TSTP Solution File: SYO331^5 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SYO331^5 : TPTP v7.5.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Tue Mar 29 00:51:10 EDT 2022
% Result : Timeout 285.81s 286.11s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYO331^5 : TPTP v7.5.0. Released v4.0.0.
% 0.11/0.12 % Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.32 % Computer : n003.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPUModel : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % RAMPerCPU : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % DateTime : Sat Mar 12 04:20:26 EST 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27'
% 0.12/0.33 Python 2.7.5
% 0.77/1.01 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox2/benchmark/', '/export/starexec/sandbox2/benchmark/']
% 0.77/1.01 FOF formula (<kernel.Constant object at 0xeb0d40>, <kernel.Type object at 0xeb0b00>) of role type named a_type
% 0.77/1.01 Using role type
% 0.77/1.01 Declaring a:Type
% 0.77/1.01 FOF formula (<kernel.Constant object at 0xeb0d88>, <kernel.DependentProduct object at 0x2ab1e4f1f758>) of role type named cK
% 0.77/1.01 Using role type
% 0.77/1.01 Declaring cK:((a->Prop)->(a->Prop))
% 0.77/1.01 FOF formula ((forall (X:(a->Prop)), ((forall (Xx:a), ((X Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))->(forall (Xx:a), (((cK X) Xx)->((cK (fun (Xx0:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))) Xx)))))->(forall (Xx:a), (((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))->((cK (fun (Xx0:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))) Xx)))) of role conjecture named cTHM116_2SS_pme
% 0.77/1.01 Conjecture to prove = ((forall (X:(a->Prop)), ((forall (Xx:a), ((X Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))->(forall (Xx:a), (((cK X) Xx)->((cK (fun (Xx0:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))) Xx)))))->(forall (Xx:a), (((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))->((cK (fun (Xx0:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))) Xx)))):Prop
% 0.77/1.01 Parameter a_DUMMY:a.
% 0.77/1.01 We need to prove ['((forall (X:(a->Prop)), ((forall (Xx:a), ((X Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))->(forall (Xx:a), (((cK X) Xx)->((cK (fun (Xx0:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))) Xx)))))->(forall (Xx:a), (((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))->((cK (fun (Xx0:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))) Xx))))']
% 0.77/1.01 Parameter a:Type.
% 0.77/1.01 Parameter cK:((a->Prop)->(a->Prop)).
% 0.77/1.01 Trying to prove ((forall (X:(a->Prop)), ((forall (Xx:a), ((X Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))->(forall (Xx:a), (((cK X) Xx)->((cK (fun (Xx0:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))) Xx)))))->(forall (Xx:a), (((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))->((cK (fun (Xx0:a)=> ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx1:a), ((S Xx1)->((cK S) Xx1)))) (S Xx0)))))) Xx))))
% 0.77/1.01 Found x2:(X Xx0)
% 0.77/1.01 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 0.77/1.01 Found (fun (x2:(X Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 0.77/1.01 Found (fun (Xx0:a) (x2:(X Xx0))=> x2) as proof of ((X Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 0.77/1.01 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 0.77/1.01 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 0.77/1.01 Found (x4 Xx) as proof of ((x2 Xx)->((cK X) Xx))
% 0.77/1.01 Found (x4 Xx) as proof of ((x2 Xx)->((cK X) Xx))
% 0.77/1.01 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X) Xx))
% 0.77/1.01 Found (fun (x4:(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)))
% 0.77/1.01 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X) Xx)
% 0.77/1.01 Found ((and_rect0 ((cK X) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X) Xx)
% 0.77/1.01 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 1.20/1.42 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)
% 1.20/1.42 Found x4:(X Xx0)
% 1.20/1.42 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 1.20/1.42 Found (fun (x4:(X Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 1.20/1.42 Found (fun (Xx0:a) (x4:(X Xx0))=> x4) as proof of ((X Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 1.20/1.42 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 1.20/1.42 Found x40:=(x4 Xx):((x1 Xx)->((cK x1) Xx))
% 1.20/1.42 Found (x4 Xx) as proof of ((x1 Xx)->((cK X) Xx))
% 1.20/1.42 Found (x4 Xx) as proof of ((x1 Xx)->((cK X) Xx))
% 1.20/1.42 Found (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx)) as proof of ((x1 Xx)->((cK X) Xx))
% 1.20/1.42 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)))
% 1.20/1.42 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X) Xx)
% 1.20/1.42 Found ((and_rect0 ((cK X) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X) Xx)
% 1.20/1.42 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)
% 1.20/1.42 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)
% 1.20/1.42 Found x6:(X Xx0)
% 1.20/1.42 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 1.20/1.42 Found (fun (x6:(X Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 1.20/1.42 Found (fun (Xx0:a) (x6:(X Xx0))=> x6) as proof of ((X Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 1.20/1.42 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 1.20/1.42 Found x300:=(x30 x4):((cK x1) Xx)
% 1.20/1.42 Found (x30 x4) as proof of ((cK X) Xx)
% 1.20/1.42 Found ((x3 Xx) x4) as proof of ((cK X) Xx)
% 1.20/1.42 Found ((x3 Xx) x4) as proof of ((cK X) Xx)
% 1.20/1.42 Found ((x3 Xx) x4) as proof of ((cK X) Xx)
% 1.20/1.42 Found x4:(X0 Xx0)
% 1.20/1.42 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 1.20/1.42 Found (fun (x4:(X0 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 1.20/1.42 Found (fun (Xx0:a) (x4:(X0 Xx0))=> x4) as proof of ((X0 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 1.20/1.42 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 1.20/1.42 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 1.20/1.42 Found (x4 Xx) as proof of ((x2 Xx)->((cK X0) Xx))
% 1.20/1.42 Found (x4 Xx) as proof of ((x2 Xx)->((cK X0) Xx))
% 1.20/1.42 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X0) Xx))
% 1.20/1.42 Found (fun (x4:(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)))
% 1.85/2.04 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% 1.85/2.04 Found ((and_rect0 ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% 1.85/2.04 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 1.85/2.04 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 1.85/2.04 Found x4:(X0 Xx0)
% 1.85/2.04 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 1.85/2.04 Found (fun (x4:(X0 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 1.85/2.04 Found (fun (Xx0:a) (x4:(X0 Xx0))=> x4) as proof of ((X0 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 1.85/2.04 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 1.85/2.04 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 1.85/2.04 Found (x4 Xx) as proof of ((x2 Xx)->((cK X0) Xx))
% 1.85/2.04 Found (x4 Xx) as proof of ((x2 Xx)->((cK X0) Xx))
% 1.85/2.04 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X0) Xx))
% 1.85/2.04 Found (fun (x4:(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)))
% 1.85/2.04 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% 1.85/2.04 Found ((and_rect0 ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% 1.85/2.04 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 1.85/2.04 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 1.85/2.04 Found x2:(X0 Xx0)
% 1.85/2.04 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 1.85/2.04 Found (fun (x2:(X0 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 1.85/2.04 Found (fun (Xx0:a) (x2:(X0 Xx0))=> x2) as proof of ((X0 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 1.85/2.04 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 1.85/2.04 Found x2:(X0 Xx0)
% 1.85/2.04 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 1.85/2.04 Found (fun (x2:(X0 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 1.85/2.04 Found (fun (Xx0:a) (x2:(X0 Xx0))=> x2) as proof of ((X0 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 1.85/2.04 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 1.85/2.04 Found x6:(X0 Xx0)
% 1.85/2.04 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 1.85/2.04 Found (fun (x6:(X0 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 2.15/2.32 Found (fun (Xx0:a) (x6:(X0 Xx0))=> x6) as proof of ((X0 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 2.15/2.32 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 2.15/2.32 Found x400:=(x40 x5):((cK x1) Xx)
% 2.15/2.32 Found (x40 x5) as proof of ((cK X0) Xx)
% 2.15/2.32 Found ((x4 Xx) x5) as proof of ((cK X0) Xx)
% 2.15/2.32 Found ((x4 Xx) x5) as proof of ((cK X0) Xx)
% 2.15/2.32 Found ((x4 Xx) x5) as proof of ((cK X0) Xx)
% 2.15/2.32 Found x6:(X0 Xx0)
% 2.15/2.32 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 2.15/2.32 Found (fun (x6:(X0 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 2.15/2.32 Found (fun (Xx0:a) (x6:(X0 Xx0))=> x6) as proof of ((X0 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 2.15/2.32 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 2.15/2.32 Found x400:=(x40 x5):((cK x2) Xx)
% 2.15/2.32 Found (x40 x5) as proof of ((cK X0) Xx)
% 2.15/2.32 Found ((x4 Xx) x5) as proof of ((cK X0) Xx)
% 2.15/2.32 Found ((x4 Xx) x5) as proof of ((cK X0) Xx)
% 2.15/2.32 Found ((x4 Xx) x5) as proof of ((cK X0) Xx)
% 2.15/2.32 Found x4:(X0 Xx0)
% 2.15/2.32 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 2.15/2.32 Found (fun (x4:(X0 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 2.15/2.32 Found (fun (Xx0:a) (x4:(X0 Xx0))=> x4) as proof of ((X0 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 2.15/2.32 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 2.15/2.32 Found x40:=(x4 Xx):((x1 Xx)->((cK x1) Xx))
% 2.15/2.32 Found (x4 Xx) as proof of ((x1 Xx)->((cK X0) Xx))
% 2.15/2.32 Found (x4 Xx) as proof of ((x1 Xx)->((cK X0) Xx))
% 2.15/2.32 Found (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx)) as proof of ((x1 Xx)->((cK X0) Xx))
% 2.15/2.32 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)))
% 2.15/2.32 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% 2.15/2.32 Found ((and_rect0 ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% 2.15/2.32 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)
% 2.15/2.32 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)
% 2.15/2.32 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 2.15/2.32 Found (x4 Xx) as proof of ((x2 Xx)->((cK X0) Xx))
% 2.15/2.32 Found (x4 Xx) as proof of ((x2 Xx)->((cK X0) Xx))
% 2.15/2.32 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X0) Xx))
% 2.15/2.32 Found (fun (x4:(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)))
% 2.15/2.32 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% 2.15/2.32 Found ((and_rect0 ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% 2.15/2.32 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 2.83/3.04 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)
% 2.83/3.04 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 2.83/3.04 Found (x4 Xx) as proof of ((x2 Xx)->((cK X0) Xx))
% 2.83/3.04 Found (x4 Xx) as proof of ((x2 Xx)->((cK X0) Xx))
% 2.83/3.04 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X0) Xx))
% 2.83/3.04 Found (fun (x4:(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)))
% 2.83/3.04 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% 2.83/3.04 Found ((and_rect0 ((cK X0) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X0) Xx)
% 2.83/3.04 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 2.83/3.04 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)
% 2.83/3.04 Found x6:(X0 Xx0)
% 2.83/3.04 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 2.83/3.04 Found (fun (x6:(X0 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 2.83/3.04 Found (fun (Xx0:a) (x6:(X0 Xx0))=> x6) as proof of ((X0 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 2.83/3.04 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 2.83/3.04 Found x300:=(x30 x4):((cK x1) Xx)
% 2.83/3.04 Found (x30 x4) as proof of ((cK X0) Xx)
% 2.83/3.04 Found ((x3 Xx) x4) as proof of ((cK X0) Xx)
% 2.83/3.04 Found ((x3 Xx) x4) as proof of ((cK X0) Xx)
% 2.83/3.04 Found ((x3 Xx) x4) as proof of ((cK X0) Xx)
% 2.83/3.04 Found x6:(X1 Xx0)
% 2.83/3.04 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 2.83/3.04 Found (fun (x6:(X1 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 2.83/3.04 Found (fun (Xx0:a) (x6:(X1 Xx0))=> x6) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 2.83/3.04 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 2.83/3.04 Found x400:=(x40 x5):((cK x2) Xx)
% 2.83/3.04 Found (x40 x5) as proof of ((cK X1) Xx)
% 2.83/3.04 Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% 2.83/3.04 Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% 2.83/3.04 Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% 2.83/3.04 Found x6:(X1 Xx0)
% 2.83/3.04 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 2.83/3.04 Found (fun (x6:(X1 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 2.83/3.04 Found (fun (Xx0:a) (x6:(X1 Xx0))=> x6) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 2.83/3.04 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 2.83/3.04 Found x400:=(x40 x5):((cK x2) Xx)
% 2.83/3.04 Found (x40 x5) as proof of ((cK X1) Xx)
% 2.83/3.04 Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% 3.13/3.32 Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% 3.13/3.32 Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% 3.13/3.32 Found x4:(X1 Xx0)
% 3.13/3.32 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 3.13/3.32 Found (fun (x4:(X1 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 3.13/3.32 Found (fun (Xx0:a) (x4:(X1 Xx0))=> x4) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 3.13/3.32 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 3.13/3.32 Found x4:(X1 Xx0)
% 3.13/3.32 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 3.13/3.32 Found (fun (x4:(X1 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 3.13/3.32 Found (fun (Xx0:a) (x4:(X1 Xx0))=> x4) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 3.13/3.32 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 3.13/3.32 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 3.13/3.32 Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% 3.13/3.32 Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% 3.13/3.32 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X1) Xx))
% 3.13/3.32 Found (fun (x4:(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)))
% 3.13/3.32 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% 3.13/3.32 Found ((and_rect0 ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% 3.13/3.32 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 3.13/3.32 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 3.13/3.32 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 3.13/3.32 Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% 3.13/3.32 Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% 3.13/3.32 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X1) Xx))
% 3.13/3.32 Found (fun (x4:(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)))
% 3.13/3.32 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% 3.13/3.32 Found ((and_rect0 ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% 3.13/3.32 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 3.13/3.32 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 3.13/3.32 Found x4:(X1 Xx0)
% 3.13/3.32 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 3.13/3.32 Found (fun (x4:(X1 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 3.13/3.32 Found (fun (Xx0:a) (x4:(X1 Xx0))=> x4) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 3.56/3.73 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 3.56/3.73 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 3.56/3.73 Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% 3.56/3.73 Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% 3.56/3.73 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X1) Xx))
% 3.56/3.73 Found (fun (x4:(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)))
% 3.56/3.73 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% 3.56/3.73 Found ((and_rect0 ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% 3.56/3.73 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 3.56/3.73 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 3.56/3.73 Found x4:(X1 Xx0)
% 3.56/3.73 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 3.56/3.73 Found (fun (x4:(X1 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 3.56/3.73 Found (fun (Xx0:a) (x4:(X1 Xx0))=> x4) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 3.56/3.73 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 3.56/3.73 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 3.56/3.73 Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% 3.56/3.73 Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% 3.56/3.73 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X1) Xx))
% 3.56/3.73 Found (fun (x4:(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)))
% 3.56/3.73 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% 3.56/3.73 Found ((and_rect0 ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% 3.56/3.73 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 3.56/3.73 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 3.56/3.73 Found x4:(X1 Xx0)
% 3.56/3.73 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 3.56/3.73 Found (fun (x4:(X1 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 3.56/3.73 Found (fun (Xx0:a) (x4:(X1 Xx0))=> x4) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 3.56/3.73 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 3.56/3.73 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 3.56/3.73 Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% 3.56/3.73 Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% 3.56/3.73 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X1) Xx))
% 4.17/4.33 Found (fun (x4:(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)))
% 4.17/4.33 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% 4.17/4.33 Found ((and_rect0 ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% 4.17/4.33 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 4.17/4.33 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 4.17/4.33 Found x4:(X1 Xx0)
% 4.17/4.33 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 4.17/4.33 Found (fun (x4:(X1 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 4.17/4.33 Found (fun (Xx0:a) (x4:(X1 Xx0))=> x4) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 4.17/4.33 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 4.17/4.33 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 4.17/4.33 Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% 4.17/4.33 Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% 4.17/4.33 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X1) Xx))
% 4.17/4.33 Found (fun (x4:(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)))
% 4.17/4.33 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% 4.17/4.33 Found ((and_rect0 ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% 4.17/4.33 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 4.17/4.33 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 4.17/4.33 Found x2:(X1 Xx0)
% 4.17/4.33 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 4.17/4.33 Found (fun (x2:(X1 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 4.17/4.33 Found (fun (Xx0:a) (x2:(X1 Xx0))=> x2) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 4.17/4.33 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 4.17/4.33 Found x2:(X1 Xx0)
% 4.17/4.33 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 4.17/4.33 Found (fun (x2:(X1 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 4.17/4.33 Found (fun (Xx0:a) (x2:(X1 Xx0))=> x2) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 4.17/4.33 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 4.17/4.33 Found x2:(X1 Xx0)
% 4.17/4.33 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 4.84/5.03 Found (fun (x2:(X1 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 4.84/5.03 Found (fun (Xx0:a) (x2:(X1 Xx0))=> x2) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 4.84/5.03 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 4.84/5.03 Found x2:(X1 Xx0)
% 4.84/5.03 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 4.84/5.03 Found (fun (x2:(X1 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 4.84/5.03 Found (fun (Xx0:a) (x2:(X1 Xx0))=> x2) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 4.84/5.03 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 4.84/5.03 Found x6:(X1 Xx0)
% 4.84/5.03 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 4.84/5.03 Found (fun (x6:(X1 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 4.84/5.03 Found (fun (Xx0:a) (x6:(X1 Xx0))=> x6) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 4.84/5.03 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 4.84/5.03 Found x400:=(x40 x5):((cK x1) Xx)
