ((cR X) x0)
% Found (fun (x5:((((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)->((cR X0) x0)))=> (x5 x40)) as proof of (((((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)->((cR X0) x0))->((cR X) x0))
% Found x50:((cR X0) x0)
% Found x50 as proof of ((cR X0) x0)
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x20:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x20 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x3 x20) as proof of ((cR x4) X)
% Found (x3 x20) as proof of ((cR x4) X)
% Found (x3 x20) as proof of ((cR x4) X)
% Found (x3 x20) as proof of ((cR x4) X)
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x50:((cR X0) x0)
% Found x50 as proof of ((cR X0) x0)
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x12:((cR x7) X)
% Instantiate: X:=x0:fofType;X0:=x7:fofType
% Found (fun (x12:((cR x7) X))=> x12) as proof of ((cR X0) x0)
% Found (fun (x9:((cR X) x7)) (x12:((cR x7) X))=> x12) as proof of (((cR x7) X)->((cR X0) x0))
% Found (fun (x9:((cR X) x7)) (x12:((cR x7) X))=> x12) as proof of (((cR X) x7)->(((cR x7) X)->((cR X0) x0)))
% Found (and_rect20 (fun (x9:((cR X) x7)) (x12:((cR x7) X))=> x12)) as proof of ((cR X0) x0)
% Found ((and_rect2 ((cR X0) x0)) (fun (x9:((cR X) x7)) (x12:((cR x7) X))=> x12)) as proof of ((cR X0) x0)
% Found (((fun (P:Type) (x9:(((cR X) x7)->(((cR x7) X)->P)))=> (((((and_rect ((cR X) x7)) ((cR x7) X)) P) x9) x8)) ((cR X0) x0)) (fun (x9:((cR X) x7)) (x12:((cR x7) X))=> x12)) as proof of ((cR X0) x0)
% Found (fun (x8:((and ((cR X) x7)) ((cR x7) X)))=> (((fun (P:Type) (x9:(((cR X) x7)->(((cR x7) X)->P)))=> (((((and_rect ((cR X) x7)) ((cR x7) X)) P) x9) x8)) ((cR X0) x0)) (fun (x9:((cR X) x7)) (x12:((cR x7) X))=> x12))) as proof of ((cR X0) x0)
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x12:((cR x7) X0)
% Instantiate: X:=x7:fofType;X0:=x0:fofType
% Found (fun (x12:((cR x7) X0))=> x12) as proof of ((cR X) x0)
% Found (fun (x9:((cR X0) x7)) (x12:((cR x7) X0))=> x12) as proof of (((cR x7) X0)->((cR X) x0))
% Found (fun (x9:((cR X0) x7)) (x12:((cR x7) X0))=> x12) as proof of (((cR X0) x7)->(((cR x7) X0)->((cR X) x0)))
% Found (and_rect20 (fun (x9:((cR X0) x7)) (x12:((cR x7) X0))=> x12)) as proof of ((cR X) x0)
% Found ((and_rect2 ((cR X) x0)) (fun (x9:((cR X0) x7)) (x12:((cR x7) X0))=> x12)) as proof of ((cR X) x0)
% Found (((fun (P:Type) (x9:(((cR X0) x7)->(((cR x7) X0)->P)))=> (((((and_rect ((cR X0) x7)) ((cR x7) X0)) P) x9) x8)) ((cR X) x0)) (fun (x9:((cR X0) x7)) (x12:((cR x7) X0))=> x12)) as proof of ((cR X) x0)
% Found (fun (x8:((and ((cR X0) x7)) ((cR x7) X0)))=> (((fun (P:Type) (x9:(((cR X0) x7)->(((cR x7) X0)->P)))=> (((((and_rect ((cR X0) x7)) ((cR x7) X0)) P) x9) x8)) ((cR X) x0)) (fun (x9:((cR X0) x7)) (x12:((cR x7) X0))=> x12))) as proof of ((cR X) x0)
% Found x40:=(x4 x50):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found x50:((cR X0) x0)
% Found x50 as proof of ((cR X0) x0)
% Found x40:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Instantiate: X:=X0:fofType
% Found x40 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found (x4 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x4 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x20:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Instantiate: X0:=X:fofType
% Found x20 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x40:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Instantiate: X:=X0:fofType
% Found x40 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x40:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Instantiate: X:=X0:fofType
% Found x40 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x50:=(x5 x40):((cR X0) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found x40:=(x4 x50):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x40:=(x4 x50):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x50:=(x5 x40):((cR X0) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found x40:=(x4 x50):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found (x20 x6) as proof of False
% Found ((x2 x30) x6) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x2 x30) x6)) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x2 x30) x6)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found (x40 x30) as proof of False
% Found ((fun (x7:((cR X0) x0))=> ((x4 x7) x6)) x30) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((fun (x7:((cR X0) x0))=> ((x4 x7) x6)) x30)) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((fun (x7:((cR X0) x0))=> ((x4 x7) x6)) x30)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x50:=(x5 x40):((cR X0) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x40:=(x4 x50):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x50:=(x5 x40):((cR X0) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x50:((cR X0) x0)
% Found x50 as proof of ((cR X0) x0)
% Found ((x4 x50) x6) as proof of False
% Found ((x4 x50) x6) as proof of False
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found ((x2 x30) x6) as proof of False
% Found ((x2 x30) x6) as proof of False
% Found x12:((cR x7) X0)
% Instantiate: X:=x7:fofType;X0:=x0:fofType
% Found (fun (x12:((cR x7) X0))=> x12) as proof of ((cR X) x0)
% Found (fun (x9:((cR X0) x7)) (x12:((cR x7) X0))=> x12) as proof of (((cR x7) X0)->((cR X) x0))
% Found (fun (x9:((cR X0) x7)) (x12:((cR x7) X0))=> x12) as proof of (((cR X0) x7)->(((cR x7) X0)->((cR X) x0)))
% Found (and_rect20 (fun (x9:((cR X0) x7)) (x12:((cR x7) X0))=> x12)) as proof of ((cR X) x0)
% Found ((and_rect2 ((cR X) x0)) (fun (x9:((cR X0) x7)) (x12:((cR x7) X0))=> x12)) as proof of ((cR X) x0)
% Found (((fun (P:Type) (x9:(((cR X0) x7)->(((cR x7) X0)->P)))=> (((((and_rect ((cR X0) x7)) ((cR x7) X0)) P) x9) x8)) ((cR X) x0)) (fun (x9:((cR X0) x7)) (x12:((cR x7) X0))=> x12)) as proof of ((cR X) x0)
% Found (((fun (P:Type) (x9:(((cR X0) x7)->(((cR x7) X0)->P)))=> (((((and_rect ((cR X0) x7)) ((cR x7) X0)) P) x9) x8)) ((cR X) x0)) (fun (x9:((cR X0) x7)) (x12:((cR x7) X0))=> x12)) as proof of ((cR X) x0)
% Found x12:((cR x7) X)
% Instantiate: X:=x0:fofType;X0:=x7:fofType
% Found (fun (x12:((cR x7) X))=> x12) as proof of ((cR X0) x0)
% Found (fun (x9:((cR X) x7)) (x12:((cR x7) X))=> x12) as proof of (((cR x7) X)->((cR X0) x0))
% Found (fun (x9:((cR X) x7)) (x12:((cR x7) X))=> x12) as proof of (((cR X) x7)->(((cR x7) X)->((cR X0) x0)))
% Found (and_rect20 (fun (x9:((cR X) x7)) (x12:((cR x7) X))=> x12)) as proof of ((cR X0) x0)
% Found ((and_rect2 ((cR X0) x0)) (fun (x9:((cR X) x7)) (x12:((cR x7) X))=> x12)) as proof of ((cR X0) x0)
% Found (((fun (P:Type) (x9:(((cR X) x7)->(((cR x7) X)->P)))=> (((((and_rect ((cR X) x7)) ((cR x7) X)) P) x9) x8)) ((cR X0) x0)) (fun (x9:((cR X) x7)) (x12:((cR x7) X))=> x12)) as proof of ((cR X0) x0)
% Found (((fun (P:Type) (x9:(((cR X) x7)->(((cR x7) X)->P)))=> (((((and_rect ((cR X) x7)) ((cR x7) X)) P) x9) x8)) ((cR X0) x0)) (fun (x9:((cR X) x7)) (x12:((cR x7) X))=> x12)) as proof of ((cR X0) x0)
% Found x50:=(x5 x20):((cR X0) x0)
% Found (x5 x20) as proof of ((cR X) x0)
% Found (x5 x20) as proof of ((cR X) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x7:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x7 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x7:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x7 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found (x2 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x20:=(x2 x31):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Instantiate: X0:=X:fofType
% Found (x2 x31) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x31) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x40:=(x4 x50):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x40:=(x4 x51):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Instantiate: X:=X0:fofType
% Found (x4 x51) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x4 x51) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x9:((cR x4) X)
% Instantiate: X:=x0:fofType;X0:=x4:fofType
% Found x9 as proof of ((cR X0) x0)
% Found x40:=(x4 x51):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x4 x51) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x4 x51) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x4 x51) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found x20:=(x2 x31):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x31) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x31) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x31) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found (x20 x50) as proof of False
% Found ((fun (x6:((cR X) x0))=> ((x2 x6) x00)) x50) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))=> ((fun (x6:((cR X) x0))=> ((x2 x6) x00)) x50)) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))=> ((fun (x6:((cR X) x0))=> ((x2 x6) x00)) x50)) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found (x40 x30) as proof of False
% Found ((fun (x6:((cR X0) x0))=> ((x4 x6) x00)) x30) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((fun (x6:((cR X0) x0))=> ((x4 x6) x00)) x30)) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((fun (x6:((cR X0) x0))=> ((x4 x6) x00)) x30)) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found (x20 x00) as proof of False
% Found ((x2 x30) x00) as proof of False
% Found (fun (x7:((and ((cR X0) x6)) ((cR x6) X0)))=> ((x2 x30) x00)) as proof of False
% Found (fun (x6:fofType) (x7:((and ((cR X0) x6)) ((cR x6) X0)))=> ((x2 x30) x00)) as proof of (((and ((cR X0) x6)) ((cR x6) X0))->False)
% Found (fun (x6:fofType) (x7:((and ((cR X0) x6)) ((cR x6) X0)))=> ((x2 x30) x00)) as proof of (forall (x:fofType), (((and ((cR X0) x)) ((cR x) X0))->False))
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found (x40 x00) as proof of False
% Found ((x4 x50) x00) as proof of False
% Found (fun (x7:((and ((cR X) x6)) ((cR x6) X)))=> ((x4 x50) x00)) as proof of False
% Found (fun (x6:fofType) (x7:((and ((cR X) x6)) ((cR x6) X)))=> ((x4 x50) x00)) as proof of (((and ((cR X) x6)) ((cR x6) X))->False)
% Found (fun (x6:fofType) (x7:((and ((cR X) x6)) ((cR x6) X)))=> ((x4 x50) x00)) as proof of (forall (x:fofType), (((and ((cR X) x)) ((cR x) X))->False))
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found (x40 x30) as proof of False
% Found ((fun (x6:((cR X0) x0))=> ((x4 x6) x00)) x30) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((fun (x6:((cR X0) x0))=> ((x4 x6) x00)) x30)) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((fun (x6:((cR X0) x0))=> ((x4 x6) x00)) x30)) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found (x20 x00) as proof of False
% Found ((x2 x30) x00) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x2 x30) x00)) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x2 x30) x00)) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found (x20 x50) as proof of False
% Found ((fun (x6:((cR X) x0))=> ((x2 x6) x00)) x50) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))=> ((fun (x6:((cR X) x0))=> ((x2 x6) x00)) x50)) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))=> ((fun (x6:((cR X) x0))=> ((x2 x6) x00)) x50)) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found (x40 x00) as proof of False
% Found ((x4 x50) x00) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))=> ((x4 x50) x00)) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))=> ((x4 x50) x00)) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x60:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x60 as proof of ((cR X) x0)
% Found x20:=(x2 x30):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Instantiate: X0:=X:fofType
% Found x20 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x12:((cR x7) X)
% Instantiate: X:=x0:fofType;X0:=x7:fofType
% Found (fun (x12:((cR x7) X))=> x12) as proof of ((cR X0) x0)
% Found (fun (x9:((cR X) x7)) (x12:((cR x7) X))=> x12) as proof of (((cR x7) X)->((cR X0) x0))
% Found (fun (x9:((cR X) x7)) (x12:((cR x7) X))=> x12) as proof of (((cR X) x7)->(((cR x7) X)->((cR X0) x0)))
% Found (and_rect20 (fun (x9:((cR X) x7)) (x12:((cR x7) X))=> x12)) as proof of ((cR X0) x0)
% Found ((and_rect2 ((cR X0) x0)) (fun (x9:((cR X) x7)) (x12:((cR x7) X))=> x12)) as proof of ((cR X0) x0)
% Found (((fun (P:Type) (x9:(((cR X) x7)->(((cR x7) X)->P)))=> (((((and_rect ((cR X) x7)) ((cR x7) X)) P) x9) x8)) ((cR X0) x0)) (fun (x9:((cR X) x7)) (x12:((cR x7) X))=> x12)) as proof of ((cR X0) x0)
% Found (fun (x8:((and ((cR X) x7)) ((cR x7) X)))=> (((fun (P:Type) (x9:(((cR X) x7)->(((cR x7) X)->P)))=> (((((and_rect ((cR X) x7)) ((cR x7) X)) P) x9) x8)) ((cR X0) x0)) (fun (x9:((cR X) x7)) (x12:((cR x7) X))=> x12))) as proof of ((cR X0) x0)
% Found x20:=(x2 x30):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x20 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x20:=(x2 x30):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x50:=(x5 x40):((cR X0) x0)
% Found (x5 x40) as proof of ((cR X0) x0)
% Found (x5 x40) as proof of ((cR X0) x0)
% Found ((x4 (x5 x40)) x00) as proof of False
% Found (fun (x7:((and ((cR X) x6)) ((cR x6) X)))=> ((x4 (x5 x40)) x00)) as proof of False
% Found (fun (x6:fofType) (x7:((and ((cR X) x6)) ((cR x6) X)))=> ((x4 (x5 x40)) x00)) as proof of (((and ((cR X) x6)) ((cR x6) X))->False)
