%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SEV243^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n114.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 13:33:55 EDT 2014

% Result   : Timeout 300.10s
% Output   : None 
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SEV243^5 : TPTP v6.1.0. Released v4.0.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n114.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 08:36:11 CDT 2014
% % CPUTime  : 300.10 
% 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 0x27c1f38>, <kernel.Type object at 0x27c1cb0>) of role type named a_type
% Using role type
% Declaring a:Type
% FOF formula (<kernel.Constant object at 0x2bfbcf8>, <kernel.DependentProduct object at 0x27c1b48>) of role type named cK
% Using role type
% Declaring cK:((a->Prop)->(a->Prop))
% FOF formula ((forall (Y:(a->Prop)) (X:(a->Prop)), ((forall (Xx:a), ((X Xx)->(Y Xx)))->(forall (Xx:a), (((cK X) Xx)->((cK Y) Xx)))))->(forall (Xx:a), ((iff ((cK (fun (Xx0:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))) Xx)) ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))) of role conjecture named cTHM116_C_pme
% Conjecture to prove = ((forall (Y:(a->Prop)) (X:(a->Prop)), ((forall (Xx:a), ((X Xx)->(Y Xx)))->(forall (Xx:a), (((cK X) Xx)->((cK Y) Xx)))))->(forall (Xx:a), ((iff ((cK (fun (Xx0:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))) Xx)) ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))):Prop
% Parameter a_DUMMY:a.
% We need to prove ['((forall (Y:(a->Prop)) (X:(a->Prop)), ((forall (Xx:a), ((X Xx)->(Y Xx)))->(forall (Xx:a), (((cK X) Xx)->((cK Y) Xx)))))->(forall (Xx:a), ((iff ((cK (fun (Xx0:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))) Xx)) ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx)))))))']
% Parameter a:Type.
% Parameter cK:((a->Prop)->(a->Prop)).
% Trying to prove ((forall (Y:(a->Prop)) (X:(a->Prop)), ((forall (Xx:a), ((X Xx)->(Y Xx)))->(forall (Xx:a), (((cK X) Xx)->((cK Y) Xx)))))->(forall (Xx:a), ((iff ((cK (fun (Xx0:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))) Xx)) ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx)))))))
% Found x2:(X Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X Xx0))=> x2) as proof of ((X Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X Xx0))=> x2) as proof of (forall (Xx:a), ((X Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X Xx0))=> x2) as proof of ((X Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X Xx0))=> x2) as proof of (forall (Xx:a), ((X Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X Xx0))=> x4) as proof of ((X Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X Xx0))=> x4) as proof of (forall (Xx:a), ((X Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X) Xx)
% Found ((and_rect0 ((cK X) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X) Xx)
% Found x40:=(x4 Xx):((x1 Xx)->((cK x1) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((cK X) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((cK X) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx)) as proof of ((x1 Xx)->((cK X) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->((cK X) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X) Xx)
% Found ((and_rect0 ((cK X) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((cK X) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((cK X) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X) Xx)
% Found x4:(X Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X Xx0))=> x4) as proof of ((X Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X Xx0))=> x4) as proof of (forall (Xx:a), ((X Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X) Xx)
% Found ((and_rect0 ((cK X) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X) Xx)
% Found x40:=(x4 Xx):((x1 Xx)->((cK x1) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((cK X) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((cK X) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx)) as proof of ((x1 Xx)->((cK X) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->((cK X) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X) Xx)
% Found ((and_rect0 ((cK X) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((cK X) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((cK X) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X) Xx)
% Found x6:(X Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X Xx0))=> x6) as proof of ((X Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X Xx0))=> x6) as proof of (forall (Xx:a), ((X Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x300:=(x30 x4):((cK x1) Xx)
% Found (x30 x4) as proof of ((cK X) Xx)
% Found ((x3 Xx) x4) as proof of ((cK X) Xx)
% Found ((x3 Xx) x4) as proof of ((cK X) Xx)
% Found ((x3 Xx) x4) as proof of ((cK X) Xx)
% Found x6:(X Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X Xx0))=> x6) as proof of ((X Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X Xx0))=> x6) as proof of (forall (Xx:a), ((X Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x300:=(x30 x4):((cK x1) Xx)
% Found (x30 x4) as proof of ((cK X) Xx)
% Found ((x3 Xx) x4) as proof of ((cK X) Xx)
% Found ((x3 Xx) x4) as proof of ((cK X) Xx)
% Found ((x3 Xx) x4) as proof of ((cK X) Xx)
% Found x2:(X0 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X0 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X0 Xx0))=> x2) as proof of ((X0 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X0 Xx0))=> x2) as proof of (forall (Xx:a), ((X0 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X0 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X0 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X0 Xx0))=> x4) as proof of ((X0 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X0 Xx0))=> x4) as proof of (forall (Xx:a), ((X0 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X0 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X0 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X0 Xx0))=> x2) as proof of ((X0 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X0 Xx0))=> x2) as proof of (forall (Xx:a), ((X0 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X0 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X0 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X0 Xx0))=> x4) as proof of ((X0 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X0 Xx0))=> x4) as proof of (forall (Xx:a), ((X0 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X0) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X0) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X0) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X0) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found ((and_rect0 ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found x00:(x1 Xx0)
% Instantiate: x1:=(cK X):(a->Prop)
% Found x00 as proof of ((cK X) Xx0)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X0) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X0) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X0) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X0) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found ((and_rect0 ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found x2:(X0 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X0 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X0 Xx0))=> x2) as proof of ((X0 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X0 Xx0))=> x2) as proof of (forall (Xx:a), ((X0 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X0 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X0 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X0 Xx0))=> x2) as proof of ((X0 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X0 Xx0))=> x2) as proof of (forall (Xx:a), ((X0 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X0 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X0 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X0 Xx0))=> x4) as proof of ((X0 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X0 Xx0))=> x4) as proof of (forall (Xx:a), ((X0 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X0 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X0 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X0 Xx0))=> x4) as proof of ((X0 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X0 Xx0))=> x4) as proof of (forall (Xx:a), ((X0 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x00:(x1 Xx0)
% Instantiate: x1:=(cK X):(a->Prop)
% Found x00 as proof of ((cK X) Xx0)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X0) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X0) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X0) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X0) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found ((and_rect0 ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found x4:(X0 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X0 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X0 Xx0))=> x4) as proof of ((X0 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X0 Xx0))=> x4) as proof of (forall (Xx:a), ((X0 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X0) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X0) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X0) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X0) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found ((and_rect0 ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found x40:=(x4 Xx):((x1 Xx)->((cK x1) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((cK X0) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((cK X0) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx)) as proof of ((x1 Xx)->((cK X0) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->((cK X0) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found ((and_rect0 ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X0) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X0) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X0) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X0) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found ((and_rect0 ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X0) Xx)
% Found x6:(X0 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X0 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X0 Xx0))=> x6) as proof of ((X0 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X0 Xx0))=> x6) as proof of (forall (Xx:a), ((X0 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X0) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X0) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X0) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X0) Xx)
% Found x6:(X0 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X0 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X0 Xx0))=> x6) as proof of ((X0 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X0 Xx0))=> x6) as proof of (forall (Xx:a), ((X0 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X0) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X0) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X0) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X0) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X0) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X0) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X0) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X0) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found ((and_rect0 ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X0) Xx)
% Found x4:(X0 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X0 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X0 Xx0))=> x4) as proof of ((X0 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X0 Xx0))=> x4) as proof of (forall (Xx:a), ((X0 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x40:=(x4 Xx):((x1 Xx)->((cK x1) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((cK X0) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((cK X0) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx)) as proof of ((x1 Xx)->((cK X0) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->((cK X0) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found ((and_rect0 ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X0) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X0) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X0) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X0) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found ((and_rect0 ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X0) Xx)
% Found x6:(X0 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X0 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X0 Xx0))=> x6) as proof of ((X0 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X0 Xx0))=> x6) as proof of (forall (Xx:a), ((X0 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X0) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X0) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X0) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X0) Xx)
% Found x6:(X0 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X0 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X0 Xx0))=> x6) as proof of ((X0 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X0 Xx0))=> x6) as proof of (forall (Xx:a), ((X0 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X0) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X0) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X0) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X0) Xx)
% Found x6:(X0 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X0 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X0 Xx0))=> x6) as proof of ((X0 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X0 Xx0))=> x6) as proof of (forall (Xx:a), ((X0 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x300:=(x30 x4):((cK x1) Xx)
% Found (x30 x4) as proof of ((cK X0) Xx)
% Found ((x3 Xx) x4) as proof of ((cK X0) Xx)
% Found ((x3 Xx) x4) as proof of ((cK X0) Xx)
% Found ((x3 Xx) x4) as proof of ((cK X0) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X0) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X0) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X0) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X0) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found ((and_rect0 ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X0) Xx)
% Found x6:(X0 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X0 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X0 Xx0))=> x6) as proof of ((X0 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X0 Xx0))=> x6) as proof of (forall (Xx:a), ((X0 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x300:=(x30 x4):((cK x1) Xx)