% 4.84/5.03 Found (x40 x5) as proof of ((cK X1) Xx)
% 4.84/5.03 Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% 4.84/5.03 Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% 4.84/5.03 Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% 4.84/5.03 Found x6:(X1 Xx0)
% 4.84/5.03 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 4.84/5.03 Found (fun (x6:(X1 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 4.84/5.03 Found (fun (Xx0:a) (x6:(X1 Xx0))=> x6) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 4.84/5.03 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 4.84/5.03 Found x400:=(x40 x5):((cK x2) Xx)
% 4.84/5.03 Found (x40 x5) as proof of ((cK X1) Xx)
% 4.84/5.03 Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% 4.84/5.03 Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% 4.84/5.03 Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% 4.84/5.03 Found x6:(X1 Xx0)
% 4.84/5.03 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 4.84/5.03 Found (fun (x6:(X1 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 4.84/5.03 Found (fun (Xx0:a) (x6:(X1 Xx0))=> x6) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 4.84/5.03 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 4.84/5.03 Found x400:=(x40 x5):((cK x1) Xx)
% 4.84/5.03 Found (x40 x5) as proof of ((cK X1) Xx)
% 4.84/5.03 Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% 4.84/5.03 Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% 4.84/5.03 Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% 4.84/5.03 Found x6:(X1 Xx0)
% 4.84/5.03 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 4.84/5.03 Found (fun (x6:(X1 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 4.84/5.03 Found (fun (Xx0:a) (x6:(X1 Xx0))=> x6) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 4.84/5.03 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 5.14/5.37 Found x400:=(x40 x5):((cK x2) Xx)
% 5.14/5.37 Found (x40 x5) as proof of ((cK X1) Xx)
% 5.14/5.37 Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% 5.14/5.37 Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% 5.14/5.37 Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% 5.14/5.37 Found x6:(X1 Xx0)
% 5.14/5.37 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 5.14/5.37 Found (fun (x6:(X1 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 5.14/5.37 Found (fun (Xx0:a) (x6:(X1 Xx0))=> x6) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 5.14/5.37 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 5.14/5.37 Found x400:=(x40 x5):((cK x2) Xx)
% 5.14/5.37 Found (x40 x5) as proof of ((cK X1) Xx)
% 5.14/5.37 Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% 5.14/5.37 Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% 5.14/5.37 Found ((x4 Xx) x5) as proof of ((cK X1) Xx)
% 5.14/5.37 Found x4:(X1 Xx0)
% 5.14/5.37 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 5.14/5.37 Found (fun (x4:(X1 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 5.14/5.37 Found (fun (Xx0:a) (x4:(X1 Xx0))=> x4) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 5.14/5.37 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 5.14/5.37 Found x40:=(x4 Xx):((x1 Xx)->((cK x1) Xx))
% 5.14/5.37 Found (x4 Xx) as proof of ((x1 Xx)->((cK X1) Xx))
% 5.14/5.37 Found (x4 Xx) as proof of ((x1 Xx)->((cK X1) Xx))
% 5.14/5.37 Found (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx)) as proof of ((x1 Xx)->((cK X1) Xx))
% 5.14/5.37 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)))
% 5.14/5.37 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% 5.14/5.37 Found ((and_rect0 ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% 5.14/5.37 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)
% 5.14/5.37 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)
% 5.14/5.37 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 5.14/5.37 Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% 5.14/5.37 Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% 5.14/5.37 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X1) Xx))
% 5.14/5.37 Found (fun (x4:(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)))
% 5.14/5.37 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% 5.14/5.37 Found ((and_rect0 ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% 5.14/5.37 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 5.14/5.37 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)
% 5.37/5.59 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 5.37/5.59 Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% 5.37/5.59 Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% 5.37/5.59 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X1) Xx))
% 5.37/5.59 Found (fun (x4:(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)))
% 5.37/5.59 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% 5.37/5.59 Found ((and_rect0 ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% 5.37/5.59 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 5.37/5.59 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)
% 5.37/5.59 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 5.37/5.59 Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% 5.37/5.59 Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% 5.37/5.59 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X1) Xx))
% 5.37/5.59 Found (fun (x4:(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)))
% 5.37/5.59 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% 5.37/5.59 Found ((and_rect0 ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% 5.37/5.59 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 5.37/5.59 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)
% 5.37/5.59 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 5.37/5.59 Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% 5.37/5.59 Found (x4 Xx) as proof of ((x2 Xx)->((cK X1) Xx))
% 5.37/5.59 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X1) Xx))
% 5.37/5.59 Found (fun (x4:(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)))
% 5.37/5.59 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% 5.37/5.59 Found ((and_rect0 ((cK X1) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X1) Xx)
% 5.37/5.59 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 5.37/5.59 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)
% 5.37/5.59 Found x6:(X1 Xx0)
% 5.37/5.59 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 5.37/5.59 Found (fun (x6:(X1 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 7.33/7.51 Found (fun (Xx0:a) (x6:(X1 Xx0))=> x6) as proof of ((X1 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 7.33/7.51 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 7.33/7.51 Found x300:=(x30 x4):((cK x1) Xx)
% 7.33/7.51 Found (x30 x4) as proof of ((cK X1) Xx)
% 7.33/7.51 Found ((x3 Xx) x4) as proof of ((cK X1) Xx)
% 7.33/7.51 Found ((x3 Xx) x4) as proof of ((cK X1) Xx)
% 7.33/7.51 Found ((x3 Xx) x4) as proof of ((cK X1) Xx)
% 7.33/7.51 Found x6:(X2 Xx0)
% 7.33/7.51 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 7.33/7.51 Found (fun (x6:(X2 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 7.33/7.51 Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 7.33/7.51 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 7.33/7.51 Found x400:=(x40 x5):((cK x2) Xx)
% 7.33/7.51 Found (x40 x5) as proof of ((cK X2) Xx)
% 7.33/7.51 Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% 7.33/7.51 Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% 7.33/7.51 Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% 7.33/7.51 Found x6:(X2 Xx0)
% 7.33/7.51 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 7.33/7.51 Found (fun (x6:(X2 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 7.33/7.51 Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 7.33/7.51 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 7.33/7.51 Found x400:=(x40 x5):((cK x2) Xx)
% 7.33/7.51 Found (x40 x5) as proof of ((cK X2) Xx)
% 7.33/7.51 Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% 7.33/7.51 Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% 7.33/7.51 Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% 7.33/7.51 Found x6:(X2 Xx0)
% 7.33/7.51 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 7.33/7.51 Found (fun (x6:(X2 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 7.33/7.51 Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 7.33/7.51 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 7.33/7.51 Found x400:=(x40 x5):((cK x2) Xx)
% 7.33/7.51 Found (x40 x5) as proof of ((cK X2) Xx)
% 7.33/7.51 Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% 7.33/7.51 Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% 7.33/7.51 Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% 7.33/7.52 Found x6:(X2 Xx0)
% 7.33/7.52 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 7.33/7.52 Found (fun (x6:(X2 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 7.33/7.52 Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 7.33/7.52 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 7.33/7.52 Found x400:=(x40 x5):((cK x2) Xx)
% 7.33/7.52 Found (x40 x5) as proof of ((cK X2) Xx)
% 7.33/7.52 Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% 7.33/7.52 Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% 7.33/7.52 Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% 7.33/7.52 Found x4:(X2 Xx0)
% 7.33/7.52 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 7.33/7.52 Found (fun (x4:(X2 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 7.86/8.04 Found (fun (Xx0:a) (x4:(X2 Xx0))=> x4) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 7.86/8.04 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 7.86/8.04 Found x6:(X2 Xx0)
% 7.86/8.04 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 7.86/8.04 Found (fun (x6:(X2 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 7.86/8.04 Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 7.86/8.04 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 7.86/8.04 Found x400:=(x40 x5):((cK x2) Xx)
% 7.86/8.04 Found (x40 x5) as proof of ((cK X2) Xx)
% 7.86/8.04 Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% 7.86/8.04 Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% 7.86/8.04 Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% 7.86/8.04 Found x6:(X2 Xx0)
% 7.86/8.04 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 7.86/8.04 Found (fun (x6:(X2 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 7.86/8.04 Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 7.86/8.04 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 7.86/8.04 Found x400:=(x40 x5):((cK x2) Xx)
% 7.86/8.04 Found (x40 x5) as proof of ((cK X2) Xx)
% 7.86/8.04 Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% 7.86/8.04 Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% 7.86/8.04 Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% 7.86/8.04 Found x6:(X2 Xx0)
% 7.86/8.04 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 7.86/8.04 Found (fun (x6:(X2 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 7.86/8.04 Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 7.86/8.04 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 7.86/8.04 Found x400:=(x40 x5):((cK x2) Xx)
% 7.86/8.04 Found (x40 x5) as proof of ((cK X2) Xx)
% 7.86/8.04 Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% 7.86/8.04 Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% 7.86/8.04 Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% 7.86/8.04 Found x4:(X2 Xx0)
% 7.86/8.04 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 7.86/8.04 Found (fun (x4:(X2 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 7.86/8.04 Found (fun (Xx0:a) (x4:(X2 Xx0))=> x4) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 7.86/8.04 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 7.86/8.04 Found x6:(X2 Xx0)
% 7.86/8.04 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 7.86/8.04 Found (fun (x6:(X2 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 7.86/8.04 Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 7.86/8.04 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 8.15/8.35 Found x400:=(x40 x5):((cK x2) Xx)
% 8.15/8.35 Found (x40 x5) as proof of ((cK X2) Xx)
% 8.15/8.35 Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% 8.15/8.35 Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% 8.15/8.35 Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% 8.15/8.35 Found x4:(X2 Xx0)
% 8.15/8.35 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 8.15/8.35 Found (fun (x4:(X2 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 8.15/8.35 Found (fun (Xx0:a) (x4:(X2 Xx0))=> x4) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 8.15/8.35 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 8.15/8.35 Found x4:(X2 Xx0)
% 8.15/8.35 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 8.15/8.35 Found (fun (x4:(X2 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 8.15/8.35 Found (fun (Xx0:a) (x4:(X2 Xx0))=> x4) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 8.15/8.35 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 8.15/8.35 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 8.15/8.35 Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% 8.15/8.35 Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% 8.15/8.35 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X2) Xx))
% 8.15/8.35 Found (fun (x4:(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)))
% 8.15/8.35 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% 8.15/8.35 Found ((and_rect0 ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% 8.15/8.35 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 8.15/8.35 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 8.15/8.35 Found x4:(X2 Xx0)
% 8.15/8.35 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 8.15/8.35 Found (fun (x4:(X2 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 8.15/8.35 Found (fun (Xx0:a) (x4:(X2 Xx0))=> x4) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 8.15/8.35 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 8.15/8.35 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 8.15/8.35 Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% 8.15/8.35 Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% 8.15/8.35 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X2) Xx))
% 8.15/8.35 Found (fun (x4:(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)))
% 8.15/8.35 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% 8.15/8.35 Found ((and_rect0 ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% 8.15/8.35 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 8.47/8.65 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 8.47/8.65 Found x4:(X2 Xx0)
% 8.47/8.65 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 8.47/8.65 Found (fun (x4:(X2 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 8.47/8.65 Found (fun (Xx0:a) (x4:(X2 Xx0))=> x4) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 8.47/8.65 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 8.47/8.65 Found x4:(X2 Xx0)
% 8.47/8.65 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 8.47/8.65 Found (fun (x4:(X2 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 8.47/8.65 Found (fun (Xx0:a) (x4:(X2 Xx0))=> x4) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 8.47/8.65 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 8.47/8.65 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 8.47/8.65 Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% 8.47/8.65 Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% 8.47/8.65 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X2) Xx))
% 8.47/8.65 Found (fun (x4:(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)))
% 8.47/8.65 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% 8.47/8.65 Found ((and_rect0 ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% 8.47/8.65 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 8.47/8.65 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 8.47/8.65 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 8.47/8.65 Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% 8.47/8.65 Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% 8.47/8.65 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X2) Xx))
% 8.47/8.65 Found (fun (x4:(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)))
% 8.47/8.65 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% 8.47/8.65 Found ((and_rect0 ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% 8.47/8.65 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 8.47/8.65 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 8.47/8.65 Found x4:(X2 Xx0)
% 8.47/8.65 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 8.60/8.84 Found (fun (x4:(X2 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 8.60/8.84 Found (fun (Xx0:a) (x4:(X2 Xx0))=> x4) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 8.60/8.84 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 8.60/8.84 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 8.60/8.84 Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% 8.60/8.84 Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% 8.60/8.84 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X2) Xx))
% 8.60/8.84 Found (fun (x4:(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)))
% 8.60/8.84 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% 8.60/8.84 Found ((and_rect0 ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% 8.60/8.84 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 8.60/8.84 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 8.60/8.84 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 8.60/8.84 Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% 8.60/8.84 Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% 8.60/8.84 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X2) Xx))
% 8.60/8.84 Found (fun (x4:(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)))
% 8.60/8.84 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% 8.60/8.84 Found ((and_rect0 ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% 8.60/8.84 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 8.60/8.84 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 8.60/8.84 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 8.60/8.84 Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% 8.60/8.84 Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% 8.60/8.84 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X2) Xx))
% 8.60/8.84 Found (fun (x4:(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)))
% 8.60/8.84 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% 8.60/8.84 Found ((and_rect0 ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% 8.60/8.84 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 8.60/8.84 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 9.12/9.28 Found x4:(X2 Xx0)
% 9.12/9.28 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 9.12/9.28 Found (fun (x4:(X2 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 9.12/9.28 Found (fun (Xx0:a) (x4:(X2 Xx0))=> x4) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 9.12/9.28 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 9.12/9.28 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 9.12/9.28 Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% 9.12/9.28 Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% 9.12/9.28 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X2) Xx))
% 9.12/9.28 Found (fun (x4:(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)))
% 9.12/9.28 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% 9.12/9.28 Found ((and_rect0 ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% 9.12/9.28 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 9.12/9.28 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 9.12/9.28 Found x4:(X2 Xx0)
% 9.12/9.28 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 9.12/9.28 Found (fun (x4:(X2 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 9.12/9.28 Found (fun (Xx0:a) (x4:(X2 Xx0))=> x4) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 9.12/9.28 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 9.12/9.28 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 9.12/9.28 Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% 9.12/9.28 Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% 9.12/9.28 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X2) Xx))
% 9.12/9.28 Found (fun (x4:(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)))
% 9.12/9.28 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% 9.12/9.28 Found ((and_rect0 ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% 9.12/9.28 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 9.12/9.28 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 9.12/9.28 Found x4:(X2 Xx0)
% 9.12/9.28 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 9.12/9.28 Found (fun (x4:(X2 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 9.12/9.28 Found (fun (Xx0:a) (x4:(X2 Xx0))=> x4) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 9.12/9.28 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 9.41/9.60 Found x4:(X2 Xx0)