% Found (fun (x6:fofType) (x7:((and ((cR X) x6)) ((cR x6) X)))=> ((x4 (x5 x40)) x00)) as proof of (forall (x:fofType), (((and ((cR X) x)) ((cR x) X))->False))
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found ((x2 (x3 x20)) x00) as proof of False
% Found (fun (x7:((and ((cR X0) x6)) ((cR x6) X0)))=> ((x2 (x3 x20)) x00)) as proof of False
% Found (fun (x6:fofType) (x7:((and ((cR X0) x6)) ((cR x6) X0)))=> ((x2 (x3 x20)) x00)) as proof of (((and ((cR X0) x6)) ((cR x6) X0))->False)
% Found (fun (x6:fofType) (x7:((and ((cR X0) x6)) ((cR x6) X0)))=> ((x2 (x3 x20)) x00)) as proof of (forall (x:fofType), (((and ((cR X0) x)) ((cR x) X0))->False))
% Found x12:((cR x7) X)
% Instantiate: X:=x0:fofType;X0:=x7:fofType
% Found (fun (x12:((cR x7) X))=> x12) as proof of ((cR X0) x0)
% Found (fun (x9:((cR X) x7)) (x12:((cR x7) X))=> x12) as proof of (((cR x7) X)->((cR X0) x0))
% Found (fun (x9:((cR X) x7)) (x12:((cR x7) X))=> x12) as proof of (((cR X) x7)->(((cR x7) X)->((cR X0) x0)))
% Found (and_rect20 (fun (x9:((cR X) x7)) (x12:((cR x7) X))=> x12)) as proof of ((cR X0) x0)
% Found ((and_rect2 ((cR X0) x0)) (fun (x9:((cR X) x7)) (x12:((cR x7) X))=> x12)) as proof of ((cR X0) x0)
% Found (((fun (P:Type) (x9:(((cR X) x7)->(((cR x7) X)->P)))=> (((((and_rect ((cR X) x7)) ((cR x7) X)) P) x9) x8)) ((cR X0) x0)) (fun (x9:((cR X) x7)) (x12:((cR x7) X))=> x12)) as proof of ((cR X0) x0)
% Found (((fun (P:Type) (x9:(((cR X) x7)->(((cR x7) X)->P)))=> (((((and_rect ((cR X) x7)) ((cR x7) X)) P) x9) x8)) ((cR X0) x0)) (fun (x9:((cR X) x7)) (x12:((cR x7) X))=> x12)) as proof of ((cR X0) x0)
% Found x4:(((cR X0) x0)->(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))))
% Instantiate: X:=x0:fofType;X0:=x7:fofType
% Found (fun (x9:((cR X) x7))=> x4) as proof of (((cR x7) X)->(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))))
% Found (fun (x9:((cR X) x7))=> x4) as proof of (((cR X) x7)->(((cR x7) X)->(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))))
% Found (and_rect20 (fun (x9:((cR X) x7))=> x4)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found ((and_rect2 (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))) (fun (x9:((cR X) x7))=> x4)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (((fun (P:Type) (x9:(((cR X) x7)->(((cR x7) X)->P)))=> (((((and_rect ((cR X) x7)) ((cR x7) X)) P) x9) x8)) (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))) (fun (x9:((cR X) x7))=> x4)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (((fun (P:Type) (x9:(((cR X) x7)->(((cR x7) X)->P)))=> (((((and_rect ((cR X) x7)) ((cR x7) X)) P) x9) x8)) (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))) (fun (x9:((cR X) x7))=> x4)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x5 (((fun (P:Type) (x9:(((cR X) x7)->(((cR x7) X)->P)))=> (((((and_rect ((cR X) x7)) ((cR x7) X)) P) x9) x8)) (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))) (fun (x9:((cR X) x7))=> x4))) as proof of ((cR X0) x0)
% Found (fun (x8:((and ((cR X) x7)) ((cR x7) X)))=> (x5 (((fun (P:Type) (x9:(((cR X) x7)->(((cR x7) X)->P)))=> (((((and_rect ((cR X) x7)) ((cR x7) X)) P) x9) x8)) (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))) (fun (x9:((cR X) x7))=> x4)))) as proof of ((cR X0) x0)
% Found x40:=(x4 x50):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x4:(((cR X0) x0)->(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))))
% Instantiate: X:=x0:fofType;X0:=x7:fofType
% Found (fun (x9:((cR X) x7))=> x4) as proof of (((cR x7) X)->(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))))
% Found (fun (x9:((cR X) x7))=> x4) as proof of (((cR X) x7)->(((cR x7) X)->(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))))
% Found (and_rect20 (fun (x9:((cR X) x7))=> x4)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found ((and_rect2 (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))) (fun (x9:((cR X) x7))=> x4)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (((fun (P:Type) (x9:(((cR X) x7)->(((cR x7) X)->P)))=> (((((and_rect ((cR X) x7)) ((cR x7) X)) P) x9) x8)) (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))) (fun (x9:((cR X) x7))=> x4)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (fun (x8:((and ((cR X) x7)) ((cR x7) X)))=> (((fun (P:Type) (x9:(((cR X) x7)->(((cR x7) X)->P)))=> (((((and_rect ((cR X) x7)) ((cR x7) X)) P) x9) x8)) (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))) (fun (x9:((cR X) x7))=> x4))) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found x20:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x20 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x20:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x20 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found ((x4 x30) x00) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x4 x30) x00)) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x4 x30) x00)) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x40:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x40 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found x40:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x40 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found ((x2 x30) x00) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x2 x30) x00)) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x2 x30) x00)) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x40:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Instantiate: X:=X0:fofType
% Found x40 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x40:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Instantiate: X:=X0:fofType
% Found x40 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x20:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Instantiate: X0:=X:fofType
% Found x20 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found x20:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Instantiate: X0:=X:fofType
% Found x20 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x30:((cR X) x0)
% Instantiate: X:=x0:fofType;x4:=X:fofType
% Found x30 as proof of ((cR x4) X)
% Found x30:((cR X) x0)
% Instantiate: x4:=x0:fofType
% Found x30 as proof of ((cR X) x4)
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x4)
% Found ((conj00 x30) x30) as proof of ((and ((cR X) x4)) ((cR x4) X))
% Found (((conj0 ((cR x4) X)) x30) x30) as proof of ((and ((cR X) x4)) ((cR x4) X))
% Found ((((conj ((cR X) x4)) ((cR x4) X)) x30) x30) as proof of ((and ((cR X) x4)) ((cR x4) X))
% Found ((((conj ((cR X) x4)) ((cR x4) X)) x30) x30) as proof of ((and ((cR X) x4)) ((cR x4) X))
% Found (ex_intro000 ((((conj ((cR X) x4)) ((cR x4) X)) x30) x30)) as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found ((ex_intro00 X) ((((conj ((cR X) X)) ((cR X) X)) x30) x30)) as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found (((ex_intro0 (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))) X) ((((conj ((cR X) X)) ((cR X) X)) x30) x30)) as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found ((((ex_intro fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))) X) ((((conj ((cR X) X)) ((cR X) X)) x30) x30)) as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found ((((ex_intro fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))) X) ((((conj ((cR X) X)) ((cR X) X)) x30) x30)) as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found (x20 ((((ex_intro fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))) X) ((((conj ((cR X) X)) ((cR X) X)) x30) x30))) as proof of False
% Found ((x2 x31) ((((ex_intro fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))) X) ((((conj ((cR X) X)) ((cR X) X)) x30) x30))) as proof of False
% Found ((x2 x31) ((((ex_intro fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))) X) ((((conj ((cR X) X)) ((cR X) X)) x30) x30))) as proof of False
% Found x30:((cR X) x0)
% Found (fun (x5:((((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)->((cR X0) x0)))=> x30) as proof of ((cR X) x0)
% Found (fun (x5:((((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)->((cR X0) x0)))=> x30) as proof of (((((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)->((cR X0) x0))->((cR X) x0))
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x000:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x000 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x000:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x000 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x8:((cR x5) X)
% Instantiate: X:=x0:fofType;X0:=x5:fofType
% Found x8 as proof of ((cR X0) x0)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Instantiate: X0:=X:fofType
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x50:=(x5 x40):((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found x60:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x60 as proof of ((cR X) x0)
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x50:=(x5 x40):((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found x50:=(x5 x40):((cR X0) x0)
% Found (x5 x40) as proof of ((cR X0) x0)
% Found (x5 x40) as proof of ((cR X0) x0)
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x20:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Instantiate: X0:=X:fofType
% Found x20 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found (x20 x6) as proof of False
% Found ((x2 x30) x6) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x2 x30) x6)) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x2 x30) x6)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found (x40 x30) as proof of False
% Found ((fun (x7:((cR X0) x0))=> ((x4 x7) x6)) x30) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((fun (x7:((cR X0) x0))=> ((x4 x7) x6)) x30)) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((fun (x7:((cR X0) x0))=> ((x4 x7) x6)) x30)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x50:=(x5 x41):((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found (x5 x41) as proof of ((cR X) x0)
% Found (x5 x41) as proof of ((cR X) x0)
% Found x20:=(fun (x9:((cR X) x0))=> ((x2 x9) x00)):(((cR X) x0)->False)
% Instantiate: X:=x6:fofType;X0:=x0:fofType
% Found (fun (x9:((cR X) x0))=> ((x2 x9) x00)) as proof of (((cR x6) X0)->False)
% Found (fun (x8:((cR X0) x6)) (x9:((cR X) x0))=> ((x2 x9) x00)) as proof of (((cR x6) X0)->False)
% Found (fun (x8:((cR X0) x6)) (x9:((cR X) x0))=> ((x2 x9) x00)) as proof of (((cR X0) x6)->(((cR x6) X0)->False))
% Found (and_rect20 (fun (x8:((cR X0) x6)) (x9:((cR X) x0))=> ((x2 x9) x00))) as proof of False
% Found ((and_rect2 False) (fun (x8:((cR X0) x6)) (x9:((cR X) x0))=> ((x2 x9) x00))) as proof of False
% Found (((fun (P:Type) (x8:(((cR X0) x6)->(((cR x6) X0)->P)))=> (((((and_rect ((cR X0) x6)) ((cR x6) X0)) P) x8) x7)) False) (fun (x8:((cR X0) x6)) (x9:((cR X) x0))=> ((x2 x9) x00))) as proof of False
% Found (fun (x7:((and ((cR X0) x6)) ((cR x6) X0)))=> (((fun (P:Type) (x8:(((cR X0) x6)->(((cR x6) X0)->P)))=> (((((and_rect ((cR X0) x6)) ((cR x6) X0)) P) x8) x7)) False) (fun (x8:((cR X0) x6)) (x9:((cR X) x0))=> ((x2 x9) x00)))) as proof of False
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found ((x2 x30) x6) as proof of False
% Found (fun (x8:((and ((cR X0) x7)) ((cR x7) X0)))=> ((x2 x30) x6)) as proof of False
% Found (fun (x8:((and ((cR X0) x7)) ((cR x7) X0)))=> ((x2 x30) x6)) as proof of (((and ((cR X0) x7)) ((cR x7) X0))->False)
% Found x50:((cR X0) x0)
% Found x50 as proof of ((cR X0) x0)
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found ((x4 x50) x6) as proof of False
% Found (fun (x8:((and ((cR X) x7)) ((cR x7) X)))=> ((x4 x50) x6)) as proof of False
% Found (fun (x8:((and ((cR X) x7)) ((cR x7) X)))=> ((x4 x50) x6)) as proof of (((and ((cR X) x7)) ((cR x7) X))->False)
% Found x50:=(x5 x41):((cR X0) x0)
% Found (x5 x41) as proof of ((cR X0) x0)
% Found (x5 x41) as proof of ((cR X0) x0)
% Found x4:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x4 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x20:=(x2 x30):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x4:(((cR X0) x0)->(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))))
% Instantiate: X:=x0:fofType;X0:=x7:fofType
% Found (fun (x9:((cR X) x7))=> x4) as proof of (((cR x7) X)->(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))))
% Found (fun (x9:((cR X) x7))=> x4) as proof of (((cR X) x7)->(((cR x7) X)->(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))))
% Found (and_rect20 (fun (x9:((cR X) x7))=> x4)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found ((and_rect2 (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))) (fun (x9:((cR X) x7))=> x4)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (((fun (P:Type) (x9:(((cR X) x7)->(((cR x7) X)->P)))=> (((((and_rect ((cR X) x7)) ((cR x7) X)) P) x9) x8)) (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))) (fun (x9:((cR X) x7))=> x4)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (fun (x8:((and ((cR X) x7)) ((cR x7) X)))=> (((fun (P:Type) (x9:(((cR X) x7)->(((cR x7) X)->P)))=> (((((and_rect ((cR X) x7)) ((cR x7) X)) P) x9) x8)) (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))) (fun (x9:((cR X) x7))=> x4))) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x31:((cR X) x0)
% Instantiate: x4:=x0:fofType
% Found x31 as proof of ((cR X) x4)
% Found x31:((cR X) x0)