% Found (x30 x4) as proof of ((cK X0) Xx)
% Found ((x3 Xx) x4) as proof of ((cK X0) Xx)
% Found ((x3 Xx) x4) as proof of ((cK X0) Xx)
% Found ((x3 Xx) x4) as proof of ((cK X0) Xx)
% Found x2:(X1 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X1 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X1 Xx0))=> x2) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X1 Xx0))=> x2) as proof of (forall (Xx:a), ((X1 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X1 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X1 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X1 Xx0))=> x4) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X1 Xx0))=> x4) as proof of (forall (Xx:a), ((X1 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X1 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X1 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X1 Xx0))=> x2) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X1 Xx0))=> x2) as proof of (forall (Xx:a), ((X1 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X1 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X1 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X1 Xx0))=> x2) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X1 Xx0))=> x2) as proof of (forall (Xx:a), ((X1 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X1 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X1 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X1 Xx0))=> x4) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X1 Xx0))=> x4) as proof of (forall (Xx:a), ((X1 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X1 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X1 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X1 Xx0))=> x2) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X1 Xx0))=> x2) as proof of (forall (Xx:a), ((X1 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X1 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X1 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X1 Xx0))=> x4) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X1 Xx0))=> x4) as proof of (forall (Xx:a), ((X1 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X1 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X1 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X1 Xx0))=> x4) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X1 Xx0))=> x4) as proof of (forall (Xx:a), ((X1 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X1 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X1 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X1 Xx0))=> x4) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X1 Xx0))=> x4) as proof of (forall (Xx:a), ((X1 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X1) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found ((and_rect0 ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X1) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found ((and_rect0 ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found x4:(X1 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X1 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X1 Xx0))=> x4) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X1 Xx0))=> x4) as proof of (forall (Xx:a), ((X1 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x6:(X1 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X1 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X1 Xx0))=> x6) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X1 Xx0))=> x6) as proof of (forall (Xx:a), ((X1 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X1) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% Found x2:(X1 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X1 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X1 Xx0))=> x2) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X1 Xx0))=> x2) as proof of (forall (Xx:a), ((X1 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X1) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found ((and_rect0 ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X1) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found ((and_rect0 ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X1) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found ((and_rect0 ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found x2:(X1 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X1 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X1 Xx0))=> x2) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X1 Xx0))=> x2) as proof of (forall (Xx:a), ((X1 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X1 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X1 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X1 Xx0))=> x2) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X1 Xx0))=> x2) as proof of (forall (Xx:a), ((X1 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x6:(X1 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X1 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X1 Xx0))=> x6) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X1 Xx0))=> x6) as proof of (forall (Xx:a), ((X1 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X1) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% Found x4:(X1 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X1 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X1 Xx0))=> x4) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X1 Xx0))=> x4) as proof of (forall (Xx:a), ((X1 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X1) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found ((and_rect0 ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found x2:(X1 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X1 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X1 Xx0))=> x2) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X1 Xx0))=> x2) as proof of (forall (Xx:a), ((X1 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X1 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X1 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X1 Xx0))=> x4) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X1 Xx0))=> x4) as proof of (forall (Xx:a), ((X1 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X1 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X1 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X1 Xx0))=> x4) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X1 Xx0))=> x4) as proof of (forall (Xx:a), ((X1 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X1 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X1 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X1 Xx0))=> x4) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X1 Xx0))=> x4) as proof of (forall (Xx:a), ((X1 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X1 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X1 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X1 Xx0))=> x4) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X1 Xx0))=> x4) as proof of (forall (Xx:a), ((X1 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X1 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X1 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X1 Xx0))=> x4) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X1 Xx0))=> x4) as proof of (forall (Xx:a), ((X1 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X1) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found ((and_rect0 ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X1) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found ((and_rect0 ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found x4:(X1 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X1 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X1 Xx0))=> x4) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X1 Xx0))=> x4) as proof of (forall (Xx:a), ((X1 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x6:(X1 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X1 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X1 Xx0))=> x6) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X1 Xx0))=> x6) as proof of (forall (Xx:a), ((X1 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X1) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X1) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found ((and_rect0 ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X1) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found ((and_rect0 ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X1) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found ((and_rect0 ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found x6:(X1 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X1 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X1 Xx0))=> x6) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X1 Xx0))=> x6) as proof of (forall (Xx:a), ((X1 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X1) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X1) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found ((and_rect0 ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found x6:(X1 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X1 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X1 Xx0))=> x6) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X1 Xx0))=> x6) as proof of (forall (Xx:a), ((X1 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X1) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% Found x6:(X1 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X1 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X1 Xx0))=> x6) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X1 Xx0))=> x6) as proof of (forall (Xx:a), ((X1 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X1) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% Found x40:=(x4 Xx):((x1 Xx)->((cK x1) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((cK X1) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx)) as proof of ((x1 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->((cK X1) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found ((and_rect0 ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X1) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found ((and_rect0 ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X1) Xx)
% Found x6:(X1 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X1 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X1 Xx0))=> x6) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X1 Xx0))=> x6) as proof of (forall (Xx:a), ((X1 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X1) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% Found x6:(X1 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X1 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X1 Xx0))=> x6) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X1 Xx0))=> x6) as proof of (forall (Xx:a), ((X1 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X1) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% Found x4:(X1 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X1 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X1 Xx0))=> x4) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X1 Xx0))=> x4) as proof of (forall (Xx:a), ((X1 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X1) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found ((and_rect0 ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X1) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X1) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found ((and_rect0 ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X1) Xx)
% Found x6:(X1 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X1 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X1 Xx0))=> x6) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X1 Xx0))=> x6) as proof of (forall (Xx:a), ((X1 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X1) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X1) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found ((and_rect0 ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X1) Xx)
% Found x40:=(x4 Xx):((x1 Xx)->((cK x1) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((cK X1) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx)) as proof of ((x1 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->((cK X1) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found ((and_rect0 ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X1) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found ((and_rect0 ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X1) Xx)
% Found x6:(X1 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X1 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X1 Xx0))=> x6) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X1 Xx0))=> x6) as proof of (forall (Xx:a), ((X1 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x300:=(x30 x4):((cK x1) Xx)
% Found (x30 x4) as proof of ((cK X1) Xx)
% Found ((x3 Xx) x4) as proof of ((cK X1) Xx)
% Found ((x3 Xx) x4) as proof of ((cK X1) Xx)
% Found ((x3 Xx) x4) as proof of ((cK X1) Xx)
% Found x6:(X1 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X1 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X1 Xx0))=> x6) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X1 Xx0))=> x6) as proof of (forall (Xx:a), ((X1 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X1) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% Found x6:(X1 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X1 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X1 Xx0))=> x6) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X1 Xx0))=> x6) as proof of (forall (Xx:a), ((X1 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X1) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% Found x6:(X1 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X1 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X1 Xx0))=> x6) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X1 Xx0))=> x6) as proof of (forall (Xx:a), ((X1 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X1) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% Found x6:(X1 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X1 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X1 Xx0))=> x6) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X1 Xx0))=> x6) as proof of (forall (Xx:a), ((X1 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X1) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X1) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found ((and_rect0 ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X1) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X1) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found ((and_rect0 ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X1) Xx)