% 9.41/9.60 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 9.41/9.60 Found (fun (x4:(X2 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 9.41/9.60 Found (fun (Xx0:a) (x4:(X2 Xx0))=> x4) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 9.41/9.60 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 9.41/9.60 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 9.41/9.60 Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% 9.41/9.60 Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% 9.41/9.60 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X2) Xx))
% 9.41/9.60 Found (fun (x4:(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)))
% 9.41/9.60 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% 9.41/9.60 Found ((and_rect0 ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% 9.41/9.60 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 9.41/9.60 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 9.41/9.60 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 9.41/9.60 Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% 9.41/9.60 Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% 9.41/9.60 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X2) Xx))
% 9.41/9.60 Found (fun (x4:(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)))
% 9.41/9.60 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% 9.41/9.60 Found ((and_rect0 ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% 9.41/9.60 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 9.41/9.60 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 9.41/9.60 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 9.41/9.60 Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% 9.41/9.60 Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% 9.41/9.60 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X2) Xx))
% 9.41/9.60 Found (fun (x4:(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)))
% 9.41/9.60 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% 9.41/9.60 Found ((and_rect0 ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% 9.41/9.60 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 9.41/9.60 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 10.05/10.23 Found x4:(X2 Xx0)
% 10.05/10.23 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 10.05/10.23 Found (fun (x4:(X2 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 10.05/10.23 Found (fun (Xx0:a) (x4:(X2 Xx0))=> x4) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 10.05/10.23 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 10.05/10.23 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 10.05/10.23 Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% 10.05/10.23 Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% 10.05/10.23 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X2) Xx))
% 10.05/10.23 Found (fun (x4:(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)))
% 10.05/10.23 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% 10.05/10.23 Found ((and_rect0 ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% 10.05/10.23 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 10.05/10.23 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 10.05/10.23 Found x4:(X2 Xx0)
% 10.05/10.23 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 10.05/10.23 Found (fun (x4:(X2 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 10.05/10.23 Found (fun (Xx0:a) (x4:(X2 Xx0))=> x4) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 10.05/10.23 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 10.05/10.23 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 10.05/10.23 Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% 10.05/10.23 Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% 10.05/10.23 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X2) Xx))
% 10.05/10.23 Found (fun (x4:(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)))
% 10.05/10.23 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% 10.05/10.23 Found ((and_rect0 ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% 10.05/10.23 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 10.05/10.23 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 10.05/10.23 Found x2:(X2 Xx0)
% 10.05/10.23 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 10.05/10.23 Found (fun (x2:(X2 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 10.24/10.46 Found (fun (Xx0:a) (x2:(X2 Xx0))=> x2) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 10.24/10.46 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 10.24/10.46 Found x2:(X2 Xx0)
% 10.24/10.46 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 10.24/10.46 Found (fun (x2:(X2 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 10.24/10.46 Found (fun (Xx0:a) (x2:(X2 Xx0))=> x2) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 10.24/10.46 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 10.24/10.46 Found x2:(X2 Xx0)
% 10.24/10.46 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 10.24/10.46 Found (fun (x2:(X2 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 10.24/10.46 Found (fun (Xx0:a) (x2:(X2 Xx0))=> x2) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 10.24/10.46 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 10.24/10.46 Found x2:(X2 Xx0)
% 10.24/10.46 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 10.24/10.46 Found (fun (x2:(X2 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 10.24/10.46 Found (fun (Xx0:a) (x2:(X2 Xx0))=> x2) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 10.24/10.46 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 10.24/10.46 Found x2:(X2 Xx0)
% 10.24/10.46 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 10.24/10.46 Found (fun (x2:(X2 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 10.24/10.46 Found (fun (Xx0:a) (x2:(X2 Xx0))=> x2) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 10.24/10.46 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 10.24/10.46 Found x2:(X2 Xx0)
% 10.24/10.46 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 10.24/10.46 Found (fun (x2:(X2 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 10.24/10.46 Found (fun (Xx0:a) (x2:(X2 Xx0))=> x2) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 10.24/10.46 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 10.24/10.46 Found x2:(X2 Xx0)
% 10.24/10.46 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 10.24/10.46 Found (fun (x2:(X2 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 10.24/10.46 Found (fun (Xx0:a) (x2:(X2 Xx0))=> x2) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 10.24/10.46 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 10.24/10.46 Found x2:(X2 Xx0)
% 10.24/10.46 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 11.87/12.09 Found (fun (x2:(X2 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 11.87/12.09 Found (fun (Xx0:a) (x2:(X2 Xx0))=> x2) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 11.87/12.09 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 11.87/12.09 Found x6:(X2 Xx0)
% 11.87/12.09 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 11.87/12.09 Found (fun (x6:(X2 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 11.87/12.09 Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 11.87/12.09 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 11.87/12.09 Found x400:=(x40 x5):((cK x1) Xx)
% 11.87/12.09 Found (x40 x5) as proof of ((cK X2) Xx)
% 11.87/12.09 Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% 11.87/12.09 Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% 11.87/12.09 Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% 11.87/12.09 Found x6:(X2 Xx0)
% 11.87/12.09 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 11.87/12.09 Found (fun (x6:(X2 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 11.87/12.09 Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 11.87/12.09 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 11.87/12.09 Found x400:=(x40 x5):((cK x2) Xx)
% 11.87/12.09 Found (x40 x5) as proof of ((cK X2) Xx)
% 11.87/12.09 Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% 11.87/12.09 Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% 11.87/12.09 Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% 11.87/12.09 Found x6:(X2 Xx0)
% 11.87/12.09 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 11.87/12.09 Found (fun (x6:(X2 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 11.87/12.09 Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 11.87/12.09 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 11.87/12.09 Found x400:=(x40 x5):((cK x1) Xx)
% 11.87/12.09 Found (x40 x5) as proof of ((cK X2) Xx)
% 11.87/12.09 Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% 11.87/12.09 Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% 11.87/12.09 Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% 11.87/12.09 Found x6:(X2 Xx0)
% 11.87/12.09 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 11.87/12.09 Found (fun (x6:(X2 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 11.87/12.09 Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 11.87/12.09 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 11.87/12.09 Found x400:=(x40 x5):((cK x2) Xx)
% 11.87/12.09 Found (x40 x5) as proof of ((cK X2) Xx)
% 11.87/12.09 Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% 11.87/12.09 Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% 11.87/12.09 Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% 11.87/12.09 Found x4:(X2 Xx0)
% 11.87/12.09 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 11.87/12.09 Found (fun (x4:(X2 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 12.17/12.34 Found (fun (Xx0:a) (x4:(X2 Xx0))=> x4) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 12.17/12.34 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 12.17/12.34 Found x6:(X2 Xx0)
% 12.17/12.34 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 12.17/12.34 Found (fun (x6:(X2 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 12.17/12.34 Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 12.17/12.34 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 12.17/12.34 Found x400:=(x40 x5):((cK x2) Xx)
% 12.17/12.34 Found (x40 x5) as proof of ((cK X2) Xx)
% 12.17/12.34 Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% 12.17/12.34 Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% 12.17/12.34 Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% 12.17/12.34 Found x6:(X2 Xx0)
% 12.17/12.34 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 12.17/12.34 Found (fun (x6:(X2 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 12.17/12.34 Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 12.17/12.34 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 12.17/12.34 Found x400:=(x40 x5):((cK x1) Xx)
% 12.17/12.34 Found (x40 x5) as proof of ((cK X2) Xx)
% 12.17/12.34 Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% 12.17/12.34 Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% 12.17/12.34 Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% 12.17/12.34 Found x6:(X2 Xx0)
% 12.17/12.34 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 12.17/12.34 Found (fun (x6:(X2 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 12.17/12.34 Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 12.17/12.34 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 12.17/12.34 Found x400:=(x40 x5):((cK x2) Xx)
% 12.17/12.34 Found (x40 x5) as proof of ((cK X2) Xx)
% 12.17/12.34 Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% 12.17/12.34 Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% 12.17/12.34 Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% 12.17/12.34 Found x6:(X2 Xx0)
% 12.17/12.34 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 12.17/12.34 Found (fun (x6:(X2 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 12.17/12.34 Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 12.17/12.34 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 12.17/12.34 Found x400:=(x40 x5):((cK x2) Xx)
% 12.17/12.34 Found (x40 x5) as proof of ((cK X2) Xx)
% 12.17/12.34 Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% 12.17/12.34 Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% 12.17/12.34 Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% 12.17/12.34 Found x6:(X2 Xx0)
% 12.17/12.34 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 12.17/12.34 Found (fun (x6:(X2 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 12.17/12.34 Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 12.67/12.88 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 12.67/12.88 Found x400:=(x40 x5):((cK x2) Xx)
% 12.67/12.88 Found (x40 x5) as proof of ((cK X2) Xx)
% 12.67/12.88 Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% 12.67/12.88 Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% 12.67/12.88 Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% 12.67/12.88 Found x6:(X2 Xx0)
% 12.67/12.88 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 12.67/12.88 Found (fun (x6:(X2 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 12.67/12.88 Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 12.67/12.88 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 12.67/12.88 Found x400:=(x40 x5):((cK x2) Xx)
% 12.67/12.88 Found (x40 x5) as proof of ((cK X2) Xx)
% 12.67/12.88 Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% 12.67/12.88 Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% 12.67/12.88 Found ((x4 Xx) x5) as proof of ((cK X2) Xx)
% 12.67/12.88 Found x40:=(x4 Xx):((x1 Xx)->((cK x1) Xx))
% 12.67/12.88 Found (x4 Xx) as proof of ((x1 Xx)->((cK X2) Xx))
% 12.67/12.88 Found (x4 Xx) as proof of ((x1 Xx)->((cK X2) Xx))
% 12.67/12.88 Found (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx)) as proof of ((x1 Xx)->((cK X2) Xx))
% 12.67/12.88 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)))
% 12.67/12.88 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% 12.67/12.88 Found ((and_rect0 ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% 12.67/12.88 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)
% 12.67/12.88 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)
% 12.67/12.88 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 12.67/12.88 Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% 12.67/12.88 Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% 12.67/12.88 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X2) Xx))
% 12.67/12.88 Found (fun (x4:(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)))
% 12.67/12.88 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% 12.67/12.88 Found ((and_rect0 ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% 12.67/12.88 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 12.67/12.88 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)
% 12.67/12.88 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 12.67/12.88 Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% 12.67/12.88 Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% 12.67/12.88 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X2) Xx))
% 12.67/12.88 Found (fun (x4:(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)))
% 12.82/13.00 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% 12.82/13.00 Found ((and_rect0 ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% 12.82/13.00 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 12.82/13.00 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)
% 12.82/13.00 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 12.82/13.00 Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% 12.82/13.00 Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% 12.82/13.00 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X2) Xx))
% 12.82/13.00 Found (fun (x4:(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)))
% 12.82/13.00 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% 12.82/13.00 Found ((and_rect0 ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% 12.82/13.00 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 12.82/13.00 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)
% 12.82/13.00 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 12.82/13.00 Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% 12.82/13.00 Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% 12.82/13.00 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X2) Xx))
% 12.82/13.00 Found (fun (x4:(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)))
% 12.82/13.00 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% 12.82/13.00 Found ((and_rect0 ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% 12.82/13.00 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 12.82/13.00 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)
% 12.82/13.00 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 12.82/13.00 Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% 12.82/13.00 Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% 12.82/13.00 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X2) Xx))
% 12.82/13.00 Found (fun (x4:(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)))
% 12.82/13.00 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% 12.82/13.00 Found ((and_rect0 ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% 12.82/13.00 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 12.95/13.13 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)
% 12.95/13.13 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 12.95/13.13 Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% 12.95/13.13 Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% 12.95/13.13 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X2) Xx))
% 12.95/13.13 Found (fun (x4:(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)))
% 12.95/13.13 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% 12.95/13.13 Found ((and_rect0 ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% 12.95/13.13 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 12.95/13.13 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)
% 12.95/13.13 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 12.95/13.13 Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% 12.95/13.13 Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% 12.95/13.13 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X2) Xx))
% 12.95/13.13 Found (fun (x4:(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)))
% 12.95/13.13 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% 12.95/13.13 Found ((and_rect0 ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% 12.95/13.13 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 12.95/13.13 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)
% 12.95/13.13 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 12.95/13.13 Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% 12.95/13.13 Found (x4 Xx) as proof of ((x2 Xx)->((cK X2) Xx))
% 12.95/13.13 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X2) Xx))
% 12.95/13.13 Found (fun (x4:(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)))
% 12.95/13.13 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% 12.95/13.13 Found ((and_rect0 ((cK X2) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X2) Xx)
% 12.95/13.13 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 12.95/13.13 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)
% 17.64/17.85 Found x6:(X2 Xx0)
% 17.64/17.85 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 17.64/17.85 Found (fun (x6:(X2 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 17.64/17.85 Found (fun (Xx0:a) (x6:(X2 Xx0))=> x6) as proof of ((X2 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 17.64/17.85 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 17.64/17.85 Found x300:=(x30 x4):((cK x1) Xx)
% 17.64/17.85 Found (x30 x4) as proof of ((cK X2) Xx)
% 17.64/17.85 Found ((x3 Xx) x4) as proof of ((cK X2) Xx)
% 17.64/17.85 Found ((x3 Xx) x4) as proof of ((cK X2) Xx)
% 17.64/17.85 Found ((x3 Xx) x4) as proof of ((cK X2) Xx)
% 17.64/17.85 Found x6:(X3 Xx0)
% 17.64/17.85 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 17.64/17.85 Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 17.64/17.85 Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 17.64/17.85 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 17.64/17.85 Found x400:=(x40 x5):((cK x2) Xx)
% 17.64/17.85 Found (x40 x5) as proof of ((cK X3) Xx)
% 17.64/17.85 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 17.64/17.85 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 17.64/17.85 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 17.64/17.85 Found x6:(X3 Xx0)
% 17.64/17.85 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 17.64/17.85 Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 17.64/17.85 Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 17.64/17.85 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 17.64/17.85 Found x400:=(x40 x5):((cK x2) Xx)
% 17.64/17.85 Found (x40 x5) as proof of ((cK X3) Xx)
% 17.64/17.85 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 17.64/17.85 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 17.64/17.85 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 17.64/17.85 Found x6:(X3 Xx0)
% 17.64/17.85 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 17.64/17.85 Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 17.64/17.85 Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 17.64/17.85 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 17.64/17.85 Found x400:=(x40 x5):((cK x2) Xx)