% Instantiate: X:=x0:fofType;x4:=X:fofType
% Found x31 as proof of ((cR x4) X)
% Found x31:((cR X) x0)
% Instantiate: X:=x0:fofType
% Found x31 as proof of ((cR x4) X)
% Found ((conj00 x31) x31) as proof of ((and ((cR X) x4)) ((cR x4) X))
% Found (((conj0 ((cR x4) X)) x31) x31) as proof of ((and ((cR X) x4)) ((cR x4) X))
% Found ((((conj ((cR X) x4)) ((cR x4) X)) x31) x31) as proof of ((and ((cR X) x4)) ((cR x4) X))
% Found ((((conj ((cR X) x4)) ((cR x4) X)) x31) x31) as proof of ((and ((cR X) x4)) ((cR x4) X))
% Found (ex_intro000 ((((conj ((cR X) x4)) ((cR x4) X)) x31) x31)) as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found ((ex_intro00 x0) ((((conj ((cR X) x0)) ((cR x0) X)) x31) x31)) as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found (((ex_intro0 (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))) x0) ((((conj ((cR X) x0)) ((cR x0) X)) x31) x31)) as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found ((((ex_intro fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))) x0) ((((conj ((cR X) x0)) ((cR x0) X)) x31) x31)) as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found ((((ex_intro fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))) x0) ((((conj ((cR X) x0)) ((cR x0) X)) x31) x31)) as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found ((x2 x31) ((((ex_intro fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))) x0) ((((conj ((cR X) x0)) ((cR x0) X)) x31) x31))) as proof of False
% Found ((x2 x31) ((((ex_intro fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))) x0) ((((conj ((cR X) x0)) ((cR x0) X)) x31) x31))) as proof of False
% Found x4:(((cR X0) x0)->(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))))
% Instantiate: X:=x0:fofType;X0:=x7:fofType
% Found (fun (x9:((cR X) x7))=> x4) as proof of (((cR x7) X)->(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))))
% Found (fun (x9:((cR X) x7))=> x4) as proof of (((cR X) x7)->(((cR x7) X)->(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))))
% Found (and_rect20 (fun (x9:((cR X) x7))=> x4)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found ((and_rect2 (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))) (fun (x9:((cR X) x7))=> x4)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (((fun (P:Type) (x9:(((cR X) x7)->(((cR x7) X)->P)))=> (((((and_rect ((cR X) x7)) ((cR x7) X)) P) x9) x8)) (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))) (fun (x9:((cR X) x7))=> x4)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (((fun (P:Type) (x9:(((cR X) x7)->(((cR x7) X)->P)))=> (((((and_rect ((cR X) x7)) ((cR x7) X)) P) x9) x8)) (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))) (fun (x9:((cR X) x7))=> x4)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x5 (((fun (P:Type) (x9:(((cR X) x7)->(((cR x7) X)->P)))=> (((((and_rect ((cR X) x7)) ((cR x7) X)) P) x9) x8)) (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))) (fun (x9:((cR X) x7))=> x4))) as proof of ((cR X0) x0)
% Found (fun (x8:((and ((cR X) x7)) ((cR x7) X)))=> (x5 (((fun (P:Type) (x9:(((cR X) x7)->(((cR x7) X)->P)))=> (((((and_rect ((cR X) x7)) ((cR x7) X)) P) x9) x8)) (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))) (fun (x9:((cR X) x7))=> x4)))) as proof of ((cR X0) x0)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found (x4 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x4 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found (x4 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x4 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x31:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x31 as proof of ((cR X0) x0)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found (x40 x30) as proof of False
% Found ((fun (x6:((cR X0) x0))=> ((x4 x6) x00)) x30) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((fun (x6:((cR X0) x0))=> ((x4 x6) x00)) x30)) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((fun (x6:((cR X0) x0))=> ((x4 x6) x00)) x30)) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found (x20 x00) as proof of False
% Found ((x2 x30) x00) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x2 x30) x00)) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x2 x30) x00)) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found (x40 x30) as proof of False
% Found ((fun (x6:((cR X0) x0))=> ((x4 x6) x00)) x30) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((fun (x6:((cR X0) x0))=> ((x4 x6) x00)) x30)) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((fun (x6:((cR X0) x0))=> ((x4 x6) x00)) x30)) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found ((x2 x50) x00) as proof of False
% Found ((x2 x50) x00) as proof of False
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x50:((cR X0) x0)
% Found x50 as proof of ((cR X0) x0)
% Found ((x4 x50) x00) as proof of False
% Found ((x4 x50) x00) as proof of False
% Found x30:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x30 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x4 x30) as proof of ((cR X) x0)
% Found (x4 x30) as proof of ((cR X) x0)
% Found (x4 x30) as proof of ((cR X) x0)
% Found x50:=(x5 x40):((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Instantiate: X0:=X:fofType
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x40:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x40 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found x20:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x20 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Instantiate: X0:=X:fofType
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x12:((cR x7) X)
% Instantiate: X:=x0:fofType;X0:=x7:fofType
% Found x12 as proof of ((cR X0) x0)
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x12:((cR x7) X0)
% Instantiate: X:=x7:fofType;X0:=x0:fofType
% Found x12 as proof of ((cR X) x0)
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x20:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x20 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x20:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x20 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x50:=(x5 x40):((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found x20:=(x2 x30):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Instantiate: X0:=X:fofType
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x20:=(x2 x30):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x20:=(x2 x30):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Instantiate: X0:=X:fofType
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x41:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x41 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x5 x41) as proof of ((cR X) x0)
% Found (x5 x41) as proof of ((cR X) x0)
% Found (x5 x41) as proof of ((cR X) x0)
% Found x20:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x20 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x20:=(x2 x30):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x20:=(fun (x9:((cR X) x0))=> ((x2 x9) x00)):(((cR X) x0)->False)
% Instantiate: X:=x6:fofType;X0:=x0:fofType
% Found (fun (x9:((cR X) x0))=> ((x2 x9) x00)) as proof of (((cR x6) X0)->False)
% Found (fun (x8:((cR X0) x6)) (x9:((cR X) x0))=> ((x2 x9) x00)) as proof of (((cR x6) X0)->False)
% Found (fun (x8:((cR X0) x6)) (x9:((cR X) x0))=> ((x2 x9) x00)) as proof of (((cR X0) x6)->(((cR x6) X0)->False))
% Found (and_rect20 (fun (x8:((cR X0) x6)) (x9:((cR X) x0))=> ((x2 x9) x00))) as proof of False
% Found ((and_rect2 False) (fun (x8:((cR X0) x6)) (x9:((cR X) x0))=> ((x2 x9) x00))) as proof of False
% Found (((fun (P:Type) (x8:(((cR X0) x6)->(((cR x6) X0)->P)))=> (((((and_rect ((cR X0) x6)) ((cR x6) X0)) P) x8) x7)) False) (fun (x8:((cR X0) x6)) (x9:((cR X) x0))=> ((x2 x9) x00))) as proof of False
% Found (fun (x7:((and ((cR X0) x6)) ((cR x6) X0)))=> (((fun (P:Type) (x8:(((cR X0) x6)->(((cR x6) X0)->P)))=> (((((and_rect ((cR X0) x6)) ((cR x6) X0)) P) x8) x7)) False) (fun (x8:((cR X0) x6)) (x9:((cR X) x0))=> ((x2 x9) x00)))) as proof of False
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x20:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x20 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x4:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x4 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x50:((cR X0) x0)
% Found (fun (x7:((and ((cR X) x6)) ((cR x6) X)))=> x50) as proof of ((cR X0) x0)
% Found (fun (x7:((and ((cR X) x6)) ((cR x6) X)))=> x50) as proof of (((and ((cR X) x6)) ((cR x6) X))->((cR X0) x0))
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found (x40 x6) as proof of False
% Found ((x4 x50) x6) as proof of False
% Found ((x4 x50) x6) as proof of False
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found (x20 x6) as proof of False
% Found ((x2 x30) x6) as proof of False
% Found ((x2 x30) x6) as proof of False
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x50:=(x5 x40):((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found x50:=(x5 x40):((cR X0) x0)
% Found (x5 x40) as proof of ((cR X0) x0)
% Found (x5 x40) as proof of ((cR X0) x0)
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x4:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x4 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x12:((cR x7) X)
% Instantiate: X:=x0:fofType;X0:=x7:fofType
% Found x12 as proof of ((cR X0) x0)
% Found x50:=(x5 x40):((cR X0) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x50:=(x5 x40):((cR X0) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found ((x2 x50) x6) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))=> ((x2 x50) x6)) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))=> ((x2 x50) x6)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found ((x4 x30) x6) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x4 x30) x6)) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x4 x30) x6)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x50:((cR X0) x0)
% Found x50 as proof of ((cR X0) x0)
% Found ((x4 x50) x6) as proof of False
% Found (fun (x8:((and ((cR X) x7)) ((cR x7) X)))=> ((x4 x50) x6)) as proof of False
% Found (fun (x7:fofType) (x8:((and ((cR X) x7)) ((cR x7) X)))=> ((x4 x50) x6)) as proof of (((and ((cR X) x7)) ((cR x7) X))->False)
% Found (fun (x7:fofType) (x8:((and ((cR X) x7)) ((cR x7) X)))=> ((x4 x50) x6)) as proof of (forall (x:fofType), (((and ((cR X) x)) ((cR x) X))->False))
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found ((x2 x30) x6) as proof of False
% Found (fun (x8:((and ((cR X0) x7)) ((cR x7) X0)))=> ((x2 x30) x6)) as proof of False
% Found (fun (x7:fofType) (x8:((and ((cR X0) x7)) ((cR x7) X0)))=> ((x2 x30) x6)) as proof of (((and ((cR X0) x7)) ((cR x7) X0))->False)
% Found (fun (x7:fofType) (x8:((and ((cR X0) x7)) ((cR x7) X0)))=> ((x2 x30) x6)) as proof of (forall (x:fofType), (((and ((cR X0) x)) ((cR x) X0))->False))
% Found x50:=(x5 x40):((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found ((x2 x30) x6) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x2 x30) x6)) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x2 x30) x6)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x20:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Instantiate: X0:=X:fofType
% Found x20 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x50:((cR X0) x0)
% Found x50 as proof of ((cR X0) x0)
% Found ((x4 x50) x6) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))=> ((x4 x50) x6)) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))=> ((x4 x50) x6)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x20:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Instantiate: X0:=X:fofType
% Found x20 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x5 x20) as proof of ((cR X0) x0)
% Found (x5 x20) as proof of ((cR X0) x0)
% Found x31:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x31 as proof of ((cR X0) x0)
% Found x20:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Instantiate: X0:=X:fofType
% Found x20 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x5 x20) as proof of ((cR X0) x0)
% Found (x5 x20) as proof of ((cR X0) x0)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Instantiate: X0:=X:fofType
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x31:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x31 as proof of ((cR X0) x0)
% Found x40:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x40 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found x20:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x20 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x40:=(x4 x50):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Instantiate: X:=X0:fofType
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found ((x4 x30) x00) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x4 x30) x00)) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x4 x30) x00)) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found ((x2 x30) x00) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x2 x30) x00)) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x2 x30) x00)) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x20:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Instantiate: X0:=X:fofType