% Found x6:(X1 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X1 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X1 Xx0))=> x6) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X1 Xx0))=> x6) as proof of (forall (Xx:a), ((X1 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X1) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X1) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found ((and_rect0 ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X1) Xx)
% Found x6:(X1 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X1 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X1 Xx0))=> x6) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X1 Xx0))=> x6) as proof of (forall (Xx:a), ((X1 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x300:=(x30 x4):((cK x1) Xx)
% Found (x30 x4) as proof of ((cK X1) Xx)
% Found ((x3 Xx) x4) as proof of ((cK X1) Xx)
% Found ((x3 Xx) x4) as proof of ((cK X1) Xx)
% Found ((x3 Xx) x4) as proof of ((cK X1) Xx)
% Found x2:(X2 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X2 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X2 Xx0))=> x2) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X2 Xx0))=> x2) as proof of (forall (Xx:a), ((X2 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X2 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X2 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X2 Xx0))=> x2) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X2 Xx0))=> x2) as proof of (forall (Xx:a), ((X2 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X2 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X2 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X2 Xx0))=> x2) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X2 Xx0))=> x2) as proof of (forall (Xx:a), ((X2 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X2 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X2 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X2 Xx0))=> x2) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X2 Xx0))=> x2) as proof of (forall (Xx:a), ((X2 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X2 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X2 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X2 Xx0))=> x4) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X2 Xx0))=> x4) as proof of (forall (Xx:a), ((X2 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X2 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X2 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X2 Xx0))=> x2) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X2 Xx0))=> x2) as proof of (forall (Xx:a), ((X2 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X2 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X2 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X2 Xx0))=> x2) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X2 Xx0))=> x2) as proof of (forall (Xx:a), ((X2 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X2 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X2 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X2 Xx0))=> x2) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X2 Xx0))=> x2) as proof of (forall (Xx:a), ((X2 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X2 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X2 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X2 Xx0))=> x4) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X2 Xx0))=> x4) as proof of (forall (Xx:a), ((X2 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X2 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X2 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X2 Xx0))=> x4) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X2 Xx0))=> x4) as proof of (forall (Xx:a), ((X2 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X2 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X2 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X2 Xx0))=> x2) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X2 Xx0))=> x2) as proof of (forall (Xx:a), ((X2 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X2 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X2 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X2 Xx0))=> x4) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X2 Xx0))=> x4) as proof of (forall (Xx:a), ((X2 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X2 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X2 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X2 Xx0))=> x4) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X2 Xx0))=> x4) as proof of (forall (Xx:a), ((X2 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X2 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X2 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X2 Xx0))=> x4) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X2 Xx0))=> x4) as proof of (forall (Xx:a), ((X2 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X2 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X2 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X2 Xx0))=> x4) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X2 Xx0))=> x4) as proof of (forall (Xx:a), ((X2 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X2 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X2 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X2 Xx0))=> x4) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X2 Xx0))=> x4) as proof of (forall (Xx:a), ((X2 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X2 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X2 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X2 Xx0))=> x4) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X2 Xx0))=> x4) as proof of (forall (Xx:a), ((X2 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X2 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X2 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X2 Xx0))=> x4) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X2 Xx0))=> x4) as proof of (forall (Xx:a), ((X2 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X2 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X2 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X2 Xx0))=> x2) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X2 Xx0))=> x2) as proof of (forall (Xx:a), ((X2 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X2) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found ((and_rect0 ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X2) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found ((and_rect0 ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X2) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found ((and_rect0 ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found x4:(X2 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X2 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X2 Xx0))=> x4) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X2 Xx0))=> x4) as proof of (forall (Xx:a), ((X2 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X2 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X2 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X2 Xx0))=> x4) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X2 Xx0))=> x4) as proof of (forall (Xx:a), ((X2 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x6:(X2 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X2 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of (forall (Xx:a), ((X2 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found x4:(X2 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X2 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X2 Xx0))=> x4) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X2 Xx0))=> x4) as proof of (forall (Xx:a), ((X2 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X2 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X2 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X2 Xx0))=> x2) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X2 Xx0))=> x2) as proof of (forall (Xx:a), ((X2 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X2 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X2 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X2 Xx0))=> x2) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X2 Xx0))=> x2) as proof of (forall (Xx:a), ((X2 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X2 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X2 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X2 Xx0))=> x2) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X2 Xx0))=> x2) as proof of (forall (Xx:a), ((X2 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x6:(X2 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X2 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of (forall (Xx:a), ((X2 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found x6:(X2 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X2 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of (forall (Xx:a), ((X2 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X2) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found ((and_rect0 ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X2) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found ((and_rect0 ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X2) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found ((and_rect0 ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X2) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found ((and_rect0 ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X2) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found ((and_rect0 ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X2) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found ((and_rect0 ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found x4:(X2 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X2 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X2 Xx0))=> x4) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X2 Xx0))=> x4) as proof of (forall (Xx:a), ((X2 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x6:(X2 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X2 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of (forall (Xx:a), ((X2 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found x4:(X2 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X2 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X2 Xx0))=> x4) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X2 Xx0))=> x4) as proof of (forall (Xx:a), ((X2 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X2 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X2 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X2 Xx0))=> x2) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X2 Xx0))=> x2) as proof of (forall (Xx:a), ((X2 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X2 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X2 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X2 Xx0))=> x2) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X2 Xx0))=> x2) as proof of (forall (Xx:a), ((X2 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X2 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X2 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X2 Xx0))=> x2) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X2 Xx0))=> x2) as proof of (forall (Xx:a), ((X2 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x6:(X2 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X2 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of (forall (Xx:a), ((X2 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found x6:(X2 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X2 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of (forall (Xx:a), ((X2 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found x6:(X2 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X2 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of (forall (Xx:a), ((X2 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found x4:(X2 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X2 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X2 Xx0))=> x4) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X2 Xx0))=> x4) as proof of (forall (Xx:a), ((X2 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X2) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found ((and_rect0 ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X2) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found ((and_rect0 ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X2) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found ((and_rect0 ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X2) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found ((and_rect0 ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found x4:(X2 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X2 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X2 Xx0))=> x4) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X2 Xx0))=> x4) as proof of (forall (Xx:a), ((X2 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X2 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X2 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X2 Xx0))=> x2) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X2 Xx0))=> x2) as proof of (forall (Xx:a), ((X2 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X2 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X2 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X2 Xx0))=> x4) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X2 Xx0))=> x4) as proof of (forall (Xx:a), ((X2 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X2 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X2 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X2 Xx0))=> x4) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X2 Xx0))=> x4) as proof of (forall (Xx:a), ((X2 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X2 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X2 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X2 Xx0))=> x4) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X2 Xx0))=> x4) as proof of (forall (Xx:a), ((X2 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x6:(X2 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X2 