% 17.64/17.85 Found (x40 x5) as proof of ((cK X3) Xx)
% 17.64/17.85 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 17.64/17.85 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 17.64/17.85 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 17.64/17.85 Found x4:(X3 Xx0)
% 17.64/17.85 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 17.64/17.85 Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 17.64/17.85 Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 17.64/17.85 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 18.53/18.75 Found x6:(X3 Xx0)
% 18.53/18.75 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 18.53/18.75 Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 18.53/18.75 Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 18.53/18.75 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 18.53/18.75 Found x400:=(x40 x5):((cK x2) Xx)
% 18.53/18.75 Found (x40 x5) as proof of ((cK X3) Xx)
% 18.53/18.75 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 18.53/18.75 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 18.53/18.75 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 18.53/18.75 Found x4:(X3 Xx0)
% 18.53/18.75 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 18.53/18.75 Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 18.53/18.75 Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 18.53/18.75 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 18.53/18.75 Found x6:(X3 Xx0)
% 18.53/18.75 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 18.53/18.75 Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 18.53/18.75 Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 18.53/18.75 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 18.53/18.75 Found x400:=(x40 x5):((cK x2) Xx)
% 18.53/18.75 Found (x40 x5) as proof of ((cK X3) Xx)
% 18.53/18.75 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 18.53/18.75 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 18.53/18.75 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 18.53/18.75 Found x6:(X3 Xx0)
% 18.53/18.75 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 18.53/18.75 Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 18.53/18.75 Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 18.53/18.75 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 18.53/18.75 Found x400:=(x40 x5):((cK x2) Xx)
% 18.53/18.75 Found (x40 x5) as proof of ((cK X3) Xx)
% 18.53/18.75 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 18.53/18.75 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 18.53/18.75 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 18.53/18.75 Found x6:(X3 Xx0)
% 18.53/18.75 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 18.53/18.75 Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 18.53/18.75 Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 18.53/18.75 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 18.53/18.75 Found x400:=(x40 x5):((cK x2) Xx)
% 18.53/18.75 Found (x40 x5) as proof of ((cK X3) Xx)
% 18.53/18.75 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 18.53/18.75 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 18.53/18.75 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 18.53/18.75 Found x6:(X3 Xx0)
% 18.53/18.75 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 19.05/19.25 Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 19.05/19.25 Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 19.05/19.25 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 19.05/19.25 Found x400:=(x40 x5):((cK x2) Xx)
% 19.05/19.25 Found (x40 x5) as proof of ((cK X3) Xx)
% 19.05/19.25 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 19.05/19.25 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 19.05/19.25 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 19.05/19.25 Found x6:(X3 Xx0)
% 19.05/19.25 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 19.05/19.25 Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 19.05/19.25 Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 19.05/19.25 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 19.05/19.25 Found x400:=(x40 x5):((cK x2) Xx)
% 19.05/19.25 Found (x40 x5) as proof of ((cK X3) Xx)
% 19.05/19.25 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 19.05/19.25 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 19.05/19.25 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 19.05/19.25 Found x4:(X3 Xx0)
% 19.05/19.25 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 19.05/19.25 Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 19.05/19.25 Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 19.05/19.25 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 19.05/19.25 Found x6:(X3 Xx0)
% 19.05/19.25 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 19.05/19.25 Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 19.05/19.25 Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 19.05/19.25 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 19.05/19.25 Found x400:=(x40 x5):((cK x2) Xx)
% 19.05/19.25 Found (x40 x5) as proof of ((cK X3) Xx)
% 19.05/19.25 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 19.05/19.25 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 19.05/19.25 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 19.05/19.25 Found x4:(X3 Xx0)
% 19.05/19.25 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 19.05/19.25 Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 19.05/19.25 Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 19.05/19.25 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 19.05/19.25 Found x4:(X3 Xx0)
% 19.05/19.25 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 19.05/19.25 Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 19.05/19.25 Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 19.05/19.25 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 19.54/19.73 Found x6:(X3 Xx0)
% 19.54/19.73 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 19.54/19.73 Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 19.54/19.73 Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 19.54/19.73 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 19.54/19.73 Found x400:=(x40 x5):((cK x2) Xx)
% 19.54/19.73 Found (x40 x5) as proof of ((cK X3) Xx)
% 19.54/19.73 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 19.54/19.73 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 19.54/19.73 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 19.54/19.73 Found x6:(X3 Xx0)
% 19.54/19.73 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 19.54/19.73 Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 19.54/19.73 Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 19.54/19.73 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 19.54/19.73 Found x400:=(x40 x5):((cK x2) Xx)
% 19.54/19.73 Found (x40 x5) as proof of ((cK X3) Xx)
% 19.54/19.73 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 19.54/19.73 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 19.54/19.73 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 19.54/19.73 Found x6:(X3 Xx0)
% 19.54/19.73 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 19.54/19.73 Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 19.54/19.73 Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 19.54/19.73 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 19.54/19.73 Found x400:=(x40 x5):((cK x2) Xx)
% 19.54/19.73 Found (x40 x5) as proof of ((cK X3) Xx)
% 19.54/19.73 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 19.54/19.73 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 19.54/19.73 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 19.54/19.73 Found x6:(X3 Xx0)
% 19.54/19.73 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 19.54/19.73 Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 19.54/19.73 Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 19.54/19.73 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 19.54/19.73 Found x400:=(x40 x5):((cK x2) Xx)
% 19.54/19.73 Found (x40 x5) as proof of ((cK X3) Xx)
% 19.54/19.73 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 19.54/19.73 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 19.54/19.73 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 19.54/19.73 Found x6:(X3 Xx0)
% 19.54/19.73 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 19.54/19.73 Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 19.54/19.73 Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 19.54/19.73 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 19.54/19.73 Found x400:=(x40 x5):((cK x2) Xx)
% 19.54/19.73 Found (x40 x5) as proof of ((cK X3) Xx)
% 20.25/20.45 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 20.25/20.45 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 20.25/20.45 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 20.25/20.45 Found x6:(X3 Xx0)
% 20.25/20.45 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 20.25/20.45 Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 20.25/20.45 Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 20.25/20.45 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 20.25/20.45 Found x400:=(x40 x5):((cK x2) Xx)
% 20.25/20.45 Found (x40 x5) as proof of ((cK X3) Xx)
% 20.25/20.45 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 20.25/20.45 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 20.25/20.45 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 20.25/20.45 Found x6:(X3 Xx0)
% 20.25/20.45 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 20.25/20.45 Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 20.25/20.45 Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 20.25/20.45 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 20.25/20.45 Found x400:=(x40 x5):((cK x2) Xx)
% 20.25/20.45 Found (x40 x5) as proof of ((cK X3) Xx)
% 20.25/20.45 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 20.25/20.45 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 20.25/20.45 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 20.25/20.45 Found x4:(X3 Xx0)
% 20.25/20.45 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 20.25/20.45 Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 20.25/20.45 Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 20.25/20.45 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 20.25/20.45 Found x4:(X3 Xx0)
% 20.25/20.45 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 20.25/20.45 Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 20.25/20.45 Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 20.25/20.45 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 20.25/20.45 Found x4:(X3 Xx0)
% 20.25/20.45 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 20.25/20.45 Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 20.25/20.45 Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 20.25/20.45 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 20.25/20.45 Found x4:(X3 Xx0)
% 20.25/20.45 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 20.25/20.45 Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 20.25/20.45 Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 20.53/20.72 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 20.53/20.72 Found x4:(X3 Xx0)
% 20.53/20.72 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 20.53/20.72 Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 20.53/20.72 Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 20.53/20.72 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 20.53/20.72 Found x6:(X3 Xx0)
% 20.53/20.72 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 20.53/20.72 Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 20.53/20.72 Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 20.53/20.72 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 20.53/20.72 Found x400:=(x40 x5):((cK x2) Xx)
% 20.53/20.72 Found (x40 x5) as proof of ((cK X3) Xx)
% 20.53/20.72 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 20.53/20.72 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 20.53/20.72 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 20.53/20.72 Found x6:(X3 Xx0)
% 20.53/20.72 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 20.53/20.72 Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 20.53/20.72 Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 20.53/20.72 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 20.53/20.72 Found x400:=(x40 x5):((cK x2) Xx)
% 20.53/20.72 Found (x40 x5) as proof of ((cK X3) Xx)
% 20.53/20.72 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 20.53/20.72 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 20.53/20.72 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 20.53/20.72 Found x6:(X3 Xx0)
% 20.53/20.72 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 20.53/20.72 Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 20.53/20.72 Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 20.53/20.72 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 20.53/20.72 Found x400:=(x40 x5):((cK x2) Xx)
% 20.53/20.72 Found (x40 x5) as proof of ((cK X3) Xx)
% 20.53/20.72 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 20.53/20.72 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 20.53/20.72 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 20.53/20.72 Found x6:(X3 Xx0)
% 20.53/20.72 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 20.53/20.72 Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 20.53/20.72 Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 20.53/20.72 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 20.53/20.72 Found x400:=(x40 x5):((cK x2) Xx)
% 20.53/20.72 Found (x40 x5) as proof of ((cK X3) Xx)
% 20.53/20.72 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 20.53/20.72 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 20.53/20.72 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 20.61/20.78 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 20.61/20.78 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 20.61/20.78 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 20.61/20.78 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% 20.61/20.78 Found (fun (x4:(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)))
% 20.61/20.78 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 20.61/20.78 Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 20.61/20.78 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 20.61/20.78 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 20.61/20.78 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 20.61/20.78 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 20.61/20.78 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 20.61/20.78 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% 20.61/20.78 Found (fun (x4:(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)))
% 20.61/20.78 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 20.61/20.78 Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 20.61/20.78 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 20.61/20.78 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 20.61/20.78 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 20.61/20.78 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 20.61/20.78 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 20.61/20.78 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% 20.61/20.78 Found (fun (x4:(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)))
% 20.61/20.78 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 20.61/20.78 Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 20.61/20.78 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 20.61/20.78 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 20.61/20.78 Found x4:(X3 Xx0)
% 20.61/20.78 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 20.61/20.78 Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 20.61/20.78 Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 20.61/20.78 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 21.46/21.63 Found x4:(X3 Xx0)
% 21.46/21.63 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 21.46/21.63 Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 21.46/21.63 Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 21.46/21.63 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 21.46/21.63 Found x4:(X3 Xx0)
% 21.46/21.63 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 21.46/21.63 Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 21.46/21.63 Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 21.46/21.63 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 21.46/21.63 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 21.46/21.63 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 21.46/21.63 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 21.46/21.63 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% 21.46/21.63 Found (fun (x4:(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)))
% 21.46/21.63 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 21.46/21.63 Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 21.46/21.63 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 21.46/21.63 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 21.46/21.63 Found x4:(X3 Xx0)
% 21.46/21.63 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 21.46/21.63 Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 21.46/21.63 Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 21.46/21.63 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 21.46/21.63 Found x4:(X3 Xx0)
% 21.46/21.63 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 21.46/21.63 Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 21.46/21.63 Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 21.46/21.63 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 21.46/21.63 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 21.46/21.63 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 21.46/21.63 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 21.46/21.63 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% 21.46/21.63 Found (fun (x4:(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)))
% 21.46/21.67 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 21.46/21.67 Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 21.46/21.67 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 21.46/21.67 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 21.46/21.67 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 21.46/21.67 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 21.46/21.67 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 21.46/21.67 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% 21.46/21.67 Found (fun (x4:(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)))
% 21.46/21.67 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 21.46/21.67 Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 21.46/21.67 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 21.46/21.67 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 21.46/21.67 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 21.46/21.67 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 21.46/21.67 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 21.46/21.67 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% 21.46/21.67 Found (fun (x4:(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)))
% 21.46/21.67 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 21.46/21.67 Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 21.46/21.67 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 21.46/21.67 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 21.46/21.67 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 21.46/21.67 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 21.46/21.67 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 21.46/21.67 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% 21.46/21.67 Found (fun (x4:(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)))
% 21.46/21.67 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 21.46/21.67 Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 21.46/21.67 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 21.55/21.77 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 21.55/21.77 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 21.55/21.77 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 21.55/21.77 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 21.55/21.77 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% 21.55/21.77 Found (fun (x4:(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)))
% 21.55/21.77 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 21.55/21.77 Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 21.55/21.77 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 21.55/21.77 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 21.55/21.77 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 21.55/21.77 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 21.55/21.77 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 21.55/21.77 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% 21.55/21.77 Found (fun (x4:(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)))