% Found x20 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x40:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Instantiate: X:=X0:fofType
% Found x40 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found (x40 x30) as proof of False
% Found ((fun (x6:((cR X0) x0))=> ((x4 x6) x00)) x30) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((fun (x6:((cR X0) x0))=> ((x4 x6) x00)) x30)) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((fun (x6:((cR X0) x0))=> ((x4 x6) x00)) x30)) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x20:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Instantiate: X0:=X:fofType
% Found x20 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x40:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Instantiate: X:=X0:fofType
% Found x40 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found (x20 x00) as proof of False
% Found ((x2 x30) x00) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x2 x30) x00)) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x2 x30) x00)) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found (x40 x30) as proof of False
% Found ((fun (x6:((cR X0) x0))=> ((x4 x6) x00)) x30) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((fun (x6:((cR X0) x0))=> ((x4 x6) x00)) x30)) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((fun (x6:((cR X0) x0))=> ((x4 x6) x00)) x30)) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x40:=(x4 x50):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Instantiate: X:=X0:fofType
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Instantiate: X0:=X:fofType
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x40:=(x4 x50):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Instantiate: X:=X0:fofType
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x30:=(x3 x20):((cR X) x0)
% Instantiate: X0:=X:fofType
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x50:=(x5 x40):((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Instantiate: X0:=X:fofType
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Instantiate: X0:=X:fofType
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x50:=(x5 x40):((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found x40:=(x4 x30):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x4 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x4 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x20:=(x2 x30):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x40:=(x4 x50):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x30:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x30 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x4 x30) as proof of ((cR X) x0)
% Found (x4 x30) as proof of ((cR X) x0)
% Found (fun (x4:((not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))->((cR X0) x0)))=> (x4 x30)) as proof of ((cR X) x0)
% Found (fun (x4:((not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))->((cR X0) x0)))=> (x4 x30)) as proof of (((not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))->((cR X0) x0))->((cR X) x0))
% Found x12:((cR x5) X)
% Instantiate: X:=x0:fofType;X0:=x5:fofType
% Found (fun (x12:((cR x5) X))=> x12) as proof of ((cR X0) x0)
% Found (fun (x9:((cR X) x5)) (x12:((cR x5) X))=> x12) as proof of (((cR x5) X)->((cR X0) x0))
% Found (fun (x9:((cR X) x5)) (x12:((cR x5) X))=> x12) as proof of (((cR X) x5)->(((cR x5) X)->((cR X0) x0)))
% Found (and_rect20 (fun (x9:((cR X) x5)) (x12:((cR x5) X))=> x12)) as proof of ((cR X0) x0)
% Found ((and_rect2 ((cR X0) x0)) (fun (x9:((cR X) x5)) (x12:((cR x5) X))=> x12)) as proof of ((cR X0) x0)
% Found (((fun (P:Type) (x9:(((cR X) x5)->(((cR x5) X)->P)))=> (((((and_rect ((cR X) x5)) ((cR x5) X)) P) x9) x6)) ((cR X0) x0)) (fun (x9:((cR X) x5)) (x12:((cR x5) X))=> x12)) as proof of ((cR X0) x0)
% Found (((fun (P:Type) (x9:(((cR X) x5)->(((cR x5) X)->P)))=> (((((and_rect ((cR X) x5)) ((cR x5) X)) P) x9) x6)) ((cR X0) x0)) (fun (x9:((cR X) x5)) (x12:((cR x5) X))=> x12)) as proof of ((cR X0) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x50:=(x5 x40):((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found (x5 x40) as proof of ((cR X) x0)
% Found (fun (x5:((((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)->((cR X0) x0)))=> (x5 x40)) as proof of ((cR X) x0)
% Found (fun (x5:((((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)->((cR X0) x0)))=> (x5 x40)) as proof of (((((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)->((cR X0) x0))->((cR X) x0))
% Found x30:=(x3 x20):((cR X) x0)
% Instantiate: X0:=X:fofType
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x30:=(x3 x20):((cR X) x0)
% Instantiate: X0:=X:fofType
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Instantiate: X0:=X:fofType
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x20:=(x2 x30):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found x50:((cR X0) x0)
% Found (fun (x7:((and ((cR X) x6)) ((cR x6) X)))=> x50) as proof of ((cR X0) x0)
% Found (fun (x7:((and ((cR X) x6)) ((cR x6) X)))=> x50) as proof of (((and ((cR X) x6)) ((cR x6) X))->((cR X0) x0))
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Instantiate: X0:=X:fofType
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Instantiate: X0:=X:fofType
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x20:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x20 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x3 x20) as proof of ((cR x4) X)
% Found (x3 x20) as proof of ((cR x4) X)
% Found (x3 x20) as proof of ((cR x4) X)
% Found (x3 x20) as proof of ((cR x4) X)
% Found x30:=(x3 x20):((cR X) x0)
% Instantiate: X0:=X:fofType
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x20:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x20 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x3 x20) as proof of ((cR x4) X)
% Found (x3 x20) as proof of ((cR x4) X)
% Found (x3 x20) as proof of ((cR x4) X)
% Found (x3 x20) as proof of ((cR x4) X)
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found x40:=(fun (x9:((cR X0) x0))=> ((x4 x9) x000)):(((cR X0) x0)->False)
% Instantiate: X:=x0:fofType;X0:=x6:fofType
% Found (fun (x9:((cR X0) x0))=> ((x4 x9) x000)) as proof of (((cR x6) X)->False)
% Found (fun (x8:((cR X) x6)) (x9:((cR X0) x0))=> ((x4 x9) x000)) as proof of (((cR x6) X)->False)
% Found (fun (x8:((cR X) x6)) (x9:((cR X0) x0))=> ((x4 x9) x000)) as proof of (((cR X) x6)->(((cR x6) X)->False))
% Found (and_rect20 (fun (x8:((cR X) x6)) (x9:((cR X0) x0))=> ((x4 x9) x000))) as proof of False
% Found ((and_rect2 False) (fun (x8:((cR X) x6)) (x9:((cR X0) x0))=> ((x4 x9) x000))) as proof of False
% Found (((fun (P:Type) (x8:(((cR X) x6)->(((cR x6) X)->P)))=> (((((and_rect ((cR X) x6)) ((cR x6) X)) P) x8) x7)) False) (fun (x8:((cR X) x6)) (x9:((cR X0) x0))=> ((x4 x9) x000))) as proof of False
% Found (fun (x7:((and ((cR X) x6)) ((cR x6) X)))=> (((fun (P:Type) (x8:(((cR X) x6)->(((cR x6) X)->P)))=> (((((and_rect ((cR X) x6)) ((cR x6) X)) P) x8) x7)) False) (fun (x8:((cR X) x6)) (x9:((cR X0) x0))=> ((x4 x9) x000)))) as proof of False
% Found x40:=(fun (x9:((cR X0) x0))=> ((x4 x9) x000)):(((cR X0) x0)->False)
% Instantiate: X:=x0:fofType;X0:=x6:fofType
% Found (fun (x9:((cR X0) x0))=> ((x4 x9) x000)) as proof of (((cR x6) X)->False)
% Found (fun (x8:((cR X) x6)) (x9:((cR X0) x0))=> ((x4 x9) x000)) as proof of (((cR x6) X)->False)
% Found (fun (x8:((cR X) x6)) (x9:((cR X0) x0))=> ((x4 x9) x000)) as proof of (((cR X) x6)->(((cR x6) X)->False))
% Found (and_rect20 (fun (x8:((cR X) x6)) (x9:((cR X0) x0))=> ((x4 x9) x000))) as proof of False
% Found ((and_rect2 False) (fun (x8:((cR X) x6)) (x9:((cR X0) x0))=> ((x4 x9) x000))) as proof of False
% Found (((fun (P:Type) (x8:(((cR X) x6)->(((cR x6) X)->P)))=> (((((and_rect ((cR X) x6)) ((cR x6) X)) P) x8) x7)) False) (fun (x8:((cR X) x6)) (x9:((cR X0) x0))=> ((x4 x9) x000))) as proof of False
% Found (fun (x000:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> (((fun (P:Type) (x8:(((cR X) x6)->(((cR x6) X)->P)))=> (((((and_rect ((cR X) x6)) ((cR x6) X)) P) x8) x7)) False) (fun (x8:((cR X) x6)) (x9:((cR X0) x0))=> ((x4 x9) x000)))) as proof of False
% Found (fun (x000:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> (((fun (P:Type) (x8:(((cR X) x6)->(((cR x6) X)->P)))=> (((((and_rect ((cR X) x6)) ((cR x6) X)) P) x8) x7)) False) (fun (x8:((cR X) x6)) (x9:((cR X0) x0))=> ((x4 x9) x000)))) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x5 (fun (x000:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> (((fun (P:Type) (x8:(((cR X) x6)->(((cR x6) X)->P)))=> (((((and_rect ((cR X) x6)) ((cR x6) X)) P) x8) x7)) False) (fun (x8:((cR X) x6)) (x9:((cR X0) x0))=> ((x4 x9) x000))))) as proof of ((cR X0) x0)
% Found (fun (x7:((and ((cR X) x6)) ((cR x6) X)))=> (x5 (fun (x000:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> (((fun (P:Type) (x8:(((cR X) x6)->(((cR x6) X)->P)))=> (((((and_rect ((cR X) x6)) ((cR x6) X)) P) x8) x7)) False) (fun (x8:((cR X) x6)) (x9:((cR X0) x0))=> ((x4 x9) x000)))))) as proof of ((cR X0) x0)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found (x40 x6) as proof of False
% Found ((x4 x50) x6) as proof of False
% Found (fun (x8:((and ((cR X) x7)) ((cR x7) X)))=> ((x4 x50) x6)) as proof of False
% Found (fun (x8:((and ((cR X) x7)) ((cR x7) X)))=> ((x4 x50) x6)) as proof of (((and ((cR X) x7)) ((cR x7) X))->False)
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found (x20 x6) as proof of False
% Found ((x2 x30) x6) as proof of False
% Found (fun (x8:((and ((cR X0) x7)) ((cR x7) X0)))=> ((x2 x30) x6)) as proof of False
% Found (fun (x8:((and ((cR X0) x7)) ((cR x7) X0)))=> ((x2 x30) x6)) as proof of (((and ((cR X0) x7)) ((cR x7) X0))->False)
% Found x40:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Instantiate: X:=X0:fofType
% Found x40 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x3 x40) as proof of ((cR X) x0)
% Found (x3 x40) as proof of ((cR X) x0)
% Found x20:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Instantiate: X0:=X:fofType
% Found x20 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x5 x20) as proof of ((cR X0) x0)
% Found (x5 x20) as proof of ((cR X0) x0)
% Found x40:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Instantiate: X:=X0:fofType
% Found x40 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x3 x40) as proof of ((cR X) x0)
% Found (x3 x40) as proof of ((cR X) x0)
% Found x40:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Instantiate: X:=X0:fofType
% Found x40 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x3 x40) as proof of ((cR X) x0)
% Found (x3 x40) as proof of ((cR X) x0)
% Found x20:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Instantiate: X0:=X:fofType
% Found x20 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x5 x20) as proof of ((cR X0) x0)
% Found (x5 x20) as proof of ((cR X0) x0)
% Found x20:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Instantiate: X0:=X:fofType
% Found x20 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x5 x20) as proof of ((cR X0) x0)
% Found (x5 x20) as proof of ((cR X0) x0)
% Found x20:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Instantiate: X0:=X:fofType
% Found x20 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x5 x20) as proof of ((cR X0) x0)
% Found (x5 x20) as proof of ((cR X0) x0)
% Found x40:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Instantiate: X:=X0:fofType
% Found x40 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x3 x40) as proof of ((cR X) x0)
% Found (x3 x40) as proof of ((cR X) x0)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found (x4 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x4 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found (x40 x00) as proof of False
% Found ((x4 x50) x00) as proof of False
% Found ((x4 x50) x00) as proof of False
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found (x20 x50) as proof of False
% Found ((fun (x6:((cR X) x0))=> ((x2 x6) x00)) x50) as proof of False
% Found ((fun (x6:((cR X) x0))=> ((x2 x6) x00)) x50) as proof of False
% Found x50:((cR X0) x0)
% Found (fun (x7:((and ((cR X) x6)) ((cR x6) X)))=> x50) as proof of ((cR X0) x0)
% Found (fun (x6:fofType) (x7:((and ((cR X) x6)) ((cR x6) X)))=> x50) as proof of (((and ((cR X) x6)) ((cR x6) X))->((cR X0) x0))
% Found (fun (x6:fofType) (x7:((and ((cR X) x6)) ((cR x6) X)))=> x50) as proof of (forall (x:fofType), (((and ((cR X) x)) ((cR x) X))->((cR X0) x0)))
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found (x2 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found (x4 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x4 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found (x2 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found (x2 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found (x4 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x4 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x000:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x000 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found (x2 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found (x2 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found (x4 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x4 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found (x4 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x4 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x50:=(x5 x40):((cR X0) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (fun (x5:((((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)->((cR X0) x0)))=> (x5 x40)) as proof of ((cR X) x0)