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of (forall (Xx:a), ((X2 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X2) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found ((and_rect0 ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found x4:(X2 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X2 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X2 Xx0))=> x4) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X2 Xx0))=> x4) as proof of (forall (Xx:a), ((X2 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X2 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X2 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X2 Xx0))=> x4) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X2 Xx0))=> x4) as proof of (forall (Xx:a), ((X2 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X2 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X2 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X2 Xx0))=> x4) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X2 Xx0))=> x4) as proof of (forall (Xx:a), ((X2 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X2 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X2 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X2 Xx0))=> x4) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X2 Xx0))=> x4) as proof of (forall (Xx:a), ((X2 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X2 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X2 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X2 Xx0))=> x4) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X2 Xx0))=> x4) as proof of (forall (Xx:a), ((X2 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X2 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X2 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X2 Xx0))=> x4) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X2 Xx0))=> x4) as proof of (forall (Xx:a), ((X2 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X2 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X2 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X2 Xx0))=> x4) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X2 Xx0))=> x4) as proof of (forall (Xx:a), ((X2 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X2) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found ((and_rect0 ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X2) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found ((and_rect0 ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X2) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found ((and_rect0 ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found x4:(X2 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X2 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X2 Xx0))=> x4) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X2 Xx0))=> x4) as proof of (forall (Xx:a), ((X2 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x6:(X2 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X2 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of (forall (Xx:a), ((X2 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found x6:(X2 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X2 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of (forall (Xx:a), ((X2 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found x6:(X2 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X2 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of (forall (Xx:a), ((X2 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found x4:(X2 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X2 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X2 Xx0))=> x4) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X2 Xx0))=> x4) as proof of (forall (Xx:a), ((X2 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X2) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found ((and_rect0 ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X2) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found ((and_rect0 ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X2) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found ((and_rect0 ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X2) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found ((and_rect0 ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X2) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found ((and_rect0 ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X2) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found ((and_rect0 ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found x6:(X2 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X2 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of (forall (Xx:a), ((X2 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found x6:(X2 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X2 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of (forall (Xx:a), ((X2 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found x6:(X2 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X2 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of (forall (Xx:a), ((X2 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found x6:(X2 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X2 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of (forall (Xx:a), ((X2 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found x6:(X2 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X2 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of (forall (Xx:a), ((X2 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X2) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found ((and_rect0 ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found x6:(X2 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X2 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of (forall (Xx:a), ((X2 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X2) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found ((and_rect0 ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X2) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found ((and_rect0 ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X2) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found ((and_rect0 ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found x40:=(x4 Xx):((x1 Xx)->((cK x1) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((cK X2) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx)) as proof of ((x1 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->((cK X2) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found ((and_rect0 ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X2) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found ((and_rect0 ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X2) Xx)
% Found x6:(X2 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X2 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of (forall (Xx:a), ((X2 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found x6:(X2 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X2 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of (forall (Xx:a), ((X2 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found x4:(X2 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X2 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X2 Xx0))=> x4) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X2 Xx0))=> x4) as proof of (forall (Xx:a), ((X2 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x6:(X2 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X2 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of (forall (Xx:a), ((X2 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found x6:(X2 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X2 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of (forall (Xx:a), ((X2 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X2) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found ((and_rect0 ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found x6:(X2 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X2 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of (forall (Xx:a), ((X2 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X2) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found ((and_rect0 ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X2) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X2) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found ((and_rect0 ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X2) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X2) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found ((and_rect0 ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X2) Xx)
% Found x6:(X2 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X2 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of (forall (Xx:a), ((X2 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found x6:(X2 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X2 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of (forall (Xx:a), ((X2 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found x6:(X2 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X2 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of (forall (Xx:a), ((X2 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X2) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found ((and_rect0 ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X2) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X2) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found ((and_rect0 ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X2) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X2) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found ((and_rect0 ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X2) Xx)
% Found x6:(X2 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X2 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of (forall (Xx:a), ((X2 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X2) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found ((and_rect0 ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X2) Xx)
% Found x6:(X2 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X2 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of (forall (Xx:a), ((X2 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x300:=(x30 x4):((cK x1) Xx)
% Found (x30 x4) as proof of ((cK X2) Xx)
% Found ((x3 Xx) x4) as proof of ((cK X2) Xx)
% Found ((x3 Xx) x4) as proof of ((cK X2) Xx)
% Found ((x3 Xx) x4) as proof of ((cK X2) Xx)
% Found x6:(X2 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X2 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of (forall (Xx:a), ((X2 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found x6:(X2 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X2 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of (forall (Xx:a), ((X2 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found x40:=(x4 Xx):((x1 Xx)->((cK x1) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((cK X2) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx)) as proof of ((x1 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->((cK X2) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found ((and_rect0 ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X2) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found ((and_rect0 ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X2) Xx)
% Found x6:(X2 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X2 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of (forall (Xx:a), ((X2 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found x6:(X2 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X2 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of (forall (Xx:a), ((X2 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found x6:(X2 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X2 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of (forall (Xx:a), ((X2 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found x6:(X2 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X2 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of (forall (Xx:a), ((X2 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X2) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found ((and_rect0 ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X2) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X2) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found ((and_rect0 ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X2) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X2) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found ((and_rect0 ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X2) Xx)
% Found x6:(X2 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X2 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of (forall (Xx:a), ((X2 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found x6:(X2 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X2 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of (forall (Xx:a), ((X2 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found x6:(X2 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X2 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of (forall (Xx:a), ((X2 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X2) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found ((and_rect0 ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X2) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X2) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found ((and_rect0 ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X2) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X2) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found ((and_rect0 ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X2) Xx)
% Found x6:(X2 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X2 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of (forall (Xx:a), ((X2 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X2) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X2) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found ((and_rect0 ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X2) Xx)
% Found x6:(X2 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X2 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of (forall (Xx:a), ((X2 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x300:=(x30 x4):((cK x1) Xx)
% Found (x30 x4) as proof of ((cK X2) Xx)
% Found ((x3 Xx) x4) as proof of ((cK X2) Xx)
% Found ((x3 Xx) x4) as proof of ((cK X2) Xx)