% 21.55/21.77 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 21.55/21.77 Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 21.55/21.77 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 21.55/21.77 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 21.55/21.77 Found x6:(X3 Xx0)
% 21.55/21.77 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 21.55/21.77 Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 21.55/21.77 Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 21.55/21.77 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 21.55/21.77 Found x400:=(x40 x5):((cK x2) Xx)
% 21.55/21.77 Found (x40 x5) as proof of ((cK X3) Xx)
% 21.55/21.77 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 21.55/21.77 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 21.55/21.77 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 21.55/21.77 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 21.55/21.77 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 21.55/21.77 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 21.55/21.77 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% 21.55/21.77 Found (fun (x4:(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)))
% 21.55/21.77 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 21.55/21.77 Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 21.75/21.98 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 21.75/21.98 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 21.75/21.98 Found x4:(X3 Xx0)
% 21.75/21.98 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 21.75/21.98 Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 21.75/21.98 Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 21.75/21.98 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 21.75/21.98 Found x4:(X3 Xx0)
% 21.75/21.98 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 21.75/21.98 Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 21.75/21.98 Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 21.75/21.98 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 21.75/21.98 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 21.75/21.98 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 21.75/21.98 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 21.75/21.98 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% 21.75/21.98 Found (fun (x4:(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)))
% 21.75/21.98 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 21.75/21.98 Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 21.75/21.98 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 21.75/21.98 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 21.75/21.98 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 21.75/21.98 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 21.75/21.98 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 21.75/21.98 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% 21.75/21.98 Found (fun (x4:(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)))
% 21.75/21.98 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 21.75/21.98 Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 21.75/21.98 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 21.75/21.98 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 22.30/22.48 Found x4:(X3 Xx0)
% 22.30/22.48 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 22.30/22.48 Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 22.30/22.48 Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 22.30/22.48 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 22.30/22.48 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 22.30/22.48 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 22.30/22.48 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 22.30/22.48 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% 22.30/22.48 Found (fun (x4:(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)))
% 22.30/22.48 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 22.30/22.48 Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 22.30/22.48 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 22.30/22.48 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 22.30/22.48 Found x4:(X3 Xx0)
% 22.30/22.48 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 22.30/22.48 Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 22.30/22.48 Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 22.30/22.48 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 22.30/22.48 Found x4:(X3 Xx0)
% 22.30/22.48 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 22.30/22.48 Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 22.30/22.48 Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 22.30/22.48 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 22.30/22.48 Found x4:(X3 Xx0)
% 22.30/22.48 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 22.30/22.48 Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 22.30/22.48 Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 22.30/22.48 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 22.30/22.48 Found x4:(X3 Xx0)
% 22.30/22.48 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 22.30/22.48 Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 22.30/22.48 Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 22.94/23.10 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 22.94/23.10 Found x4:(X3 Xx0)
% 22.94/23.10 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 22.94/23.10 Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 22.94/23.10 Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 22.94/23.10 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 22.94/23.10 Found x4:(X3 Xx0)
% 22.94/23.10 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 22.94/23.10 Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 22.94/23.10 Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 22.94/23.10 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 22.94/23.10 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 22.94/23.10 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 22.94/23.10 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 22.94/23.10 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% 22.94/23.10 Found (fun (x4:(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)))
% 22.94/23.10 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 22.94/23.10 Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 22.94/23.10 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 22.94/23.10 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 22.94/23.10 Found x4:(X3 Xx0)
% 22.94/23.10 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 22.94/23.10 Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 22.94/23.10 Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 22.94/23.10 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 22.94/23.10 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 22.94/23.10 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 22.94/23.10 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 22.94/23.10 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% 22.94/23.10 Found (fun (x4:(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)))
% 22.94/23.10 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 22.94/23.10 Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 22.94/23.10 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 22.98/23.18 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 22.98/23.18 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 22.98/23.18 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 22.98/23.18 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 22.98/23.18 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% 22.98/23.18 Found (fun (x4:(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)))
% 22.98/23.18 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 22.98/23.18 Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 22.98/23.18 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 22.98/23.18 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 22.98/23.18 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 22.98/23.18 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 22.98/23.18 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 22.98/23.18 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% 22.98/23.18 Found (fun (x4:(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)))
% 22.98/23.18 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 22.98/23.18 Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 22.98/23.18 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 22.98/23.18 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 22.98/23.18 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 22.98/23.18 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 22.98/23.18 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 22.98/23.18 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% 22.98/23.18 Found (fun (x4:(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)))
% 22.98/23.18 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 22.98/23.18 Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 22.98/23.18 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 22.98/23.18 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 22.98/23.18 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 22.98/23.18 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 22.98/23.18 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 22.98/23.22 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% 22.98/23.22 Found (fun (x4:(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)))
% 22.98/23.22 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 22.98/23.22 Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 22.98/23.22 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 22.98/23.22 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 22.98/23.22 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 22.98/23.22 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 22.98/23.22 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 22.98/23.22 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% 22.98/23.22 Found (fun (x4:(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)))
% 22.98/23.22 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 22.98/23.22 Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 22.98/23.22 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 22.98/23.22 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 22.98/23.22 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 22.98/23.22 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 22.98/23.22 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 22.98/23.22 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% 22.98/23.22 Found (fun (x4:(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)))
% 22.98/23.22 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 22.98/23.22 Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 22.98/23.22 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 22.98/23.22 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 22.98/23.22 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 22.98/23.22 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 22.98/23.22 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 22.98/23.22 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% 22.98/23.22 Found (fun (x4:(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)))
% 22.98/23.22 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 22.98/23.22 Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 22.98/23.22 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 23.65/23.86 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 23.65/23.86 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 23.65/23.86 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 23.65/23.86 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 23.65/23.86 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% 23.65/23.86 Found (fun (x4:(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)))
% 23.65/23.86 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 23.65/23.86 Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 23.65/23.86 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 23.65/23.86 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 23.65/23.86 Found x4:(X3 Xx0)
% 23.65/23.86 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 23.65/23.86 Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 23.65/23.86 Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 23.65/23.86 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 23.65/23.86 Found x4:(X3 Xx0)
% 23.65/23.86 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 23.65/23.86 Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 23.65/23.86 Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 23.65/23.86 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 23.65/23.86 Found x4:(X3 Xx0)
% 23.65/23.86 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 23.65/23.86 Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 23.65/23.86 Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 23.65/23.86 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 23.65/23.86 Found x2:(X3 Xx0)
% 23.65/23.86 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 23.65/23.86 Found (fun (x2:(X3 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 23.65/23.86 Found (fun (Xx0:a) (x2:(X3 Xx0))=> x2) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 23.65/23.86 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 24.01/24.21 Found x4:(X3 Xx0)
% 24.01/24.21 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 24.01/24.21 Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 24.01/24.21 Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 24.01/24.21 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 24.01/24.21 Found x2:(X3 Xx0)
% 24.01/24.21 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 24.01/24.21 Found (fun (x2:(X3 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 24.01/24.21 Found (fun (Xx0:a) (x2:(X3 Xx0))=> x2) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 24.01/24.21 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 24.01/24.21 Found x2:(X3 Xx0)
% 24.01/24.21 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 24.01/24.21 Found (fun (x2:(X3 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 24.01/24.21 Found (fun (Xx0:a) (x2:(X3 Xx0))=> x2) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 24.01/24.21 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 24.01/24.21 Found x2:(X3 Xx0)
% 24.01/24.21 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 24.01/24.21 Found (fun (x2:(X3 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 24.01/24.21 Found (fun (Xx0:a) (x2:(X3 Xx0))=> x2) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 24.01/24.21 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 24.01/24.21 Found x2:(X3 Xx0)
% 24.01/24.21 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 24.01/24.21 Found (fun (x2:(X3 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 24.01/24.21 Found (fun (Xx0:a) (x2:(X3 Xx0))=> x2) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 24.01/24.21 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 24.01/24.21 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 24.01/24.21 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 24.01/24.21 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 24.01/24.21 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% 24.01/24.21 Found (fun (x4:(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)))
% 24.01/24.21 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 24.01/24.21 Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 24.01/24.21 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 24.01/24.21 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 24.01/24.22 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 24.01/24.22 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 24.01/24.22 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 24.01/24.22 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% 24.01/24.22 Found (fun (x4:(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)))
% 24.01/24.22 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 24.01/24.22 Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 24.01/24.22 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 24.01/24.22 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 24.01/24.22 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 24.01/24.22 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 24.01/24.22 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 24.01/24.22 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% 24.01/24.22 Found (fun (x4:(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)))
% 24.01/24.22 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 24.01/24.22 Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 24.01/24.22 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 24.01/24.22 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 24.01/24.22 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 24.01/24.22 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 24.01/24.22 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 24.01/24.22 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% 24.01/24.22 Found (fun (x4:(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)))
% 24.01/24.22 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 24.01/24.22 Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 24.01/24.22 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 24.01/24.22 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 24.01/24.22 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 24.01/24.22 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 24.01/24.22 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 24.01/24.22 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% 24.01/24.22 Found (fun (x4:(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)))
% 24.15/24.33 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 24.15/24.33 Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 24.15/24.33 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 24.15/24.33 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 24.15/24.33 Found x2:(X3 Xx0)
% 24.15/24.33 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 24.15/24.33 Found (fun (x2:(X3 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 24.15/24.33 Found (fun (Xx0:a) (x2:(X3 Xx0))=> x2) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 24.15/24.33 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 24.15/24.33 Found x2:(X3 Xx0)
% 24.15/24.33 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 24.15/24.33 Found (fun (x2:(X3 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 24.15/24.33 Found (fun (Xx0:a) (x2:(X3 Xx0))=> x2) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 24.15/24.33 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 24.15/24.33 Found x2:(X3 Xx0)
% 24.15/24.33 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 24.15/24.33 Found (fun (x2:(X3 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 24.15/24.33 Found (fun (Xx0:a) (x2:(X3 Xx0))=> x2) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 24.15/24.33 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 24.15/24.33 Found x2:(X3 Xx0)
% 24.15/24.33 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 24.15/24.33 Found (fun (x2:(X3 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 24.15/24.33 Found (fun (Xx0:a) (x2:(X3 Xx0))=> x2) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 24.15/24.33 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 24.15/24.33 Found x2:(X3 Xx0)
% 24.15/24.33 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 24.15/24.33 Found (fun (x2:(X3 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 24.15/24.33 Found (fun (Xx0:a) (x2:(X3 Xx0))=> x2) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 24.15/24.33 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 24.15/24.33 Found x2:(X3 Xx0)
% 24.15/24.33 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 24.33/24.59 Found (fun (x2:(X3 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 24.33/24.59 Found (fun (Xx0:a) (x2:(X3 Xx0))=> x2) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 24.33/24.59 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 24.33/24.59 Found x4:(X3 Xx0)
% 24.33/24.59 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 24.33/24.59 Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 24.33/24.59 Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 24.33/24.59 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 24.33/24.59 Found x2:(X3 Xx0)
% 24.33/24.59 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 24.33/24.59 Found (fun (x2:(X3 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 24.33/24.59 Found (fun (Xx0:a) (x2:(X3 Xx0))=> x2) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 24.33/24.59 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 24.33/24.59 Found x2:(X3 Xx0)