% Found (fun (x5:((((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)->((cR X0) x0)))=> (x5 x40)) as proof of (((((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)->((cR X0) x0))->((cR X) x0))
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found ((x2 (x3 x20)) x6) as proof of False
% Found (fun (x8:((and ((cR X0) x7)) ((cR x7) X0)))=> ((x2 (x3 x20)) x6)) as proof of False
% Found (fun (x8:((and ((cR X0) x7)) ((cR x7) X0)))=> ((x2 (x3 x20)) x6)) as proof of (((and ((cR X0) x7)) ((cR x7) X0))->False)
% Found x50:=(x5 x40):((cR X0) x0)
% Found (x5 x40) as proof of ((cR X0) x0)
% Found (x5 x40) as proof of ((cR X0) x0)
% Found ((x4 (x5 x40)) x6) as proof of False
% Found (fun (x8:((and ((cR X) x7)) ((cR x7) X)))=> ((x4 (x5 x40)) x6)) as proof of False
% Found (fun (x8:((and ((cR X) x7)) ((cR x7) X)))=> ((x4 (x5 x40)) x6)) as proof of (((and ((cR X) x7)) ((cR x7) X))->False)
% Found x60:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x60 as proof of ((cR X) x0)
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found ((x4 x30) x6) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x4 x30) x6)) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x4 x30) x6)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x9:((cR x6) X)
% Instantiate: X:=x0:fofType;X0:=x6:fofType
% Found (fun (x9:((cR x6) X))=> x9) as proof of ((cR X0) x0)
% Found (fun (x8:((cR X) x6)) (x9:((cR x6) X))=> x9) as proof of (((cR x6) X)->((cR X0) x0))
% Found (fun (x8:((cR X) x6)) (x9:((cR x6) X))=> x9) as proof of (((cR X) x6)->(((cR x6) X)->((cR X0) x0)))
% Found (and_rect20 (fun (x8:((cR X) x6)) (x9:((cR x6) X))=> x9)) as proof of ((cR X0) x0)
% Found ((and_rect2 ((cR X0) x0)) (fun (x8:((cR X) x6)) (x9:((cR x6) X))=> x9)) as proof of ((cR X0) x0)
% Found (((fun (P:Type) (x8:(((cR X) x6)->(((cR x6) X)->P)))=> (((((and_rect ((cR X) x6)) ((cR x6) X)) P) x8) x7)) ((cR X0) x0)) (fun (x8:((cR X) x6)) (x9:((cR x6) X))=> x9)) as proof of ((cR X0) x0)
% Found (fun (x7:((and ((cR X) x6)) ((cR x6) X)))=> (((fun (P:Type) (x8:(((cR X) x6)->(((cR x6) X)->P)))=> (((((and_rect ((cR X) x6)) ((cR x6) X)) P) x8) x7)) ((cR X0) x0)) (fun (x8:((cR X) x6)) (x9:((cR x6) X))=> x9))) as proof of ((cR X0) x0)
% Found x51:((cR X0) x0)
% Found x51 as proof of ((cR X0) x0)
% Found (x4 x51) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x4 x51) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x4 x51) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x50:((cR X0) x0)
% Found x50 as proof of ((cR X0) x0)
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found x31:((cR X) x0)
% Found x31 as proof of ((cR X) x0)
% Found (x2 x31) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x31) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x31) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x50:=(x5 x40):((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found (x5 x40) as proof of ((cR X) x0)
% Found (fun (x5:((not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))->((cR X0) x0)))=> (x5 x40)) as proof of ((cR X) x0)
% Found (fun (x5:((not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))->((cR X0) x0)))=> (x5 x40)) as proof of (((not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))->((cR X0) x0))->((cR X) x0))
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found ((x2 x30) x6) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x2 x30) x6)) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x2 x30) x6)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x40:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Instantiate: X:=X0:fofType
% Found x40 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x9:((cR x6) X)
% Instantiate: X:=x0:fofType;X0:=x6:fofType
% Found (fun (x9:((cR x6) X))=> x9) as proof of ((cR X0) x0)
% Found (fun (x8:((cR X) x6)) (x9:((cR x6) X))=> x9) as proof of (((cR x6) X)->((cR X0) x0))
% Found (fun (x8:((cR X) x6)) (x9:((cR x6) X))=> x9) as proof of (((cR X) x6)->(((cR x6) X)->((cR X0) x0)))
% Found (and_rect20 (fun (x8:((cR X) x6)) (x9:((cR x6) X))=> x9)) as proof of ((cR X0) x0)
% Found ((and_rect2 ((cR X0) x0)) (fun (x8:((cR X) x6)) (x9:((cR x6) X))=> x9)) as proof of ((cR X0) x0)
% Found (((fun (P:Type) (x8:(((cR X) x6)->(((cR x6) X)->P)))=> (((((and_rect ((cR X) x6)) ((cR x6) X)) P) x8) x7)) ((cR X0) x0)) (fun (x8:((cR X) x6)) (x9:((cR x6) X))=> x9)) as proof of ((cR X0) x0)
% Found (((fun (P:Type) (x8:(((cR X) x6)->(((cR x6) X)->P)))=> (((((and_rect ((cR X) x6)) ((cR x6) X)) P) x8) x7)) ((cR X0) x0)) (fun (x8:((cR X) x6)) (x9:((cR x6) X))=> x9)) as proof of ((cR X0) x0)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x20:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Instantiate: X0:=X:fofType
% Found x20 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x2:(((cR X) x0)->(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))))
% Instantiate: X:=x7:fofType;X0:=x0:fofType
% Found (fun (x9:((cR X0) x7))=> x2) as proof of (((cR x7) X0)->(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))))
% Found (fun (x9:((cR X0) x7))=> x2) as proof of (((cR X0) x7)->(((cR x7) X0)->(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))))
% Found (and_rect20 (fun (x9:((cR X0) x7))=> x2)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found ((and_rect2 (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))) (fun (x9:((cR X0) x7))=> x2)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (((fun (P:Type) (x9:(((cR X0) x7)->(((cR x7) X0)->P)))=> (((((and_rect ((cR X0) x7)) ((cR x7) X0)) P) x9) x8)) (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))) (fun (x9:((cR X0) x7))=> x2)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (((fun (P:Type) (x9:(((cR X0) x7)->(((cR x7) X0)->P)))=> (((((and_rect ((cR X0) x7)) ((cR x7) X0)) P) x9) x8)) (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))) (fun (x9:((cR X0) x7))=> x2)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x3 (((fun (P:Type) (x9:(((cR X0) x7)->(((cR x7) X0)->P)))=> (((((and_rect ((cR X0) x7)) ((cR x7) X0)) P) x9) x8)) (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))) (fun (x9:((cR X0) x7))=> x2))) as proof of ((cR X) x0)
% Found (fun (x8:((and ((cR X0) x7)) ((cR x7) X0)))=> (x3 (((fun (P:Type) (x9:(((cR X0) x7)->(((cR x7) X0)->P)))=> (((((and_rect ((cR X0) x7)) ((cR x7) X0)) P) x9) x8)) (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))) (fun (x9:((cR X0) x7))=> x2)))) as proof of ((cR X) x0)
% Found x4:(((cR X0) x0)->(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))))
% Instantiate: X:=x0:fofType;X0:=x7:fofType
% Found (fun (x9:((cR X) x7))=> x4) as proof of (((cR x7) X)->(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))))
% Found (fun (x9:((cR X) x7))=> x4) as proof of (((cR X) x7)->(((cR x7) X)->(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))))
% Found (and_rect20 (fun (x9:((cR X) x7))=> x4)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found ((and_rect2 (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))) (fun (x9:((cR X) x7))=> x4)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (((fun (P:Type) (x9:(((cR X) x7)->(((cR x7) X)->P)))=> (((((and_rect ((cR X) x7)) ((cR x7) X)) P) x9) x8)) (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))) (fun (x9:((cR X) x7))=> x4)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (((fun (P:Type) (x9:(((cR X) x7)->(((cR x7) X)->P)))=> (((((and_rect ((cR X) x7)) ((cR x7) X)) P) x9) x8)) (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))) (fun (x9:((cR X) x7))=> x4)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x5 (((fun (P:Type) (x9:(((cR X) x7)->(((cR x7) X)->P)))=> (((((and_rect ((cR X) x7)) ((cR x7) X)) P) x9) x8)) (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))) (fun (x9:((cR X) x7))=> x4))) as proof of ((cR X0) x0)
% Found (fun (x8:((and ((cR X) x7)) ((cR x7) X)))=> (x5 (((fun (P:Type) (x9:(((cR X) x7)->(((cR x7) X)->P)))=> (((((and_rect ((cR X) x7)) ((cR x7) X)) P) x9) x8)) (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))) (fun (x9:((cR X) x7))=> x4)))) as proof of ((cR X0) x0)
% Found x40:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Instantiate: X:=X0:fofType
% Found x40 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x2:(((cR X) x0)->(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))))
% Instantiate: X:=x7:fofType;X0:=x0:fofType
% Found (fun (x9:((cR X0) x7))=> x2) as proof of (((cR x7) X0)->(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))))
% Found (fun (x9:((cR X0) x7))=> x2) as proof of (((cR X0) x7)->(((cR x7) X0)->(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))))
% Found (and_rect20 (fun (x9:((cR X0) x7))=> x2)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found ((and_rect2 (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))) (fun (x9:((cR X0) x7))=> x2)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (((fun (P:Type) (x9:(((cR X0) x7)->(((cR x7) X0)->P)))=> (((((and_rect ((cR X0) x7)) ((cR x7) X0)) P) x9) x8)) (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))) (fun (x9:((cR X0) x7))=> x2)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (fun (x8:((and ((cR X0) x7)) ((cR x7) X0)))=> (((fun (P:Type) (x9:(((cR X0) x7)->(((cR x7) X0)->P)))=> (((((and_rect ((cR X0) x7)) ((cR x7) X0)) P) x9) x8)) (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))) (fun (x9:((cR X0) x7))=> x2))) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x4:(((cR X0) x0)->(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))))
% Instantiate: X:=x0:fofType;X0:=x7:fofType
% Found (fun (x9:((cR X) x7))=> x4) as proof of (((cR x7) X)->(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))))
% Found (fun (x9:((cR X) x7))=> x4) as proof of (((cR X) x7)->(((cR x7) X)->(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))))
% Found (and_rect20 (fun (x9:((cR X) x7))=> x4)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found ((and_rect2 (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))) (fun (x9:((cR X) x7))=> x4)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (((fun (P:Type) (x9:(((cR X) x7)->(((cR x7) X)->P)))=> (((((and_rect ((cR X) x7)) ((cR x7) X)) P) x9) x8)) (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))) (fun (x9:((cR X) x7))=> x4)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (fun (x8:((and ((cR X) x7)) ((cR x7) X)))=> (((fun (P:Type) (x9:(((cR X) x7)->(((cR x7) X)->P)))=> (((((and_rect ((cR X) x7)) ((cR x7) X)) P) x9) x8)) (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))) (fun (x9:((cR X) x7))=> x4))) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x50:=(x5 x40):((cR X0) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x50:=(x5 x40):((cR X0) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x50:((cR X0) x0)
% Found x50 as proof of ((cR X0) x0)
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x50:=(x5 x20):((cR X0) x0)
% Found (x5 x20) as proof of ((cR X) x0)
% Found (x5 x20) as proof of ((cR X) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x40:=(x4 x50):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x20:=(x2 x30):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x50:=(x5 x40):((cR X0) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found x50:=(x5 x40):((cR X0) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found x8:((cR x5) X)
% Instantiate: X:=x0:fofType;X0:=x5:fofType
% Found x8 as proof of ((cR X0) x0)
% Found x4:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x4 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found x20:=(x2 x30):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x40:=(x4 x50):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x40:=(x4 x50):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x20:=(x2 x30):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x21:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Instantiate: X0:=X:fofType
% Found x21 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x40:=(x4 x50):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x20:=(x2 x30):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x40:=(x4 x50):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x20:=(x2 x30):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x50:((cR X0) x0)
% Found x50 as proof of ((cR X0) x0)
% Found ((x4 x50) x00) as proof of False
% Found (fun (x7:((and ((cR X) x6)) ((cR x6) X)))=> ((x4 x50) x00)) as proof of False
% Found (fun (x6:fofType) (x7:((and ((cR X) x6)) ((cR x6) X)))=> ((x4 x50) x00)) as proof of (((and ((cR X) x6)) ((cR x6) X))->False)
% Found (fun (x6:fofType) (x7:((and ((cR X) x6)) ((cR x6) X)))=> ((x4 x50) x00)) as proof of (forall (x:fofType), (((and ((cR X) x)) ((cR x) X))->False))
% Found (ex_ind10 (fun (x6:fofType) (x7:((and ((cR X) x6)) ((cR x6) X)))=> ((x4 x50) x00))) as proof of False
% Found ((ex_ind1 False) (fun (x6:fofType) (x7:((and ((cR X) x6)) ((cR x6) X)))=> ((x4 x50) x00))) as proof of False