% Found ((x3 Xx) x4) as proof of ((cK X2) Xx)
% Found x2:(X3 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X3 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X3 Xx0))=> x2) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X3 Xx0))=> x2) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X3 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X3 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X3 Xx0))=> x2) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X3 Xx0))=> x2) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X3 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X3 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X3 Xx0))=> x2) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X3 Xx0))=> x2) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X3 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X3 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X3 Xx0))=> x2) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X3 Xx0))=> x2) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X3 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X3 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X3 Xx0))=> x2) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X3 Xx0))=> x2) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X3 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X3 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X3 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X3 Xx0))=> x2) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X3 Xx0))=> x2) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X3 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X3 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X3 Xx0))=> x2) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X3 Xx0))=> x2) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X3 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X3 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X3 Xx0))=> x2) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X3 Xx0))=> x2) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X3 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X3 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X3 Xx0))=> x2) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X3 Xx0))=> x2) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X3 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X3 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X3 Xx0))=> x2) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X3 Xx0))=> x2) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X3 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X3 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X3 Xx0))=> x2) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X3 Xx0))=> x2) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X3 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X3 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X3 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X3 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X3 Xx0))=> x2) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X3 Xx0))=> x2) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X3 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X3 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X3 Xx0))=> x2) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X3 Xx0))=> x2) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X3 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X3 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X3 Xx0))=> x2) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X3 Xx0))=> x2) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X3 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X3 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X3 Xx0))=> x2) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X3 Xx0))=> x2) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X3 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X3 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X3 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X3 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X3 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X3 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X3 Xx0))=> x2) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X3 Xx0))=> x2) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X3 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X3 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X3 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X3 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X3 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X3 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X3 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X3 Xx0))=> x2) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X3 Xx0))=> x2) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X3 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X3 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X3 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X3 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X3 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X3 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x6:(X3 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x2:(X3 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X3 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X3 Xx0))=> x2) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X3 Xx0))=> x2) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X3 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X3 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X3 Xx0))=> x2) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X3 Xx0))=> x2) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X3 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X3 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X3 Xx0))=> x2) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X3 Xx0))=> x2) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X3 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X3 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X3 Xx0))=> x2) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X3 Xx0))=> x2) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found x4:(X3 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X3 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X3 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found x4:(X3 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X3 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X3 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x6:(X3 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x6:(X3 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x4:(X3 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X3 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X3 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X3 Xx0))=> x2) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X3 Xx0))=> x2) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X3 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X3 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X3 Xx0))=> x2) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X3 Xx0))=> x2) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X3 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X3 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X3 Xx0))=> x2) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X3 Xx0))=> x2) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X3 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X3 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X3 Xx0))=> x2) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X3 Xx0))=> x2) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X3 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X3 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X3 Xx0))=> x2) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X3 Xx0))=> x2) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X3 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X3 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X3 Xx0))=> x2) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X3 Xx0))=> x2) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X3 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x6:(X3 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x6:(X3 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x6:(X3 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x6:(X3 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found x4:(X3 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X3 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X3 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found x4:(X3 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X3 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x6:(X3 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x6:(X3 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x6:(X3 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x2:(X3 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X3 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X3 Xx0))=> x2) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X3 Xx0))=> x2) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X3 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X3 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X3 Xx0))=> x2) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X3 Xx0))=> x2) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X3 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X3 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X3 Xx0))=> x2) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X3 Xx0))=> x2) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X3 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X3 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X3 Xx0))=> x2) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X3 Xx0))=> x2) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X3 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X3 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x6:(X3 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x6:(X3 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x6:(X3 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x6:(X3 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x6:(X3 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x6:(X3 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x4:(X3 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found x4:(X3 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found x2:(X3 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X3 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X3 Xx0))=> x2) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X3 Xx0))=> x2) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X3 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X3 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X3 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x6:(X3 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x4:(X3 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X3 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X3 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x6:(X3 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x6:(X3 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x6:(X3 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x6:(X3 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found x4:(X3 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X3 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X3 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X3 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X3 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X3 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X3 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X3 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x6:(X3 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found x4:(X3 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X3 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X3 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x6:(X3 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found x4:(X3 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X3 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X3 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X3 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x6:(X3 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x6:(X3 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x4:(X3 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X3 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X3 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x6:(X3 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found x6:(X3 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found x6:(X3 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x6:(X3 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found x4:(X3 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x6:(X3 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x6:(X3 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x6:(X3 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x6:(X3 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x6:(X3 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x6:(X3 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x6:(X3 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x4:(X3 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X3 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x6:(X3 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found x6:(X3 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x6:(X3 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found x6:(X3 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found x6:(X3 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x6:(X3 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x1 Xx)->((cK x1) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx)) as proof of ((x1 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X3) Xx)
% Found x6:(X3 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x6:(X3 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x6:(X3 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x6:(X3 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x6:(X3 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x6:(X3 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X3) Xx)