% 24.33/24.59 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 24.33/24.59 Found (fun (x2:(X3 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 24.33/24.59 Found (fun (Xx0:a) (x2:(X3 Xx0))=> x2) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 24.33/24.59 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 24.33/24.59 Found x2:(X3 Xx0)
% 24.33/24.59 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 24.33/24.59 Found (fun (x2:(X3 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 24.33/24.59 Found (fun (Xx0:a) (x2:(X3 Xx0))=> x2) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 24.33/24.59 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 24.33/24.59 Found x2:(X3 Xx0)
% 24.33/24.59 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 24.33/24.59 Found (fun (x2:(X3 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 24.33/24.59 Found (fun (Xx0:a) (x2:(X3 Xx0))=> x2) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 24.33/24.59 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 24.33/24.59 Found x2:(X3 Xx0)
% 24.33/24.59 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 24.33/24.59 Found (fun (x2:(X3 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 24.33/24.59 Found (fun (Xx0:a) (x2:(X3 Xx0))=> x2) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 24.33/24.59 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 27.84/28.08 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 27.84/28.08 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 27.84/28.08 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 27.84/28.08 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% 27.84/28.08 Found (fun (x4:(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)))
% 27.84/28.08 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 27.84/28.08 Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 27.84/28.08 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 27.84/28.08 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 27.84/28.08 Found x6:(X3 Xx0)
% 27.84/28.08 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 27.84/28.08 Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 27.84/28.08 Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 27.84/28.08 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 27.84/28.08 Found x400:=(x40 x5):((cK x1) Xx)
% 27.84/28.08 Found (x40 x5) as proof of ((cK X3) Xx)
% 27.84/28.08 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 27.84/28.08 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 27.84/28.08 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 27.84/28.08 Found x6:(X3 Xx0)
% 27.84/28.08 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 27.84/28.08 Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 27.84/28.08 Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 27.84/28.08 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 27.84/28.08 Found x400:=(x40 x5):((cK x2) Xx)
% 27.84/28.08 Found (x40 x5) as proof of ((cK X3) Xx)
% 27.84/28.08 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 27.84/28.08 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 27.84/28.08 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 27.84/28.08 Found x4:(X3 Xx0)
% 27.84/28.08 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 27.84/28.08 Found (fun (x4:(X3 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 27.84/28.08 Found (fun (Xx0:a) (x4:(X3 Xx0))=> x4) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 27.84/28.08 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 27.84/28.08 Found x6:(X3 Xx0)
% 27.84/28.08 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 27.84/28.08 Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 27.84/28.08 Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 27.84/28.08 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 28.51/28.68 Found x400:=(x40 x5):((cK x1) Xx)
% 28.51/28.68 Found (x40 x5) as proof of ((cK X3) Xx)
% 28.51/28.68 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 28.51/28.68 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 28.51/28.68 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 28.51/28.68 Found x6:(X3 Xx0)
% 28.51/28.68 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 28.51/28.68 Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 28.51/28.68 Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 28.51/28.68 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 28.51/28.68 Found x400:=(x40 x5):((cK x2) Xx)
% 28.51/28.68 Found (x40 x5) as proof of ((cK X3) Xx)
% 28.51/28.68 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 28.51/28.68 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 28.51/28.68 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 28.51/28.68 Found x6:(X3 Xx0)
% 28.51/28.68 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 28.51/28.68 Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 28.51/28.68 Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 28.51/28.68 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 28.51/28.68 Found x400:=(x40 x5):((cK x2) Xx)
% 28.51/28.68 Found (x40 x5) as proof of ((cK X3) Xx)
% 28.51/28.68 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 28.51/28.68 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 28.51/28.68 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 28.51/28.68 Found x6:(X3 Xx0)
% 28.51/28.68 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 28.51/28.68 Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 28.51/28.68 Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 28.51/28.68 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 28.51/28.68 Found x400:=(x40 x5):((cK x1) Xx)
% 28.51/28.68 Found (x40 x5) as proof of ((cK X3) Xx)
% 28.51/28.68 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 28.51/28.68 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 28.51/28.68 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 28.51/28.68 Found x6:(X3 Xx0)
% 28.51/28.68 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 28.51/28.68 Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 28.51/28.68 Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 28.51/28.68 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 28.51/28.68 Found x400:=(x40 x5):((cK x2) Xx)
% 28.51/28.68 Found (x40 x5) as proof of ((cK X3) Xx)
% 28.51/28.68 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 28.51/28.68 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 28.51/28.68 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 28.51/28.68 Found x6:(X3 Xx0)
% 28.51/28.68 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 28.51/28.68 Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 28.51/28.68 Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 28.86/29.05 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 28.86/29.05 Found x400:=(x40 x5):((cK x2) Xx)
% 28.86/29.05 Found (x40 x5) as proof of ((cK X3) Xx)
% 28.86/29.05 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 28.86/29.05 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 28.86/29.05 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 28.86/29.05 Found x6:(X3 Xx0)
% 28.86/29.05 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 28.86/29.05 Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 28.86/29.05 Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 28.86/29.05 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 28.86/29.05 Found x400:=(x40 x5):((cK x2) Xx)
% 28.86/29.05 Found (x40 x5) as proof of ((cK X3) Xx)
% 28.86/29.05 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 28.86/29.05 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 28.86/29.05 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 28.86/29.05 Found x6:(X3 Xx0)
% 28.86/29.05 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 28.86/29.05 Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 28.86/29.05 Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 28.86/29.05 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 28.86/29.05 Found x400:=(x40 x5):((cK x1) Xx)
% 28.86/29.05 Found (x40 x5) as proof of ((cK X3) Xx)
% 28.86/29.05 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 28.86/29.05 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 28.86/29.05 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 28.86/29.05 Found x6:(X3 Xx0)
% 28.86/29.05 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 28.86/29.05 Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 28.86/29.05 Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 28.86/29.05 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 28.86/29.05 Found x400:=(x40 x5):((cK x2) Xx)
% 28.86/29.05 Found (x40 x5) as proof of ((cK X3) Xx)
% 28.86/29.05 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 28.86/29.05 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 28.86/29.05 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 28.86/29.05 Found x6:(X3 Xx0)
% 28.86/29.05 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 28.86/29.05 Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 28.86/29.05 Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 28.86/29.05 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 28.86/29.05 Found x400:=(x40 x5):((cK x2) Xx)
% 28.86/29.05 Found (x40 x5) as proof of ((cK X3) Xx)
% 28.86/29.05 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 28.86/29.05 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 28.86/29.05 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 28.86/29.05 Found x6:(X3 Xx0)
% 28.86/29.05 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 28.86/29.05 Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 28.86/29.05 Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 29.24/29.43 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 29.24/29.43 Found x400:=(x40 x5):((cK x2) Xx)
% 29.24/29.43 Found (x40 x5) as proof of ((cK X3) Xx)
% 29.24/29.43 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 29.24/29.43 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 29.24/29.43 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 29.24/29.43 Found x6:(X3 Xx0)
% 29.24/29.43 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 29.24/29.43 Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 29.24/29.43 Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 29.24/29.43 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 29.24/29.43 Found x400:=(x40 x5):((cK x2) Xx)
% 29.24/29.43 Found (x40 x5) as proof of ((cK X3) Xx)
% 29.24/29.43 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 29.24/29.43 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 29.24/29.43 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 29.24/29.43 Found x6:(X3 Xx0)
% 29.24/29.43 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 29.24/29.43 Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 29.24/29.43 Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 29.24/29.43 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 29.24/29.43 Found x400:=(x40 x5):((cK x2) Xx)
% 29.24/29.43 Found (x40 x5) as proof of ((cK X3) Xx)
% 29.24/29.43 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 29.24/29.43 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 29.24/29.43 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 29.24/29.43 Found x6:(X3 Xx0)
% 29.24/29.43 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 29.24/29.43 Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 29.24/29.43 Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 29.24/29.43 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 29.24/29.43 Found x400:=(x40 x5):((cK x2) Xx)
% 29.24/29.43 Found (x40 x5) as proof of ((cK X3) Xx)
% 29.24/29.43 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 29.24/29.43 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 29.24/29.43 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 29.24/29.43 Found x6:(X3 Xx0)
% 29.24/29.43 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 29.24/29.43 Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 29.24/29.43 Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 29.24/29.43 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 29.24/29.43 Found x400:=(x40 x5):((cK x2) Xx)
% 29.24/29.43 Found (x40 x5) as proof of ((cK X3) Xx)
% 29.24/29.43 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 29.24/29.43 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 29.24/29.43 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 29.24/29.43 Found x40:=(x4 Xx):((x1 Xx)->((cK x1) Xx))
% 29.24/29.43 Found (x4 Xx) as proof of ((x1 Xx)->((cK X3) Xx))
% 29.24/29.43 Found (x4 Xx) as proof of ((x1 Xx)->((cK X3) Xx))
% 29.24/29.43 Found (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx)) as proof of ((x1 Xx)->((cK X3) Xx))
% 29.24/29.43 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)))
% 29.69/29.87 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 29.69/29.87 Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 29.69/29.87 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)
% 29.69/29.87 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)
% 29.69/29.87 Found x6:(X3 Xx0)
% 29.69/29.87 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 29.69/29.87 Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 29.69/29.87 Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 29.69/29.87 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 29.69/29.87 Found x400:=(x40 x5):((cK x2) Xx)
% 29.69/29.87 Found (x40 x5) as proof of ((cK X3) Xx)
% 29.69/29.87 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 29.69/29.87 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 29.69/29.87 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 29.69/29.87 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 29.69/29.87 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 29.69/29.87 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 29.69/29.87 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% 29.69/29.87 Found (fun (x4:(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)))
% 29.69/29.87 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 29.69/29.87 Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 29.69/29.87 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 29.69/29.87 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)
% 29.69/29.87 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 29.69/29.87 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 29.69/29.87 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 29.69/29.87 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% 29.69/29.87 Found (fun (x4:(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)))
% 29.69/29.87 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 29.69/29.87 Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 29.69/29.87 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 29.69/29.87 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)
% 29.73/29.90 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 29.73/29.90 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 29.73/29.90 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 29.73/29.90 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% 29.73/29.90 Found (fun (x4:(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)))
% 29.73/29.90 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 29.73/29.90 Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 29.73/29.90 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 29.73/29.90 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)
% 29.73/29.90 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 29.73/29.90 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 29.73/29.90 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 29.73/29.90 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% 29.73/29.90 Found (fun (x4:(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)))
% 29.73/29.90 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 29.73/29.90 Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 29.73/29.90 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 29.73/29.90 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)
% 29.73/29.90 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 29.73/29.90 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 29.73/29.90 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 29.73/29.90 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% 29.73/29.90 Found (fun (x4:(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)))
% 29.73/29.90 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 29.73/29.90 Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 29.73/29.90 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 29.73/29.90 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)
% 29.73/29.90 Found x6:(X3 Xx0)
% 29.73/29.90 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 29.73/29.90 Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 30.06/30.30 Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 30.06/30.30 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 30.06/30.30 Found x400:=(x40 x5):((cK x2) Xx)
% 30.06/30.30 Found (x40 x5) as proof of ((cK X3) Xx)
% 30.06/30.30 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 30.06/30.30 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 30.06/30.30 Found ((x4 Xx) x5) as proof of ((cK X3) Xx)
% 30.06/30.30 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 30.06/30.30 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 30.06/30.30 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 30.06/30.30 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% 30.06/30.30 Found (fun (x4:(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)))
% 30.06/30.30 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 30.06/30.30 Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 30.06/30.30 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 30.06/30.30 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)
% 30.06/30.30 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 30.06/30.30 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 30.06/30.30 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 30.06/30.30 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% 30.06/30.30 Found (fun (x4:(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)))
% 30.06/30.30 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 30.06/30.30 Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 30.06/30.30 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 30.06/30.30 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)
% 30.06/30.30 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 30.06/30.30 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 30.06/30.30 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 30.06/30.30 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% 30.06/30.30 Found (fun (x4:(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)))
% 30.06/30.30 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 30.06/30.30 Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 30.06/30.30 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 30.06/30.30 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)
% 30.34/30.52 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 30.34/30.52 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 30.34/30.52 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 30.34/30.52 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% 30.34/30.52 Found (fun (x4:(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)))
% 30.34/30.52 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 30.34/30.52 Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 30.34/30.52 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 30.34/30.52 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)
% 30.34/30.52 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 30.34/30.52 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 30.34/30.52 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 30.34/30.52 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% 30.34/30.52 Found (fun (x4:(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)))
% 30.34/30.52 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 30.34/30.52 Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 30.34/30.52 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 30.34/30.52 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)
% 30.34/30.52 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 30.34/30.52 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 30.34/30.52 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 30.34/30.52 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% 30.34/30.52 Found (fun (x4:(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)))
% 30.34/30.52 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 30.34/30.52 Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 30.34/30.52 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 30.34/30.52 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)
% 30.34/30.52 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 30.34/30.52 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 30.34/30.52 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 30.34/30.53 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% 30.34/30.53 Found (fun (x4:(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)))