% Found (((fun (P:Prop) (x6:(forall (x:fofType), (((and ((cR X) x)) ((cR x) X))->P)))=> (((((ex_ind fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))) P) x6) x00)) False) (fun (x6:fofType) (x7:((and ((cR X) x6)) ((cR x6) X)))=> ((x4 x50) x00))) as proof of False
% Found (((fun (P:Prop) (x6:(forall (x:fofType), (((and ((cR X) x)) ((cR x) X))->P)))=> (((((ex_ind fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))) P) x6) x00)) False) (fun (x6:fofType) (x7:((and ((cR X) x6)) ((cR x6) X)))=> ((x4 x50) x00))) as proof of False
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found ((x2 x30) x00) as proof of False
% Found (fun (x7:((and ((cR X0) x6)) ((cR x6) X0)))=> ((x2 x30) x00)) as proof of False
% Found (fun (x6:fofType) (x7:((and ((cR X0) x6)) ((cR x6) X0)))=> ((x2 x30) x00)) as proof of (((and ((cR X0) x6)) ((cR x6) X0))->False)
% Found (fun (x6:fofType) (x7:((and ((cR X0) x6)) ((cR x6) X0)))=> ((x2 x30) x00)) as proof of (forall (x:fofType), (((and ((cR X0) x)) ((cR x) X0))->False))
% Found (ex_ind10 (fun (x6:fofType) (x7:((and ((cR X0) x6)) ((cR x6) X0)))=> ((x2 x30) x00))) as proof of False
% Found ((ex_ind1 False) (fun (x6:fofType) (x7:((and ((cR X0) x6)) ((cR x6) X0)))=> ((x2 x30) x00))) as proof of False
% Found (((fun (P:Prop) (x6:(forall (x:fofType), (((and ((cR X0) x)) ((cR x) X0))->P)))=> (((((ex_ind fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))) P) x6) x00)) False) (fun (x6:fofType) (x7:((and ((cR X0) x6)) ((cR x6) X0)))=> ((x2 x30) x00))) as proof of False
% Found (((fun (P:Prop) (x6:(forall (x:fofType), (((and ((cR X0) x)) ((cR x) X0))->P)))=> (((((ex_ind fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))) P) x6) x00)) False) (fun (x6:fofType) (x7:((and ((cR X0) x6)) ((cR x6) X0)))=> ((x2 x30) x00))) as proof of False
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x40:=(x4 x50):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x50:=(x5 x40):((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found x40:=(x4 x20):((cR X0) x0)
% Found (x4 x20) as proof of ((cR X) x0)
% Found (x4 x20) as proof of ((cR X) x0)
% Found (fun (x4:((((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)->((cR X0) x0)))=> (x4 x20)) as proof of ((cR X) x0)
% Found (fun (x3:(((cR X0) x0)->(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False))) (x4:((((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)->((cR X0) x0)))=> (x4 x20)) as proof of (((((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)->((cR X0) x0))->((cR X) x0))
% Found (fun (x3:(((cR X0) x0)->(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False))) (x4:((((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)->((cR X0) x0)))=> (x4 x20)) as proof of ((((cR X0) x0)->(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False))->(((((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)->((cR X0) x0))->((cR X) x0)))
% Found (and_rect10 (fun (x3:(((cR X0) x0)->(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False))) (x4:((((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)->((cR X0) x0)))=> (x4 x20))) as proof of ((cR X) x0)
% Found ((and_rect1 ((cR X) x0)) (fun (x3:(((cR X0) x0)->(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False))) (x4:((((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)->((cR X0) x0)))=> (x4 x20))) as proof of ((cR X) x0)
% Found (((fun (P:Type) (x3:((((cR X0) x0)->(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False))->(((((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)->((cR X0) x0))->P)))=> (((((and_rect (((cR X0) x0)->(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False))) ((((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)->((cR X0) x0))) P) x3) x11)) ((cR X) x0)) (fun (x3:(((cR X0) x0)->(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False))) (x4:((((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)->((cR X0) x0)))=> (x4 x20))) as proof of ((cR X) x0)
% Found (((fun (P:Type) (x3:((((cR X) x0)->(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False))->(((((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)->((cR X) x0))->P)))=> (((((and_rect (((cR X) x0)->(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False))) ((((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)->((cR X) x0))) P) x3) (x1 X))) ((cR X) x0)) (fun (x3:(((cR X) x0)->(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False))) (x4:((((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)->((cR X) x0)))=> (x4 x20))) as proof of ((cR X) x0)
% Found (((fun (P:Type) (x3:((((cR X) x0)->(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False))->(((((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)->((cR X) x0))->P)))=> (((((and_rect (((cR X) x0)->(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False))) ((((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)->((cR X) x0))) P) x3) (x1 X))) ((cR X) x0)) (fun (x3:(((cR X) x0)->(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False))) (x4:((((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)->((cR X) x0)))=> (x4 x20))) as proof of ((cR X) x0)
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Instantiate: X0:=X:fofType
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x20:=(x2 x31):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Instantiate: X0:=X:fofType
% Found (x2 x31) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x2 x31) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x40:=(x4 x50):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x4 x50) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x40:=(x4 x51):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Instantiate: X:=X0:fofType
% Found (x4 x51) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x4 x51) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found (x40 x30) as proof of False
% Found ((fun (x7:((cR X0) x0))=> ((x4 x7) x6)) x30) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((fun (x7:((cR X0) x0))=> ((x4 x7) x6)) x30)) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((fun (x7:((cR X0) x0))=> ((x4 x7) x6)) x30)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found (x20 x50) as proof of False
% Found ((fun (x7:((cR X) x0))=> ((x2 x7) x6)) x50) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))=> ((fun (x7:((cR X) x0))=> ((x2 x7) x6)) x50)) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))=> ((fun (x7:((cR X) x0))=> ((x2 x7) x6)) x50)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x20:=(x2 x30):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x5:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x5 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found (x20 x00) as proof of False
% Found ((x2 x30) x00) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x2 x30) x00)) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x2 x30) x00)) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found (x40 x30) as proof of False
% Found ((fun (x6:((cR X0) x0))=> ((x4 x6) x00)) x30) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((fun (x6:((cR X0) x0))=> ((x4 x6) x00)) x30)) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((fun (x6:((cR X0) x0))=> ((x4 x6) x00)) x30)) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x000:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x000 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x50:=(x5 x40):((cR X0) x0)
% Found (x5 x40) as proof of ((cR X0) x0)
% Found (x5 x40) as proof of ((cR X0) x0)
% Found x50:=(x5 x41):((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found (x5 x41) as proof of ((cR X) x0)
% Found (x5 x41) as proof of ((cR X) x0)
% Found x41:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Instantiate: X:=X0:fofType
% Found x41 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x3 x41) as proof of ((cR X) x0)
% Found (x3 x41) as proof of ((cR X) x0)
% Found x50:=(x5 x41):((cR X0) x0)
% Found (x5 x41) as proof of ((cR X) x0)
% Found (x5 x41) as proof of ((cR X) x0)
% Found (x5 x41) as proof of ((cR X) x0)
% Found x50:((cR X0) x0)
% Found (fun (x7:((and ((cR X) x6)) ((cR x6) X)))=> x50) as proof of ((cR X0) x0)
% Found (fun (x6:fofType) (x7:((and ((cR X) x6)) ((cR x6) X)))=> x50) as proof of (((and ((cR X) x6)) ((cR x6) X))->((cR X0) x0))
% Found (fun (x6:fofType) (x7:((and ((cR X) x6)) ((cR x6) X)))=> x50) as proof of (forall (x:fofType), (((and ((cR X) x)) ((cR x) X))->((cR X0) x0)))
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x000:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x000 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found (x40 x6) as proof of False
% Found ((x4 x50) x6) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))=> ((x4 x50) x6)) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))=> ((x4 x50) x6)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found (x20 x50) as proof of False
% Found ((fun (x7:((cR X) x0))=> ((x2 x7) x6)) x50) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))=> ((fun (x7:((cR X) x0))=> ((x2 x7) x6)) x50)) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))=> ((fun (x7:((cR X) x0))=> ((x2 x7) x6)) x50)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found (x20 x6) as proof of False
% Found ((x2 x30) x6) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x2 x30) x6)) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x2 x30) x6)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found (x40 x30) as proof of False
% Found ((fun (x7:((cR X0) x0))=> ((x4 x7) x6)) x30) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((fun (x7:((cR X0) x0))=> ((x4 x7) x6)) x30)) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((fun (x7:((cR X0) x0))=> ((x4 x7) x6)) x30)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x20:=(x2 x31):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x31) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x31) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x9:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x9 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x30:=(x3 x21):((cR X) x0)
% Found (x3 x21) as proof of ((cR X) x0)
% Found (x3 x21) as proof of ((cR X) x0)
% Found x9:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x9 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x20:=(x2 x31):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x31) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x2 x31) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x2 x31) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x40:=(x4 x51):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x4 x51) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x4 x51) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x4 x51) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x40:=(fun (x9:((cR X0) x0))=> ((x4 x9) x00)):(((cR X0) x0)->False)
% Instantiate: X:=x0:fofType;X0:=x6:fofType
% Found (fun (x9:((cR X0) x0))=> ((x4 x9) x00)) as proof of (((cR x6) X)->False)
% Found (fun (x8:((cR X) x6)) (x9:((cR X0) x0))=> ((x4 x9) x00)) as proof of (((cR x6) X)->False)
% Found (fun (x8:((cR X) x6)) (x9:((cR X0) x0))=> ((x4 x9) x00)) as proof of (((cR X) x6)->(((cR x6) X)->False))
% Found (and_rect20 (fun (x8:((cR X) x6)) (x9:((cR X0) x0))=> ((x4 x9) x00))) as proof of False
% Found ((and_rect2 False) (fun (x8:((cR X) x6)) (x9:((cR X0) x0))=> ((x4 x9) x00))) as proof of False
% Found (((fun (P:Type) (x8:(((cR X) x6)->(((cR x6) X)->P)))=> (((((and_rect ((cR X) x6)) ((cR x6) X)) P) x8) x7)) False) (fun (x8:((cR X) x6)) (x9:((cR X0) x0))=> ((x4 x9) x00))) as proof of False
% Found (fun (x7:((and ((cR X) x6)) ((cR x6) X)))=> (((fun (P:Type) (x8:(((cR X) x6)->(((cR x6) X)->P)))=> (((((and_rect ((cR X) x6)) ((cR x6) X)) P) x8) x7)) False) (fun (x8:((cR X) x6)) (x9:((cR X0) x0))=> ((x4 x9) x00)))) as proof of False
% Found x5:(((cR X0) x0)->(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))))
% Instantiate: X:=x0:fofType;X0:=x7:fofType
% Found (fun (x9:((cR X) x7))=> x5) as proof of (((cR x7) X)->(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))))
% Found (fun (x9:((cR X) x7))=> x5) as proof of (((cR X) x7)->(((cR x7) X)->(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))))
% Found (and_rect20 (fun (x9:((cR X) x7))=> x5)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found ((and_rect2 (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))) (fun (x9:((cR X) x7))=> x5)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (((fun (P:Type) (x9:(((cR X) x7)->(((cR x7) X)->P)))=> (((((and_rect ((cR X) x7)) ((cR x7) X)) P) x9) x8)) (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))) (fun (x9:((cR X) x7))=> x5)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (((fun (P:Type) (x9:(((cR X) x7)->(((cR x7) X)->P)))=> (((((and_rect ((cR X) x7)) ((cR x7) X)) P) x9) x8)) (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))) (fun (x9:((cR X) x7))=> x5)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x6 (((fun (P:Type) (x9:(((cR X) x7)->(((cR x7) X)->P)))=> (((((and_rect ((cR X) x7)) ((cR x7) X)) P) x9) x8)) (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))) (fun (x9:((cR X) x7))=> x5))) as proof of ((cR X0) x0)