% Found x6:(X3 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found x6:(X3 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x6:(X3 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found x6:(X3 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x6:(X3 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x6:(X3 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x6:(X3 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x6:(X3 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x6:(X3 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found x6:(X3 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x6:(X3 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x6:(X3 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x6:(X3 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x6:(X3 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X3) Xx)
% Found x6:(X3 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x300:=(x30 x4):((cK x1) Xx)
% Found (x30 x4) as proof of ((cK X3) Xx)
% Found ((x3 Xx) x4) as proof of ((cK X3) Xx)
% Found ((x3 Xx) x4) as proof of ((cK X3) Xx)
% Found ((x3 Xx) x4) as proof of ((cK X3) Xx)
% Found x6:(X3 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x6:(X3 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x6:(X3 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X3) Xx)
% Found x6:(X3 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x1 Xx)->((cK x1) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx)) as proof of ((x1 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found x6:(X3 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X3) Xx)
% Found x6:(X3 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x6:(X3 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x6:(X3 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x6:(X3 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x6:(X3 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X3) Xx)
% Found x6:(X3 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x6:(X3 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x6:(X3 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X3) Xx)
% Found x6:(X3 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X3) Xx)
% Found x6:(X3 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x6:(X3 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X3) Xx)
% Found x6:(X3 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x300:=(x30 x4):((cK x1) Xx)
% Found (x30 x4) as proof of ((cK X3) Xx)
% Found ((x3 Xx) x4) as proof of ((cK X3) Xx)
% Found ((x3 Xx) x4) as proof of ((cK X3) Xx)
% Found ((x3 Xx) x4) as proof of ((cK X3) Xx)
% Found x6:(X3 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x6:(X3 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x6:(X3 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X3) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X3) Xx)
% Found x6:(X3 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of (forall (Xx:a), ((X3 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% Found x2:(X Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X Xx0))=> x2) as proof of ((X Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X Xx0))=> x2) as proof of (forall (Xx:a), ((X Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X Xx0))=> x2) as proof of ((X Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X Xx0))=> x2) as proof of (forall (Xx:a), ((X Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X Xx0))=> x2) as proof of ((X Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X Xx0))=> x2) as proof of (forall (Xx:a), ((X Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X Xx0))=> x4) as proof of ((X Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X Xx0))=> x4) as proof of (forall (Xx:a), ((X Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x40:=(x4 Xx):((x1 Xx)->((cK x1) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((cK X) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((cK X) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx)) as proof of ((x1 Xx)->((cK X) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->((cK X) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X) Xx)
% Found ((and_rect0 ((cK X) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((cK X) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((cK X) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X) Xx)
% Found ((and_rect0 ((cK X) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X) Xx)
% Found x4:(X Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X Xx0))=> x4) as proof of ((X Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X Xx0))=> x4) as proof of (forall (Xx:a), ((X Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X Xx0))=> x4) as proof of ((X Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X Xx0))=> x4) as proof of (forall (Xx:a), ((X Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x40:=(x4 Xx):((x1 Xx)->((cK x1) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((cK X) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((cK X) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx)) as proof of ((x1 Xx)->((cK X) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->((cK X) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X) Xx)
% Found ((and_rect0 ((cK X) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((cK X) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((cK X) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X) Xx)
% Found ((and_rect0 ((cK X) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X) Xx)
% Found x40:=(x4 Xx):((x1 Xx)->((cK x1) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((cK X) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((cK X) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx)) as proof of ((x1 Xx)->((cK X) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->((cK X) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X) Xx)
% Found ((and_rect0 ((cK X) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((cK X) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((cK X) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X) Xx)
% Found ((and_rect0 ((cK X) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X) Xx)
% Found x6:(X Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X Xx0))=> x6) as proof of ((X Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X Xx0))=> x6) as proof of (forall (Xx:a), ((X Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x300:=(x30 x4):((cK x1) Xx)
% Found (x30 x4) as proof of ((cK X) Xx)
% Found ((x3 Xx) x4) as proof of ((cK X) Xx)
% Found ((x3 Xx) x4) as proof of ((cK X) Xx)
% Found ((x3 Xx) x4) as proof of ((cK X) Xx)
% Found x6:(X Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X Xx0))=> x6) as proof of ((X Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X Xx0))=> x6) as proof of (forall (Xx:a), ((X Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x300:=(x30 x4):((cK x1) Xx)
% Found (x30 x4) as proof of ((cK X) Xx)
% Found ((x3 Xx) x4) as proof of ((cK X) Xx)
% Found ((x3 Xx) x4) as proof of ((cK X) Xx)
% Found ((x3 Xx) x4) as proof of ((cK X) Xx)
% Found x6:(X Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X Xx0))=> x6) as proof of ((X Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X Xx0))=> x6) as proof of (forall (Xx:a), ((X Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x300:=(x30 x4):((cK x1) Xx)
% Found (x30 x4) as proof of ((cK X) Xx)
% Found ((x3 Xx) x4) as proof of ((cK X) Xx)
% Found ((x3 Xx) x4) as proof of ((cK X) Xx)
% Found ((x3 Xx) x4) as proof of ((cK X) Xx)
% Found x2:(X4 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X4 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X4 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X4 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X4 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X4 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X4 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X4 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X4 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X4 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X4 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X4 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X4 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X4 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X4 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X4 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X4 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X4 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X4 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X4 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X4 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X4 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X4 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X4 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X4 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X4 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X4 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X4 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X4 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X4 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X4 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X4 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X4 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X4 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X4 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X4 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X4 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X4 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X4 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X4 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X4 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X4 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X4 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x2:(X4 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X4 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X4 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X4 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X4 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X0 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X0 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X0 Xx0))=> x2) as proof of ((X0 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X0 Xx0))=> x2) as proof of (forall (Xx:a), ((X0 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X4 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X4 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X4 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X4 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X4 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X4 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X4 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X4 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X4 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X4 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X0 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X0 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X0 Xx0))=> x4) as proof of ((X0 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X0 Xx0))=> x4) as proof of (forall (Xx:a), ((X0 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x2:(X0 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X0 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X0 Xx0))=> x2) as proof of ((X0 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X0 Xx0))=> x2) as proof of (forall (Xx:a), ((X0 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X0 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X0 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X0 Xx0))=> x4) as proof of ((X0 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X0 Xx0))=> x4) as proof of (forall (Xx:a), ((X0 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X4 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X4 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X4 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X4 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X4 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X0) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X0) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X0) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X0) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found ((and_rect0 ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x00:(x1 Xx0)
% Instantiate: x1:=(cK X):(a->Prop)
% Found x00 as proof of ((cK X) Xx0)
% Found x2:(X4 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X0) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X0) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X0) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X0) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found ((and_rect0 ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X0 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X0 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X0 Xx0))=> x2) as proof of ((X0 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X0 Xx0))=> x2) as proof of (forall (Xx:a), ((X0 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X0 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X0 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X0 Xx0))=> x2) as proof of ((X0 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X0 Xx0))=> x2) as proof of (forall (Xx:a), ((X0 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x2:(X0 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X0 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X0 Xx0))=> x2) as proof of ((X0 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X0 Xx0))=> x2) as proof of (forall (Xx:a), ((X0 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X0 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X0 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X0 Xx0))=> x2) as proof of ((X0 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X0 Xx0))=> x2) as proof of (forall (Xx:a), ((X0 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X0 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X0 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X0 Xx0))=> x4) as proof of ((X0 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X0 Xx0))=> x4) as proof of (forall (Xx:a), ((X0 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x4:(X0 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X0 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X0 Xx0))=> x4) as proof of ((X0 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X0 Xx0))=> x4) as proof of (forall (Xx:a), ((X0 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X0 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X0 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X0 Xx0))=> x4) as proof of ((X0 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X0 Xx0))=> x4) as proof of (forall (Xx:a), ((X0 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X0 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X0 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X0 Xx0))=> x4) as proof of ((X0 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X0 Xx0))=> x4) as proof of (forall (Xx:a), ((X0 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x00:(x1 Xx0)