% 30.34/30.53 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 30.34/30.53 Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 30.34/30.53 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 30.34/30.53 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)
% 30.34/30.53 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 30.34/30.53 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 30.34/30.53 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 30.34/30.53 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% 30.34/30.53 Found (fun (x4:(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)))
% 30.34/30.53 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 30.34/30.53 Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 30.34/30.53 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 30.34/30.53 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)
% 30.34/30.53 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 30.34/30.53 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 30.34/30.53 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 30.34/30.53 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% 30.34/30.53 Found (fun (x4:(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)))
% 30.34/30.53 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 30.34/30.53 Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 30.34/30.53 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 30.34/30.53 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)
% 30.34/30.53 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 30.34/30.53 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 30.34/30.53 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 30.34/30.53 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% 30.34/30.53 Found (fun (x4:(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)))
% 30.34/30.53 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 39.96/40.14 Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 39.96/40.14 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 39.96/40.14 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)
% 39.96/40.14 Found x6:(X3 Xx0)
% 39.96/40.14 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 39.96/40.14 Found (fun (x6:(X3 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 39.96/40.14 Found (fun (Xx0:a) (x6:(X3 Xx0))=> x6) as proof of ((X3 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 39.96/40.14 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 39.96/40.14 Found x300:=(x30 x4):((cK x1) Xx)
% 39.96/40.14 Found (x30 x4) as proof of ((cK X3) Xx)
% 39.96/40.14 Found ((x3 Xx) x4) as proof of ((cK X3) Xx)
% 39.96/40.14 Found ((x3 Xx) x4) as proof of ((cK X3) Xx)
% 39.96/40.14 Found ((x3 Xx) x4) as proof of ((cK X3) Xx)
% 39.96/40.14 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 39.96/40.14 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 39.96/40.14 Found (x4 Xx) as proof of ((x2 Xx)->((cK X3) Xx))
% 39.96/40.14 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X3) Xx))
% 39.96/40.14 Found (fun (x4:(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)))
% 39.96/40.14 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 39.96/40.14 Found ((and_rect0 ((cK X3) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X3) Xx)
% 39.96/40.14 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((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)
% 39.96/40.14 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)
% 39.96/40.14 Found x6:(X4 Xx0)
% 39.96/40.14 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 39.96/40.14 Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 39.96/40.14 Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 39.96/40.14 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 39.96/40.14 Found x400:=(x40 x5):((cK x2) Xx)
% 39.96/40.14 Found (x40 x5) as proof of ((cK X4) Xx)
% 39.96/40.14 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 39.96/40.14 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 39.96/40.14 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 39.96/40.14 Found x4:(X4 Xx0)
% 39.96/40.14 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 39.96/40.14 Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 39.96/40.14 Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 43.36/43.62 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 43.36/43.62 Found x4:(X4 Xx0)
% 43.36/43.62 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 43.36/43.62 Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 43.36/43.62 Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 43.36/43.62 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 43.36/43.62 Found x6:(X4 Xx0)
% 43.36/43.62 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 43.36/43.62 Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 43.36/43.62 Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 43.36/43.62 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 43.36/43.62 Found x400:=(x40 x5):((cK x2) Xx)
% 43.36/43.62 Found (x40 x5) as proof of ((cK X4) Xx)
% 43.36/43.62 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 43.36/43.62 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 43.36/43.62 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 43.36/43.62 Found x6:(X4 Xx0)
% 43.36/43.62 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 43.36/43.62 Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 43.36/43.62 Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 43.36/43.62 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 43.36/43.62 Found x400:=(x40 x5):((cK x2) Xx)
% 43.36/43.62 Found (x40 x5) as proof of ((cK X4) Xx)
% 43.36/43.62 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 43.36/43.62 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 43.36/43.62 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 43.36/43.62 Found x6:(X4 Xx0)
% 43.36/43.62 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 43.36/43.62 Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 43.36/43.62 Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 43.36/43.62 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 43.36/43.62 Found x400:=(x40 x5):((cK x2) Xx)
% 43.36/43.62 Found (x40 x5) as proof of ((cK X4) Xx)
% 43.36/43.62 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 43.36/43.62 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 43.36/43.62 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 43.36/43.62 Found x4:(X4 Xx0)
% 43.36/43.62 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 43.36/43.62 Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 43.36/43.62 Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 43.36/43.62 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 43.36/43.62 Found x4:(X4 Xx0)
% 43.36/43.62 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 43.65/43.84 Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 43.65/43.84 Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 43.65/43.84 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 43.65/43.84 Found x6:(X4 Xx0)
% 43.65/43.84 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 43.65/43.84 Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 43.65/43.84 Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 43.65/43.84 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 43.65/43.84 Found x400:=(x40 x5):((cK x2) Xx)
% 43.65/43.84 Found (x40 x5) as proof of ((cK X4) Xx)
% 43.65/43.84 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 43.65/43.84 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 43.65/43.84 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 43.65/43.84 Found x6:(X4 Xx0)
% 43.65/43.84 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 43.65/43.84 Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 43.65/43.84 Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 43.65/43.84 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 43.65/43.84 Found x400:=(x40 x5):((cK x2) Xx)
% 43.65/43.84 Found (x40 x5) as proof of ((cK X4) Xx)
% 43.65/43.84 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 43.65/43.84 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 43.65/43.84 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 43.65/43.84 Found x6:(X4 Xx0)
% 43.65/43.84 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 43.65/43.84 Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 43.65/43.84 Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 43.65/43.84 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 43.65/43.84 Found x400:=(x40 x5):((cK x2) Xx)
% 43.65/43.84 Found (x40 x5) as proof of ((cK X4) Xx)
% 43.65/43.84 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 43.65/43.84 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 43.65/43.84 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 43.65/43.84 Found x6:(X4 Xx0)
% 43.65/43.84 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 43.65/43.84 Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 43.65/43.84 Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 43.65/43.84 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 43.65/43.84 Found x400:=(x40 x5):((cK x2) Xx)
% 43.65/43.84 Found (x40 x5) as proof of ((cK X4) Xx)
% 43.65/43.84 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 43.65/43.84 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 43.65/43.84 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 43.65/43.84 Found x6:(X4 Xx0)
% 43.65/43.84 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 43.65/43.84 Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 43.65/43.84 Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 45.40/45.65 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 45.40/45.65 Found x400:=(x40 x5):((cK x2) Xx)
% 45.40/45.65 Found (x40 x5) as proof of ((cK X4) Xx)
% 45.40/45.65 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 45.40/45.65 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 45.40/45.65 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 45.40/45.65 Found x6:(X4 Xx0)
% 45.40/45.65 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 45.40/45.65 Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 45.40/45.65 Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 45.40/45.65 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 45.40/45.65 Found x400:=(x40 x5):((cK x2) Xx)
% 45.40/45.65 Found (x40 x5) as proof of ((cK X4) Xx)
% 45.40/45.65 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 45.40/45.65 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 45.40/45.65 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 45.40/45.65 Found x4:(X4 Xx0)
% 45.40/45.65 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 45.40/45.65 Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 45.40/45.65 Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 45.40/45.65 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 45.40/45.65 Found x4:(X4 Xx0)
% 45.40/45.65 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 45.40/45.65 Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 45.40/45.65 Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 45.40/45.65 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 45.40/45.65 Found x4:(X4 Xx0)
% 45.40/45.65 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 45.40/45.65 Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 45.40/45.65 Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 45.40/45.65 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 45.40/45.65 Found x4:(X4 Xx0)
% 45.40/45.65 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 45.40/45.65 Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 45.40/45.65 Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 45.40/45.65 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 45.40/45.65 Found x6:(X4 Xx0)
% 45.40/45.65 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 45.40/45.65 Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 45.63/45.84 Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 45.63/45.84 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 45.63/45.84 Found x400:=(x40 x5):((cK x2) Xx)
% 45.63/45.84 Found (x40 x5) as proof of ((cK X4) Xx)
% 45.63/45.84 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 45.63/45.84 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 45.63/45.84 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 45.63/45.84 Found x6:(X4 Xx0)
% 45.63/45.84 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 45.63/45.84 Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 45.63/45.84 Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 45.63/45.84 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 45.63/45.84 Found x400:=(x40 x5):((cK x2) Xx)
% 45.63/45.84 Found (x40 x5) as proof of ((cK X4) Xx)
% 45.63/45.84 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 45.63/45.84 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 45.63/45.84 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 45.63/45.84 Found x6:(X4 Xx0)
% 45.63/45.84 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 45.63/45.84 Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 45.63/45.84 Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 45.63/45.84 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 45.63/45.84 Found x400:=(x40 x5):((cK x2) Xx)
% 45.63/45.84 Found (x40 x5) as proof of ((cK X4) Xx)
% 45.63/45.84 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 45.63/45.84 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 45.63/45.84 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 45.63/45.84 Found x6:(X4 Xx0)
% 45.63/45.84 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 45.63/45.84 Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 45.63/45.84 Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 45.63/45.84 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 45.63/45.84 Found x400:=(x40 x5):((cK x2) Xx)
% 45.63/45.84 Found (x40 x5) as proof of ((cK X4) Xx)
% 45.63/45.84 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 45.63/45.84 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 45.63/45.84 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 45.63/45.84 Found x6:(X4 Xx0)
% 45.63/45.84 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 45.63/45.84 Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 45.63/45.84 Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 45.63/45.84 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 45.63/45.84 Found x400:=(x40 x5):((cK x2) Xx)
% 45.63/45.84 Found (x40 x5) as proof of ((cK X4) Xx)
% 45.63/45.84 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 45.63/45.84 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 45.63/45.84 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 45.63/45.84 Found x6:(X4 Xx0)
% 45.63/45.84 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 45.63/45.84 Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 45.93/46.15 Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 45.93/46.15 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 45.93/46.15 Found x400:=(x40 x5):((cK x2) Xx)
% 45.93/46.15 Found (x40 x5) as proof of ((cK X4) Xx)
% 45.93/46.15 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 45.93/46.15 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 45.93/46.15 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 45.93/46.15 Found x6:(X4 Xx0)
% 45.93/46.15 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 45.93/46.15 Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 45.93/46.15 Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 45.93/46.15 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 45.93/46.15 Found x400:=(x40 x5):((cK x2) Xx)
% 45.93/46.15 Found (x40 x5) as proof of ((cK X4) Xx)
% 45.93/46.15 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 45.93/46.15 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 45.93/46.15 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 45.93/46.15 Found x6:(X4 Xx0)
% 45.93/46.15 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 45.93/46.15 Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 45.93/46.15 Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 45.93/46.15 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 45.93/46.15 Found x400:=(x40 x5):((cK x2) Xx)
% 45.93/46.15 Found (x40 x5) as proof of ((cK X4) Xx)
% 45.93/46.15 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 45.93/46.15 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 45.93/46.15 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 45.93/46.15 Found x6:(X4 Xx0)
% 45.93/46.15 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 45.93/46.15 Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 45.93/46.15 Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 45.93/46.15 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 45.93/46.15 Found x400:=(x40 x5):((cK x2) Xx)
% 45.93/46.15 Found (x40 x5) as proof of ((cK X4) Xx)
% 45.93/46.15 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 45.93/46.15 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 45.93/46.15 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 45.93/46.15 Found x6:(X4 Xx0)
% 45.93/46.15 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 45.93/46.15 Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 45.93/46.15 Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 45.93/46.15 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 45.93/46.15 Found x400:=(x40 x5):((cK x2) Xx)
% 45.93/46.15 Found (x40 x5) as proof of ((cK X4) Xx)
% 45.93/46.15 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 45.93/46.15 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 45.93/46.15 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 45.93/46.15 Found x6:(X4 Xx0)
% 45.93/46.15 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 45.93/46.15 Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 47.51/47.71 Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 47.51/47.71 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 47.51/47.71 Found x400:=(x40 x5):((cK x2) Xx)
% 47.51/47.71 Found (x40 x5) as proof of ((cK X4) Xx)
% 47.51/47.71 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 47.51/47.71 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 47.51/47.71 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 47.51/47.71 Found x4:(X4 Xx0)
% 47.51/47.71 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 47.51/47.71 Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 47.51/47.71 Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 47.51/47.71 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 47.51/47.71 Found x4:(X4 Xx0)
% 47.51/47.71 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 47.51/47.71 Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 47.51/47.71 Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 47.51/47.71 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 47.51/47.71 Found x4:(X4 Xx0)
% 47.51/47.71 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 47.51/47.71 Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 47.51/47.71 Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 47.51/47.71 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 47.51/47.71 Found x4:(X4 Xx0)
% 47.51/47.71 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 47.51/47.71 Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 47.51/47.71 Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 47.51/47.71 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 47.51/47.71 Found x4:(X4 Xx0)
% 47.51/47.71 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 47.51/47.71 Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 47.51/47.71 Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 47.51/47.71 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 47.51/47.71 Found x4:(X4 Xx0)
% 47.51/47.71 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 47.51/47.71 Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 47.51/47.71 Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 47.79/48.06 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 47.79/48.06 Found x6:(X4 Xx0)
% 47.79/48.06 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 47.79/48.06 Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 47.79/48.06 Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 47.79/48.06 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 47.79/48.06 Found x400:=(x40 x5):((cK x2) Xx)
% 47.79/48.06 Found (x40 x5) as proof of ((cK X4) Xx)
% 47.79/48.06 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 47.79/48.06 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 47.79/48.06 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 47.79/48.06 Found x6:(X4 Xx0)
% 47.79/48.06 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 47.79/48.06 Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 47.79/48.06 Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 47.79/48.06 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 47.79/48.06 Found x400:=(x40 x5):((cK x2) Xx)
% 47.79/48.06 Found (x40 x5) as proof of ((cK X4) Xx)