% Found (fun (x8:((and ((cR X) x7)) ((cR x7) X)))=> (x6 (((fun (P:Type) (x9:(((cR X) x7)->(((cR x7) X)->P)))=> (((((and_rect ((cR X) x7)) ((cR x7) X)) P) x9) x8)) (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))) (fun (x9:((cR X) x7))=> x5)))) as proof of ((cR X0) x0)
% Found x5:(((cR X0) x0)->(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))))
% Instantiate: X:=x0:fofType;X0:=x7:fofType
% Found (fun (x9:((cR X) x7))=> x5) as proof of (((cR x7) X)->(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))))
% Found (fun (x9:((cR X) x7))=> x5) as proof of (((cR X) x7)->(((cR x7) X)->(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))))
% Found (and_rect20 (fun (x9:((cR X) x7))=> x5)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found ((and_rect2 (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))) (fun (x9:((cR X) x7))=> x5)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (((fun (P:Type) (x9:(((cR X) x7)->(((cR x7) X)->P)))=> (((((and_rect ((cR X) x7)) ((cR x7) X)) P) x9) x8)) (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))) (fun (x9:((cR X) x7))=> x5)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (fun (x8:((and ((cR X) x7)) ((cR x7) X)))=> (((fun (P:Type) (x9:(((cR X) x7)->(((cR x7) X)->P)))=> (((((and_rect ((cR X) x7)) ((cR x7) X)) P) x9) x8)) (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))) (fun (x9:((cR X) x7))=> x5))) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x20:=(fun (x9:((cR X) x0))=> ((x2 x9) x00)):(((cR X) x0)->False)
% Instantiate: X:=x6:fofType;X0:=x0:fofType
% Found (fun (x9:((cR X) x0))=> ((x2 x9) x00)) as proof of (((cR x6) X0)->False)
% Found (fun (x8:((cR X0) x6)) (x9:((cR X) x0))=> ((x2 x9) x00)) as proof of (((cR x6) X0)->False)
% Found (fun (x8:((cR X0) x6)) (x9:((cR X) x0))=> ((x2 x9) x00)) as proof of (((cR X0) x6)->(((cR x6) X0)->False))
% Found (and_rect20 (fun (x8:((cR X0) x6)) (x9:((cR X) x0))=> ((x2 x9) x00))) as proof of False
% Found ((and_rect2 False) (fun (x8:((cR X0) x6)) (x9:((cR X) x0))=> ((x2 x9) x00))) as proof of False
% Found (((fun (P:Type) (x8:(((cR X0) x6)->(((cR x6) X0)->P)))=> (((((and_rect ((cR X0) x6)) ((cR x6) X0)) P) x8) x7)) False) (fun (x8:((cR X0) x6)) (x9:((cR X) x0))=> ((x2 x9) x00))) as proof of False
% Found (fun (x7:((and ((cR X0) x6)) ((cR x6) X0)))=> (((fun (P:Type) (x8:(((cR X0) x6)->(((cR x6) X0)->P)))=> (((((and_rect ((cR X0) x6)) ((cR x6) X0)) P) x8) x7)) False) (fun (x8:((cR X0) x6)) (x9:((cR X) x0))=> ((x2 x9) x00)))) as proof of False
% Found x30:((cR X) x0)
% Instantiate: x4:=x0:fofType
% Found x30 as proof of ((cR X) x4)
% Found x30:((cR X) x0)
% Instantiate: X:=x0:fofType;x4:=X:fofType
% Found x30 as proof of ((cR x4) X)
% Found x30:((cR X) x0)
% Instantiate: X:=x0:fofType
% Found x30 as proof of ((cR x4) X)
% Found ((conj00 x30) x30) as proof of ((and ((cR X) x4)) ((cR x4) X))
% Found (((conj0 ((cR x4) X)) x30) x30) as proof of ((and ((cR X) x4)) ((cR x4) X))
% Found ((((conj ((cR X) x4)) ((cR x4) X)) x30) x30) as proof of ((and ((cR X) x4)) ((cR x4) X))
% Found ((((conj ((cR X) x4)) ((cR x4) X)) x30) x30) as proof of ((and ((cR X) x4)) ((cR x4) X))
% Found (ex_intro000 ((((conj ((cR X) x4)) ((cR x4) X)) x30) x30)) as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found ((ex_intro00 x0) ((((conj ((cR X) x0)) ((cR x0) X)) x30) x30)) as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found (((ex_intro0 (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))) x0) ((((conj ((cR X) x0)) ((cR x0) X)) x30) x30)) as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found ((((ex_intro fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))) x0) ((((conj ((cR X) x0)) ((cR x0) X)) x30) x30)) as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found ((((ex_intro fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))) x0) ((((conj ((cR X) x0)) ((cR x0) X)) x30) x30)) as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found (x20 ((((ex_intro fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))) x0) ((((conj ((cR X) x0)) ((cR x0) X)) x30) x30))) as proof of False
% Found ((x2 x31) ((((ex_intro fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))) x0) ((((conj ((cR X) x0)) ((cR x0) X)) x30) x30))) as proof of False
% Found ((x2 x31) ((((ex_intro fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))) x0) ((((conj ((cR X) x0)) ((cR x0) X)) x30) x30))) as proof of False
% Found x50:((cR X0) x0)
% Found x50 as proof of ((cR X0) x0)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found ((x4 x50) x00) as proof of False
% Found (fun (x7:((and ((cR X) x6)) ((cR x6) X)))=> ((x4 x50) x00)) as proof of False
% Found (fun (x6:fofType) (x7:((and ((cR X) x6)) ((cR x6) X)))=> ((x4 x50) x00)) as proof of (((and ((cR X) x6)) ((cR x6) X))->False)
% Found (fun (x6:fofType) (x7:((and ((cR X) x6)) ((cR x6) X)))=> ((x4 x50) x00)) as proof of (forall (x:fofType), (((and ((cR X) x)) ((cR x) X))->False))
% Found (ex_ind10 (fun (x6:fofType) (x7:((and ((cR X) x6)) ((cR x6) X)))=> ((x4 x50) x00))) as proof of False
% Found ((ex_ind1 False) (fun (x6:fofType) (x7:((and ((cR X) x6)) ((cR x6) X)))=> ((x4 x50) x00))) as proof of False
% Found (((fun (P:Prop) (x6:(forall (x:fofType), (((and ((cR X) x)) ((cR x) X))->P)))=> (((((ex_ind fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))) P) x6) x00)) False) (fun (x6:fofType) (x7:((and ((cR X) x6)) ((cR x6) X)))=> ((x4 x50) x00))) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))=> (((fun (P:Prop) (x6:(forall (x:fofType), (((and ((cR X) x)) ((cR x) X))->P)))=> (((((ex_ind fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))) P) x6) x00)) False) (fun (x6:fofType) (x7:((and ((cR X) x6)) ((cR x6) X)))=> ((x4 x50) x00)))) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))=> (((fun (P:Prop) (x6:(forall (x:fofType), (((and ((cR X) x)) ((cR x) X))->P)))=> (((((ex_ind fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))) P) x6) x00)) False) (fun (x6:fofType) (x7:((and ((cR X) x6)) ((cR x6) X)))=> ((x4 x50) x00)))) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found ((x2 x30) x00) as proof of False
% Found (fun (x7:((and ((cR X0) x6)) ((cR x6) X0)))=> ((x2 x30) x00)) as proof of False
% Found (fun (x6:fofType) (x7:((and ((cR X0) x6)) ((cR x6) X0)))=> ((x2 x30) x00)) as proof of (((and ((cR X0) x6)) ((cR x6) X0))->False)
% Found (fun (x6:fofType) (x7:((and ((cR X0) x6)) ((cR x6) X0)))=> ((x2 x30) x00)) as proof of (forall (x:fofType), (((and ((cR X0) x)) ((cR x) X0))->False))
% Found (ex_ind10 (fun (x6:fofType) (x7:((and ((cR X0) x6)) ((cR x6) X0)))=> ((x2 x30) x00))) as proof of False
% Found ((ex_ind1 False) (fun (x6:fofType) (x7:((and ((cR X0) x6)) ((cR x6) X0)))=> ((x2 x30) x00))) as proof of False
% Found (((fun (P:Prop) (x6:(forall (x:fofType), (((and ((cR X0) x)) ((cR x) X0))->P)))=> (((((ex_ind fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))) P) x6) x00)) False) (fun (x6:fofType) (x7:((and ((cR X0) x6)) ((cR x6) X0)))=> ((x2 x30) x00))) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> (((fun (P:Prop) (x6:(forall (x:fofType), (((and ((cR X0) x)) ((cR x) X0))->P)))=> (((((ex_ind fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))) P) x6) x00)) False) (fun (x6:fofType) (x7:((and ((cR X0) x6)) ((cR x6) X0)))=> ((x2 x30) x00)))) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> (((fun (P:Prop) (x6:(forall (x:fofType), (((and ((cR X0) x)) ((cR x) X0))->P)))=> (((((ex_ind fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))) P) x6) x00)) False) (fun (x6:fofType) (x7:((and ((cR X0) x6)) ((cR x6) X0)))=> ((x2 x30) x00)))) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x30:=(x3 x20):((cR X) x0)
% Instantiate: X0:=X:fofType
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x20:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x20 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x40:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x40 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found x40:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x40 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found x20:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x20 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x50:((cR X0) x0)
% Found x50 as proof of ((cR X0) x0)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x50:((cR X0) x0)
% Found x50 as proof of ((cR X0) x0)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x40:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x40 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found (x20 x6) as proof of False
% Found ((x2 x30) x6) as proof of False
% Found (fun (x8:((and ((cR X0) x7)) ((cR x7) X0)))=> ((x2 x30) x6)) as proof of False
% Found (fun (x7:fofType) (x8:((and ((cR X0) x7)) ((cR x7) X0)))=> ((x2 x30) x6)) as proof of (((and ((cR X0) x7)) ((cR x7) X0))->False)
% Found (fun (x7:fofType) (x8:((and ((cR X0) x7)) ((cR x7) X0)))=> ((x2 x30) x6)) as proof of (forall (x:fofType), (((and ((cR X0) x)) ((cR x) X0))->False))
% Found x20:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x20 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x20:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x20 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x40:=(x4 x50):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Instantiate: X:=X0:fofType
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x50:=(x5 x40):((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Instantiate: X0:=X:fofType
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x50:=(x5 x40):((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found x40:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x40 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found x40:=(x4 x50):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Instantiate: X:=X0:fofType
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x12:((cR x5) X)
% Instantiate: X:=x0:fofType;X0:=x5:fofType
% Found x12 as proof of ((cR X0) x0)
% Found x4:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x4 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Instantiate: X0:=X:fofType
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x50:((cR X0) x0)
% Found x50 as proof of ((cR X0) x0)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x50:((cR X0) x0)
% Found x50 as proof of ((cR X0) x0)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x30:=(x3 x20):((cR X) x0)
% Instantiate: X0:=X:fofType
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found (x40 x6) as proof of False
% Found ((x4 x50) x6) as proof of False
% Found (fun (x8:((and ((cR X) x7)) ((cR x7) X)))=> ((x4 x50) x6)) as proof of False
% Found (fun (x7:fofType) (x8:((and ((cR X) x7)) ((cR x7) X)))=> ((x4 x50) x6)) as proof of (((and ((cR X) x7)) ((cR x7) X))->False)
% Found (fun (x7:fofType) (x8:((and ((cR X) x7)) ((cR x7) X)))=> ((x4 x50) x6)) as proof of (forall (x:fofType), (((and ((cR X) x)) ((cR x) X))->False))
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x50:=(x5 x40):((cR X0) x0)
% Found (x5 x40) as proof of ((cR X0) x0)
% Found (x5 x40) as proof of ((cR X0) x0)
% Found x40:=(x4 x50):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x4 x50) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found x60:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x60 as proof of ((cR X) x0)
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found x50:=(x5 x40):((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found ((x2 (x5 x40)) x00) as proof of False
% Found (fun (x5:((((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)->((cR X0) x0)))=> ((x2 (x5 x40)) x00)) as proof of False
% Found (fun (x5:((((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)->((cR X0) x0)))=> ((x2 (x5 x40)) x00)) as proof of (((((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)->((cR X0) x0))->False)
% Found x50:=(x5 x40):((cR X0) x0)
% Found (x5 x40) as proof of ((cR X0) x0)
% Found (x5 x40) as proof of ((cR X0) x0)
% Found ((x4 (x5 x40)) x00) as proof of False
% Found (fun (x5:((((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)->((cR X0) x0)))=> ((x4 (x5 x40)) x00)) as proof of False
% Found (fun (x5:((((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)->((cR X0) x0)))=> ((x4 (x5 x40)) x00)) as proof of (((((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)->((cR X0) x0))->False)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found ((x4 x30) x6) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x4 x30) x6)) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x4 x30) x6)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x50:=(x5 x40):((cR X0) x0)
% Found (x5 x40) as proof of ((cR X0) x0)
% Found (x5 x40) as proof of ((cR X0) x0)
% Found ((x4 (x5 x40)) x6) as proof of False
% Found (fun (x8:((and ((cR X) x7)) ((cR x7) X)))=> ((x4 (x5 x40)) x6)) as proof of False
% Found (fun (x7:fofType) (x8:((and ((cR X) x7)) ((cR x7) X)))=> ((x4 (x5 x40)) x6)) as proof of (((and ((cR X) x7)) ((cR x7) X))->False)
% Found (fun (x7:fofType) (x8:((and ((cR X) x7)) ((cR x7) X)))=> ((x4 (x5 x40)) x6)) as proof of (forall (x:fofType), (((and ((cR X) x)) ((cR x) X))->False))
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found ((x2 (x3 x20)) x6) as proof of False
% Found (fun (x8:((and ((cR X0) x7)) ((cR x7) X0)))=> ((x2 (x3 x20)) x6)) as proof of False