% Instantiate: x1:=(cK X):(a->Prop)
% Found x00 as proof of ((cK X) Xx0)
% Found x00:(x1 Xx0)
% Instantiate: x1:=(cK X):(a->Prop)
% Found x00 as proof of ((cK X) Xx0)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X0) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X0) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X0) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X0) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found ((and_rect0 ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X0) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X0) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X0) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X0) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found ((and_rect0 ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x1 Xx)->((cK x1) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx)) as proof of ((x1 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x4:(X0 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X0 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X0 Xx0))=> x4) as proof of ((X0 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X0 Xx0))=> x4) as proof of (forall (Xx:a), ((X0 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X4) Xx)
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X0) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X0) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X0) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X0) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found ((and_rect0 ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X0) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X0) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X0) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X0) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found ((and_rect0 ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X4) Xx)
% Found x4:(X4 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x1 Xx)->((cK x1) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((cK X0) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((cK X0) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx)) as proof of ((x1 Xx)->((cK X0) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->((cK X0) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found ((and_rect0 ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X0) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X0) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X0) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X0) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found ((and_rect0 ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X0) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x6:(X0 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X0 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X0 Xx0))=> x6) as proof of ((X0 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X0 Xx0))=> x6) as proof of (forall (Xx:a), ((X0 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X0) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X0) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X0) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X0) Xx)
% Found x6:(X0 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X0 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X0 Xx0))=> x6) as proof of ((X0 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X0 Xx0))=> x6) as proof of (forall (Xx:a), ((X0 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X0) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X0) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X0) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X0) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x300:=(x30 x4):((cK x1) Xx)
% Found (x30 x4) as proof of ((cK X4) Xx)
% Found ((x3 Xx) x4) as proof of ((cK X4) Xx)
% Found ((x3 Xx) x4) as proof of ((cK X4) Xx)
% Found ((x3 Xx) x4) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X0) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X0) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X0) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X0) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found ((and_rect0 ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X0) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x4:(X0 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X0 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X0 Xx0))=> x4) as proof of ((X0 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X0 Xx0))=> x4) as proof of (forall (Xx:a), ((X0 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x4:(X0 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X0 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X0 Xx0))=> x4) as proof of ((X0 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X0 Xx0))=> x4) as proof of (forall (Xx:a), ((X0 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x1 Xx)->((cK x1) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx)) as proof of ((x1 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x1 Xx)->((cK x1) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((cK X0) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((cK X0) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx)) as proof of ((x1 Xx)->((cK X0) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->((cK X0) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found ((and_rect0 ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found x40:=(x4 Xx):((x1 Xx)->((cK x1) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((cK X0) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((cK X0) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx)) as proof of ((x1 Xx)->((cK X0) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->((cK X0) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found ((and_rect0 ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X0) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X0) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X0) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X0) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found ((and_rect0 ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X0) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X0) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X0) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X0) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X0) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found ((and_rect0 ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X0) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X0 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X0 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X0 Xx0))=> x6) as proof of ((X0 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X0 Xx0))=> x6) as proof of (forall (Xx:a), ((X0 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X0) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X0) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X0) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X0) Xx)
% Found x6:(X0 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X0 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X0 Xx0))=> x6) as proof of ((X0 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X0 Xx0))=> x6) as proof of (forall (Xx:a), ((X0 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X0) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X0) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X0) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X0) Xx)
% Found x6:(X0 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X0 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X0 Xx0))=> x6) as proof of ((X0 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X0 Xx0))=> x6) as proof of (forall (Xx:a), ((X0 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X0) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X0) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X0) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X0) Xx)
% Found x6:(X0 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X0 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X0 Xx0))=> x6) as proof of ((X0 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X0 Xx0))=> x6) as proof of (forall (Xx:a), ((X0 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X0) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X0) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X0) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X0) Xx)
% Found x6:(X0 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X0 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X0 Xx0))=> x6) as proof of ((X0 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X0 Xx0))=> x6) as proof of (forall (Xx:a), ((X0 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x300:=(x30 x4):((cK x1) Xx)
% Found (x30 x4) as proof of ((cK X0) Xx)
% Found ((x3 Xx) x4) as proof of ((cK X0) Xx)
% Found ((x3 Xx) x4) as proof of ((cK X0) Xx)
% Found ((x3 Xx) x4) as proof of ((cK X0) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X0) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X0) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X0) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X0) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found ((and_rect0 ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X0) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X0) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X0) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X0) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X0) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found ((and_rect0 ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X0) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x300:=(x30 x4):((cK x1) Xx)
% Found (x30 x4) as proof of ((cK X4) Xx)
% Found ((x3 Xx) x4) as proof of ((cK X4) Xx)
% Found ((x3 Xx) x4) as proof of ((cK X4) Xx)
% Found ((x3 Xx) x4) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X4) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X4) Xx)
% Found x6:(X0 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X0 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X0 Xx0))=> x6) as proof of ((X0 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X0 Xx0))=> x6) as proof of (forall (Xx:a), ((X0 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x300:=(x30 x4):((cK x1) Xx)
% Found (x30 x4) as proof of ((cK X0) Xx)
% Found ((x3 Xx) x4) as proof of ((cK X0) Xx)
% Found ((x3 Xx) x4) as proof of ((cK X0) Xx)
% Found ((x3 Xx) x4) as proof of ((cK X0) Xx)
% Found x6:(X0 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X0 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X0 Xx0))=> x6) as proof of ((X0 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X0 Xx0))=> x6) as proof of (forall (Xx:a), ((X0 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x300:=(x30 x4):((cK x1) Xx)
% Found (x30 x4) as proof of ((cK X0) Xx)
% Found ((x3 Xx) x4) as proof of ((cK X0) Xx)
% Found ((x3 Xx) x4) as proof of ((cK X0) Xx)
% Found ((x3 Xx) x4) as proof of ((cK X0) Xx)
% Found x6:(X4 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of (forall (Xx:a), ((X4 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% Found x2:(X1 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X1 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X1 Xx0))=> x2) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X1 Xx0))=> x2) as proof of (forall (Xx:a), ((X1 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X1 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X1 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X1 Xx0))=> x2) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X1 Xx0))=> x2) as proof of (forall (Xx:a), ((X1 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X1 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X1 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X1 Xx0))=> x2) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X1 Xx0))=> x2) as proof of (forall (Xx:a), ((X1 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X1 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X1 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X1 Xx0))=> x4) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X1 Xx0))=> x4) as proof of (forall (Xx:a), ((X1 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X1 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X1 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X1 Xx0))=> x4) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X1 Xx0))=> x4) as proof of (forall (Xx:a), ((X1 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X1 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X1 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X1 Xx0))=> x2) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X1 Xx0))=> x2) as proof of (forall (Xx:a), ((X1 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X1 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X1 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X1 Xx0))=> x4) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X1 Xx0))=> x4) as proof of (forall (Xx:a), ((X1 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X1 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X1 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X1 Xx0))=> x4) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X1 Xx0))=> x4) as proof of (forall (Xx:a), ((X1 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X1 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X1 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X1 Xx0))=> x4) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X1 Xx0))=> x4) as proof of (forall (Xx:a), ((X1 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X1) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found ((and_rect0 ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X1) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found ((and_rect0 ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found x4:(X1 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X1 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X1 Xx0))=> x4) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X1 Xx0))=> x4) as proof of (forall (Xx:a), ((X1 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x6:(X1 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X1 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X1 Xx0))=> x6) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X1 Xx0))=> x6) as proof of (forall (Xx:a), ((X1 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X1) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% Found x2:(X1 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X1 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X1 Xx0))=> x2) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X1 Xx0))=> x2) as proof of (forall (Xx:a), ((X1 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X1 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X1 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X1 Xx0))=> x2) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X1 Xx0))=> x2) as proof of (forall (Xx:a), ((X1 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X1) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found ((and_rect0 ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X1) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found ((and_rect0 ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X1) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found ((and_rect0 ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found x2:(X1 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X1 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X1 Xx0))=> x2) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X1 Xx0))=> x2) as proof of (forall (Xx:a), ((X1 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X1 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X1 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X1 Xx0))=> x2) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X1 Xx0))=> x2) as proof of (forall (Xx:a), ((X1 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X1 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X1 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X1 Xx0))=> x2) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X1 Xx0))=> x2) as proof of (forall (Xx:a), ((X1 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X1 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X1 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X1 Xx0))=> x2) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X1 Xx0))=> x2) as proof of (forall (Xx:a), ((X1 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x6:(X1 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X1 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X1 Xx0))=> x6) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X1 Xx0))=> x6) as proof of (forall (Xx:a), ((X1 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X1) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% Found x4:(X1 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X1 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X1 Xx0))=> x4) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X1 Xx0))=> x4) as proof of (forall (Xx:a), ((X1 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X1 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X1 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X1 Xx0))=> x4) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X1 Xx0))=> x4) as proof of (forall (Xx:a), ((X1 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X1) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found ((and_rect0 ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found x2:(X1 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X1 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X1 Xx0))=> x2) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X1 Xx0))=> x2) as proof of (forall (Xx:a), ((X1 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x2:(X1 Xx0)
% Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x2:(X1 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x2:(X1 Xx0))=> x2) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x2:(X1 Xx0))=> x2) as proof of (forall (Xx:a), ((X1 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X1 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X1 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X1 Xx0))=> x4) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X1 Xx0))=> x4) as proof of (forall (Xx:a), ((X1 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X1 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X1 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X1 Xx0))=> x4) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X1 Xx0))=> x4) as proof of (forall (Xx:a), ((X1 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X1 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X1 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X1 Xx0))=> x4) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X1 Xx0))=> x4) as proof of (forall (Xx:a), ((X1 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X1 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X1 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X1 Xx0))=> x4) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X1 Xx0))=> x4) as proof of (forall (Xx:a), ((X1 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X1 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X1 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X1 Xx0))=> x4) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X1 Xx0))=> x4) as proof of (forall (Xx:a), ((X1 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X1 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X1 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X1 Xx0))=> x4) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X1 Xx0))=> x4) as proof of (forall (Xx:a), ((X1 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X1 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X1 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X1 Xx0))=> x4) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X1 Xx0))=> x4) as proof of (forall (Xx:a), ((X1 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X1 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X1 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X1 Xx0))=> x4) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X1 Xx0))=> x4) as proof of (forall (Xx:a), ((X1 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X1 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X1 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X1 Xx0))=> x4) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X1 Xx0))=> x4) as proof of (forall (Xx:a), ((X1 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X1 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X1 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X1 Xx0))=> x4) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X1 Xx0))=> x4) as proof of (forall (Xx:a), ((X1 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X1) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found ((and_rect0 ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found x4:(X1 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X1 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X1 Xx0))=> x4) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X1 Xx0))=> x4) as proof of (forall (Xx:a), ((X1 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X1) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found ((and_rect0 ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X1) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found ((and_rect0 ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X1) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found ((and_rect0 ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found x6:(X1 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X1 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X1 Xx0))=> x6) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X1 Xx0))=> x6) as proof of (forall (Xx:a), ((X1 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X1) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% Found x6:(X1 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X1 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X1 Xx0))=> x6) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X1 Xx0))=> x6) as proof of (forall (Xx:a), ((X1 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X1) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X1) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found ((and_rect0 ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X1) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found ((and_rect0 ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X1) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found ((and_rect0 ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X1) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found ((and_rect0 ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X1) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found ((and_rect0 ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X1) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found ((and_rect0 ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found x6:(X1 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X1 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X1 Xx0))=> x6) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X1 Xx0))=> x6) as proof of (forall (Xx:a), ((X1 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X1) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% Found x6:(X1 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X1 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X1 Xx0))=> x6) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X1 Xx0))=> x6) as proof of (forall (Xx:a), ((X1 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X1) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X1) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found ((and_rect0 ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X1) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found ((and_rect0 ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found x40:=(x4 Xx):((x1 Xx)->((cK x1) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((cK X1) Xx))
% Found (x4 Xx) as proof of ((x1 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx)) as proof of ((x1 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->((cK X1) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found ((and_rect0 ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))->((x1 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0)))) (x1 Xx)) P) x4) x2)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X1) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found ((and_rect0 ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X1) Xx)
% Found x6:(X1 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X1 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X1 Xx0))=> x6) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X1 Xx0))=> x6) as proof of (forall (Xx:a), ((X1 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X1) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% Found x6:(X1 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X1 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X1 Xx0))=> x6) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X1 Xx0))=> x6) as proof of (forall (Xx:a), ((X1 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X1) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% Found x6:(X1 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X1 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X1 Xx0))=> x6) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X1 Xx0))=> x6) as proof of (forall (Xx:a), ((X1 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x1) Xx)
% Found (x40 x5) as proof of ((cK X1) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% Found x6:(X1 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X1 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X1 Xx0))=> x6) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x6:(X1 Xx0))=> x6) as proof of (forall (Xx:a), ((X1 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x400:=(x40 x5):((cK x2) Xx)
% Found (x40 x5) as proof of ((cK X1) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% Found x4:(X1 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X1 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X1 Xx0))=> x4) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X1 Xx0))=> x4) as proof of (forall (Xx:a), ((X1 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x4:(X1 Xx0)
% Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x4:(X1 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x4:(X1 Xx0))=> x4) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))
% Found (fun (Xx0:a) (x4:(X1 Xx0))=> x4) as proof of (forall (Xx:a), ((X1 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx))))))
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X1) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found ((and_rect0 ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X1) Xx)
% Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X1) Xx))
% Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X1) Xx)))
% Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found ((and_rect0 ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% Found (fun (x3:((and (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)))=> (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X1) Xx)
% Found x6:(X1 Xx0)
% Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (x6:(X1 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0))))
% Found (fun (Xx0:a) (x6:(X1 Xx0))=> x6) as proof of ((X1 Xx
% EOF
%------------------------------------------------------------------------------