% Found (fun (x7:fofType) (x8:((and ((cR X0) x7)) ((cR x7) X0)))=> ((x2 (x3 x20)) x6)) as proof of (((and ((cR X0) x7)) ((cR x7) X0))->False)
% Found (fun (x7:fofType) (x8:((and ((cR X0) x7)) ((cR x7) X0)))=> ((x2 (x3 x20)) x6)) as proof of (forall (x:fofType), (((and ((cR X0) x)) ((cR x) X0))->False))
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x30:((cR X) x0)
% Found (fun (x5:((not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))->((cR X0) x0)))=> x30) as proof of ((cR X) x0)
% Found (fun (x5:((not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))->((cR X0) x0)))=> x30) as proof of (((not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))->((cR X0) x0))->((cR X) x0))
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found ((x2 x30) x6) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x2 x30) x6)) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x2 x30) x6)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x50:=(x5 x40):((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x20:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Instantiate: X0:=X:fofType
% Found x20 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x50:=(x5 x40):((cR X0) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found x50:((cR X0) x0)
% Found x50 as proof of ((cR X0) x0)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found ((x4 x50) x00) as proof of False
% Found ((x4 x50) x00) as proof of False
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found ((x2 x30) x00) as proof of False
% Found ((x2 x30) x00) as proof of False
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x60:=(x6 x50):((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found (x6 x50) as proof of ((cR X) x0)
% Found (x6 x50) as proof of ((cR X) x0)
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x31:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x31 as proof of ((cR X0) x0)
% Found x21:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Instantiate: X0:=X:fofType
% Found x21 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x21:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Instantiate: X0:=X:fofType
% Found x21 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x50:((cR X0) x0)
% Found x50 as proof of ((cR X0) x0)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found ((x4 x50) x00) as proof of False
% Found ((x4 x50) x00) as proof of False
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found (x4 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x4 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x50:=(x5 x40):((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found (x4 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x4 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x50:((cR X0) x0)
% Found x50 as proof of ((cR X0) x0)
% Found ((x4 x50) x6) as proof of False
% Found ((x4 x50) x6) as proof of False
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found ((x2 x50) x6) as proof of False
% Found ((x2 x50) x6) as proof of False
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found (x40 x30) as proof of False
% Found ((fun (x7:((cR X0) x0))=> ((x4 x7) x6)) x30) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((fun (x7:((cR X0) x0))=> ((x4 x7) x6)) x30)) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((fun (x7:((cR X0) x0))=> ((x4 x7) x6)) x30)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x9:((cR x6) X)
% Instantiate: X:=x0:fofType;X0:=x6:fofType
% Found x9 as proof of ((cR X0) x0)
% Found x5:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x5 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x50:=(x5 x41):((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found (x5 x41) as proof of ((cR X) x0)
% Found (x5 x41) as proof of ((cR X) x0)
% Found x50:=(x5 x40):((cR X0) x0)
% Found (x5 x40) as proof of ((cR X0) x0)
% Found (x5 x40) as proof of ((cR X0) x0)
% Found x41:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Instantiate: X:=X0:fofType
% Found x41 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x3 x41) as proof of ((cR X) x0)
% Found (x3 x41) as proof of ((cR X) x0)
% Found x50:=(x5 x41):((cR X0) x0)
% Found (x5 x41) as proof of ((cR X) x0)
% Found (x5 x41) as proof of ((cR X) x0)
% Found (x5 x41) as proof of ((cR X) x0)
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found (x40 x30) as proof of False
% Found ((fun (x7:((cR X0) x0))=> ((x4 x7) x6)) x30) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((fun (x7:((cR X0) x0))=> ((x4 x7) x6)) x30)) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((fun (x7:((cR X0) x0))=> ((x4 x7) x6)) x30)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found (x20 x6) as proof of False
% Found ((x2 x30) x6) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x2 x30) x6)) as proof of False
% Found (fun (x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))=> ((x2 x30) x6)) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Instantiate: X0:=X:fofType
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x000:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x000 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x000:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x000 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x60:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x60 as proof of ((cR X) x0)
% Found x4:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x4 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found ((x2 x60) x4) as proof of False
% Found ((x2 x60) x4) as proof of False
% Found x60:((cR X0) x0)
% Found x60 as proof of ((cR X0) x0)
% Found x4:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x4 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found ((x5 x60) x4) as proof of False
% Found ((x5 x60) x4) as proof of False
% Found x50:=(x5 x40):((cR X0) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Instantiate: X0:=X:fofType
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x20:=(x2 x30):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x40:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x40 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found x60:=(x6 x50):((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found (x6 x50) as proof of ((cR X) x0)
% Found (x6 x50) as proof of ((cR X) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Instantiate: X0:=X:fofType
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Instantiate: X0:=X:fofType
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found x50:=(x5 x40):((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x50:((cR X0) x0)
% Found (fun (x7:((and ((cR X) x6)) ((cR x6) X)))=> x50) as proof of ((cR X0) x0)
% Found (fun (x7:((and ((cR X) x6)) ((cR x6) X)))=> x50) as proof of (((and ((cR X) x6)) ((cR x6) X))->((cR X0) x0))
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x30:((cR X) x0)
% Found (fun (x7:((and ((cR X0) x6)) ((cR x6) X0)))=> x30) as proof of ((cR X) x0)
% Found (fun (x7:((and ((cR X0) x6)) ((cR x6) X0)))=> x30) as proof of (((and ((cR X0) x6)) ((cR x6) X0))->((cR X) x0))
% Found x50:=(x5 x40):((cR X0) x0)
% Found (x5 x40) as proof of ((cR X0) x0)
% Found (x5 x40) as proof of ((cR X0) x0)
% Found x30:=(x3 x21):((cR X) x0)
% Instantiate: X0:=X:fofType
% Found (x3 x21) as proof of ((cR X0) x0)
% Found (x3 x21) as proof of ((cR X0) x0)
% Found x50:=(x5 x40):((cR X0) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found x20:=(x2 x30):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x6:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x6 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x30:=(x3 x21):((cR X) x0)
% Found (x3 x21) as proof of ((cR X) x0)
% Found (x3 x21) as proof of ((cR X) x0)
% Found x40:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x40 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found (x5 x40) as proof of ((cR X) x0)
% Found x20:=(fun (x13:((cR X) x0))=> ((x2 x13) x6)):(((cR X) x0)->False)
% Instantiate: X:=x8:fofType;X0:=x0:fofType
% Found (fun (x13:((cR X) x0))=> ((x2 x13) x6)) as proof of (((cR x8) X0)->False)
% Found (fun (x12:((cR X0) x8)) (x13:((cR X) x0))=> ((x2 x13) x6)) as proof of (((cR x8) X0)->False)
% Found (fun (x12:((cR X0) x8)) (x13:((cR X) x0))=> ((x2 x13) x6)) as proof of (((cR X0) x8)->(((cR x8) X0)->False))
% Found (and_rect20 (fun (x12:((cR X0) x8)) (x13:((cR X) x0))=> ((x2 x13) x6))) as proof of False
% Found ((and_rect2 False) (fun (x12:((cR X0) x8)) (x13:((cR X) x0))=> ((x2 x13) x6))) as proof of False
% Found (((fun (P:Type) (x12:(((cR X0) x8)->(((cR x8) X0)->P)))=> (((((and_rect ((cR X0) x8)) ((cR x8) X0)) P) x12) x9)) False) (fun (x12:((cR X0) x8)) (x13:((cR X) x0))=> ((x2 x13) x6))) as proof of False
% Found (fun (x9:((and ((cR X0) x8)) ((cR x8) X0)))=> (((fun (P:Type) (x12:(((cR X0) x8)->(((cR x8) X0)->P)))=> (((((and_rect ((cR X0) x8)) ((cR x8) X0)) P) x12) x9)) False) (fun (x12:((cR X0) x8)) (x13:((cR X) x0))=> ((x2 x13) x6)))) as proof of False
% Found x20:=(x2 x31):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x31) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x31) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x20:(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found x20 as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x20:=(x2 x30):(not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found (x2 x30) as proof of (not ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0)))))
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found (fun (x7:((and ((cR X) x6)) ((cR x6) X)))=> x50) as proof of ((cR X) x0)
% Found (fun (x7:((and ((cR X) x6)) ((cR x6) X)))=> x50) as proof of (((and ((cR X) x6)) ((cR x6) X))->((cR X) x0))
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found (fun (x7:((and ((cR X0) x6)) ((cR x6) X0)))=> x30) as proof of ((cR X0) x0)
% Found (fun (x7:((and ((cR X0) x6)) ((cR x6) X0)))=> x30) as proof of (((and ((cR X0) x6)) ((cR x6) X0))->((cR X0) x0))
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found ((x4 x30) x00) as proof of False
% Found ((x4 x30) x00) as proof of False
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found ((x2 x50) x00) as proof of False
% Found ((x2 x50) x00) as proof of False
% Found x4:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x4 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x50:((cR X0) x0)
% Found (fun (x7:((and ((cR X) x6)) ((cR x6) X)))=> x50) as proof of ((cR X0) x0)
% Found (fun (x7:((and ((cR X) x6)) ((cR x6) X)))=> x50) as proof of (((and ((cR X) x6)) ((cR x6) X))->((cR X0) x0))
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x50:((cR X0) x0)
% Instantiate: X:=X0:fofType
% Found x50 as proof of ((cR X) x0)
% Found ((x2 x50) x00) as proof of False
% Found ((x2 x50) x00) as proof of False
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found ((x2 x30) x00) as proof of False
% Found ((x2 x30) x00) as proof of False
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x50:((cR X0) x0)
% Found x50 as proof of ((cR X0) x0)
% Found ((x4 x50) x00) as proof of False
% Found ((x4 x50) x00) as proof of False
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found ((x4 x30) x00) as proof of False
% Found ((x4 x30) x00) as proof of False
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x20:=(x2 x30):(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x2 x30) as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x50:((cR X0) x0)
% Found x50 as proof of ((cR X0) x0)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found ((x4 x50) x00) as proof of False
% Found ((x4 x50) x00) as proof of False
% Found x30:((cR X) x0)
% Found x30 as proof of ((cR X) x0)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Instantiate: X:=X0:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Found ((x2 x30) x00) as proof of False
% Found ((x2 x30) x00) as proof of False
% Found x30:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x30 as proof of ((cR X0) x0)
% Found x30:=(x3 x20):((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found (x3 x20) as proof of ((cR X) x0)
% Found x40:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Instantiate: X:=X0:fofType
% Found x40 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x3 x40) as proof of ((cR X) x0)
% Found (x3 x40) as proof of ((cR X) x0)
% Found x31:((cR X) x0)
% Instantiate: X0:=X:fofType
% Found x31 as proof of ((cR X0) x0)
% Found x20:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found x20 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found (x3 x20) as proof of ((cR X0) x0)
% Found x40:(((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))->False)
% Instantiate: X:=X0:fofType
% Found x40 as proof of (((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))->False)
% Found (x3 x40) as proof of ((cR X) x0)
% Found (x3 x40) as proof of ((cR X) x0)
% Found x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X))))
% Instantiate: X0:=X:fofType
% Found x00 as proof of ((ex fofType) (fun (Z:fofType)=> ((and ((cR X0) Z)) ((cR Z) X0))))
% Found x50:((cR X0) x0)
% Found x50 as proof of ((cR X0) x0)
% Found ((x4 x50) x00) as proof of False
% Found (fun (x00:((ex fofType) (fun (Z:fofType)=> ((and ((cR X) Z)) ((cR Z) X)))))=
% EOF
%------------------------------------------------------------------------------