% 47.79/48.06 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 47.79/48.06 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 47.79/48.06 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 47.79/48.06 Found x6:(X4 Xx0)
% 47.79/48.06 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 47.79/48.06 Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 47.79/48.06 Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 47.79/48.06 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 47.79/48.06 Found x400:=(x40 x5):((cK x2) Xx)
% 47.79/48.06 Found (x40 x5) as proof of ((cK X4) Xx)
% 47.79/48.06 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 47.79/48.06 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 47.79/48.06 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 47.79/48.06 Found x6:(X4 Xx0)
% 47.79/48.06 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 47.79/48.06 Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 47.79/48.06 Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 47.79/48.06 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 47.79/48.06 Found x400:=(x40 x5):((cK x2) Xx)
% 47.79/48.06 Found (x40 x5) as proof of ((cK X4) Xx)
% 47.79/48.06 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 47.79/48.06 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 47.79/48.06 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 47.79/48.06 Found x6:(X4 Xx0)
% 47.79/48.06 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 47.79/48.06 Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 47.79/48.06 Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 47.79/48.06 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 48.03/48.23 Found x400:=(x40 x5):((cK x2) Xx)
% 48.03/48.23 Found (x40 x5) as proof of ((cK X4) Xx)
% 48.03/48.23 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 48.03/48.23 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 48.03/48.23 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 48.03/48.23 Found x6:(X4 Xx0)
% 48.03/48.23 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 48.03/48.23 Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 48.03/48.23 Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 48.03/48.23 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 48.03/48.23 Found x400:=(x40 x5):((cK x2) Xx)
% 48.03/48.23 Found (x40 x5) as proof of ((cK X4) Xx)
% 48.03/48.23 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 48.03/48.23 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 48.03/48.23 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 48.03/48.23 Found x6:(X4 Xx0)
% 48.03/48.23 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 48.03/48.23 Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 48.03/48.23 Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 48.03/48.23 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 48.03/48.23 Found x400:=(x40 x5):((cK x2) Xx)
% 48.03/48.23 Found (x40 x5) as proof of ((cK X4) Xx)
% 48.03/48.23 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 48.03/48.23 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 48.03/48.23 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 48.03/48.23 Found x6:(X4 Xx0)
% 48.03/48.23 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 48.03/48.23 Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 48.03/48.23 Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 48.03/48.23 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 48.03/48.23 Found x400:=(x40 x5):((cK x2) Xx)
% 48.03/48.23 Found (x40 x5) as proof of ((cK X4) Xx)
% 48.03/48.23 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 48.03/48.23 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 48.03/48.23 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 48.03/48.23 Found x6:(X4 Xx0)
% 48.03/48.23 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 48.03/48.23 Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 48.03/48.23 Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 48.03/48.23 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 48.03/48.23 Found x400:=(x40 x5):((cK x2) Xx)
% 48.03/48.23 Found (x40 x5) as proof of ((cK X4) Xx)
% 48.03/48.23 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 48.03/48.23 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 48.03/48.23 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 48.03/48.23 Found x6:(X4 Xx0)
% 48.03/48.23 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 48.03/48.23 Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 48.03/48.23 Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 48.03/48.23 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 48.32/48.53 Found x400:=(x40 x5):((cK x2) Xx)
% 48.32/48.53 Found (x40 x5) as proof of ((cK X4) Xx)
% 48.32/48.53 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 48.32/48.53 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 48.32/48.53 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 48.32/48.53 Found x6:(X4 Xx0)
% 48.32/48.53 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 48.32/48.53 Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 48.32/48.53 Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 48.32/48.53 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 48.32/48.53 Found x400:=(x40 x5):((cK x2) Xx)
% 48.32/48.53 Found (x40 x5) as proof of ((cK X4) Xx)
% 48.32/48.53 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 48.32/48.53 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 48.32/48.53 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 48.32/48.53 Found x4:(X4 Xx0)
% 48.32/48.53 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 48.32/48.53 Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 48.32/48.53 Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 48.32/48.53 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 48.32/48.53 Found x6:(X4 Xx0)
% 48.32/48.53 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 48.32/48.53 Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 48.32/48.53 Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 48.32/48.53 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 48.32/48.53 Found x400:=(x40 x5):((cK x2) Xx)
% 48.32/48.53 Found (x40 x5) as proof of ((cK X4) Xx)
% 48.32/48.53 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 48.32/48.53 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 48.32/48.53 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 48.32/48.53 Found x6:(X4 Xx0)
% 48.32/48.53 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 48.32/48.53 Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 48.32/48.53 Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 48.32/48.53 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 48.32/48.53 Found x400:=(x40 x5):((cK x2) Xx)
% 48.32/48.53 Found (x40 x5) as proof of ((cK X4) Xx)
% 48.32/48.53 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 48.32/48.53 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 48.32/48.53 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 48.32/48.53 Found x6:(X4 Xx0)
% 48.32/48.53 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 48.32/48.53 Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 48.32/48.53 Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 48.32/48.53 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 48.32/48.53 Found x400:=(x40 x5):((cK x2) Xx)
% 48.32/48.53 Found (x40 x5) as proof of ((cK X4) Xx)
% 49.03/49.27 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 49.03/49.27 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 49.03/49.27 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 49.03/49.27 Found x4:(X4 Xx0)
% 49.03/49.27 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 49.03/49.27 Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 49.03/49.27 Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 49.03/49.27 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 49.03/49.27 Found x4:(X4 Xx0)
% 49.03/49.27 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 49.03/49.27 Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 49.03/49.27 Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 49.03/49.27 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 49.03/49.27 Found x4:(X4 Xx0)
% 49.03/49.27 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 49.03/49.27 Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 49.03/49.27 Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 49.03/49.27 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 49.03/49.27 Found x4:(X4 Xx0)
% 49.03/49.27 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 49.03/49.27 Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 49.03/49.27 Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 49.03/49.27 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 49.03/49.27 Found x4:(X4 Xx0)
% 49.03/49.27 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 49.03/49.27 Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 49.03/49.27 Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 49.03/49.27 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 49.03/49.27 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 49.03/49.27 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 49.03/49.27 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 49.03/49.27 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 49.03/49.27 Found (fun (x4:(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)))
% 49.03/49.27 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 49.03/49.27 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 49.03/49.27 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 49.33/49.53 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 49.33/49.53 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 49.33/49.53 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 49.33/49.53 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 49.33/49.53 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 49.33/49.53 Found (fun (x4:(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)))
% 49.33/49.53 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 49.33/49.53 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 49.33/49.53 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 49.33/49.53 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 49.33/49.53 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 49.33/49.53 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 49.33/49.53 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 49.33/49.53 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 49.33/49.53 Found (fun (x4:(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)))
% 49.33/49.53 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 49.33/49.53 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 49.33/49.53 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 49.33/49.53 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 49.33/49.53 Found x4:(X4 Xx0)
% 49.33/49.53 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 49.33/49.53 Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 49.33/49.53 Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 49.33/49.53 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 49.33/49.53 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 49.33/49.53 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 49.33/49.53 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 49.33/49.53 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 49.33/49.53 Found (fun (x4:(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)))
% 49.33/49.53 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 49.33/49.53 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 49.33/49.53 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 49.69/49.94 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 49.69/49.94 Found x4:(X4 Xx0)
% 49.69/49.94 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 49.69/49.94 Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 49.69/49.94 Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 49.69/49.94 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 49.69/49.94 Found x4:(X4 Xx0)
% 49.69/49.94 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 49.69/49.94 Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 49.69/49.94 Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 49.69/49.94 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 49.69/49.94 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 49.69/49.94 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 49.69/49.94 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 49.69/49.94 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 49.69/49.94 Found (fun (x4:(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)))
% 49.69/49.94 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 49.69/49.94 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 49.69/49.94 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 49.69/49.94 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 49.69/49.94 Found x4:(X4 Xx0)
% 49.69/49.94 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 49.69/49.94 Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 49.69/49.94 Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 49.69/49.94 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 49.69/49.94 Found x6:(X4 Xx0)
% 49.69/49.94 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 49.69/49.94 Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 49.69/49.94 Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 49.69/49.94 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 49.69/49.94 Found x400:=(x40 x5):((cK x2) Xx)
% 49.95/50.17 Found (x40 x5) as proof of ((cK X4) Xx)
% 49.95/50.17 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 49.95/50.17 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 49.95/50.17 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 49.95/50.17 Found x2:(X4 Xx0)
% 49.95/50.17 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 49.95/50.17 Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 49.95/50.17 Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 49.95/50.17 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 49.95/50.17 Found x6:(X4 Xx0)
% 49.95/50.17 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 49.95/50.17 Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 49.95/50.17 Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 49.95/50.17 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 49.95/50.17 Found x400:=(x40 x5):((cK x2) Xx)
% 49.95/50.17 Found (x40 x5) as proof of ((cK X4) Xx)
% 49.95/50.17 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 49.95/50.17 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 49.95/50.17 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 49.95/50.17 Found x6:(X4 Xx0)
% 49.95/50.17 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 49.95/50.17 Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 49.95/50.17 Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 49.95/50.17 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 49.95/50.17 Found x400:=(x40 x5):((cK x2) Xx)
% 49.95/50.17 Found (x40 x5) as proof of ((cK X4) Xx)
% 49.95/50.17 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 49.95/50.17 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 49.95/50.17 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 49.95/50.17 Found x6:(X4 Xx0)
% 49.95/50.17 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 49.95/50.17 Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 49.95/50.17 Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 49.95/50.17 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 49.95/50.17 Found x400:=(x40 x5):((cK x2) Xx)
% 49.95/50.17 Found (x40 x5) as proof of ((cK X4) Xx)
% 49.95/50.17 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 49.95/50.17 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 49.95/50.17 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 49.95/50.17 Found x6:(X4 Xx0)
% 49.95/50.17 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 49.95/50.17 Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 49.95/50.17 Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 49.95/50.17 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 49.95/50.17 Found x400:=(x40 x5):((cK x2) Xx)
% 49.95/50.17 Found (x40 x5) as proof of ((cK X4) Xx)
% 49.95/50.17 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 49.95/50.17 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 49.95/50.17 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 50.12/50.33 Found x6:(X4 Xx0)
% 50.12/50.33 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 50.12/50.33 Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 50.12/50.33 Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 50.12/50.33 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 50.12/50.33 Found x400:=(x40 x5):((cK x2) Xx)
% 50.12/50.33 Found (x40 x5) as proof of ((cK X4) Xx)
% 50.12/50.33 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 50.12/50.33 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 50.12/50.33 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 50.12/50.33 Found x6:(X4 Xx0)
% 50.12/50.33 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 50.12/50.33 Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 50.12/50.33 Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 50.12/50.33 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 50.12/50.33 Found x400:=(x40 x5):((cK x2) Xx)
% 50.12/50.33 Found (x40 x5) as proof of ((cK X4) Xx)
% 50.12/50.33 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 50.12/50.33 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 50.12/50.33 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 50.12/50.33 Found x6:(X4 Xx0)
% 50.12/50.33 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 50.12/50.33 Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 50.12/50.33 Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 50.12/50.33 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 50.12/50.33 Found x400:=(x40 x5):((cK x2) Xx)
% 50.12/50.33 Found (x40 x5) as proof of ((cK X4) Xx)
% 50.12/50.33 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 50.12/50.33 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 50.12/50.33 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 50.12/50.33 Found x6:(X4 Xx0)
% 50.12/50.33 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 50.12/50.33 Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 50.12/50.33 Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 50.12/50.33 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 50.12/50.33 Found x400:=(x40 x5):((cK x2) Xx)
% 50.12/50.33 Found (x40 x5) as proof of ((cK X4) Xx)
% 50.12/50.33 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 50.12/50.33 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 50.12/50.33 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 50.12/50.33 Found x6:(X4 Xx0)
% 50.12/50.33 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 50.12/50.33 Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 50.12/50.33 Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 50.12/50.33 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 50.12/50.33 Found x400:=(x40 x5):((cK x2) Xx)
% 50.12/50.33 Found (x40 x5) as proof of ((cK X4) Xx)
% 50.12/50.33 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 50.12/50.33 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 50.59/50.81 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 50.59/50.81 Found x4:(X4 Xx0)
% 50.59/50.81 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 50.59/50.81 Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 50.59/50.81 Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 50.59/50.81 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 50.59/50.81 Found x6:(X4 Xx0)
% 50.59/50.81 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 50.59/50.81 Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 50.59/50.81 Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 50.59/50.81 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 50.59/50.81 Found x400:=(x40 x5):((cK x2) Xx)
% 50.59/50.81 Found (x40 x5) as proof of ((cK X4) Xx)
% 50.59/50.81 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 50.59/50.81 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 50.59/50.81 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 50.59/50.81 Found x4:(X4 Xx0)
% 50.59/50.81 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 50.59/50.81 Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 50.59/50.81 Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 50.59/50.81 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 50.59/50.81 Found x4:(X4 Xx0)
% 50.59/50.81 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 50.59/50.81 Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 50.59/50.81 Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 50.59/50.81 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 50.59/50.81 Found x2:(X4 Xx0)
% 50.59/50.81 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 50.59/50.81 Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 50.59/50.81 Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 50.59/50.81 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 50.59/50.81 Found x2:(X4 Xx0)
% 50.59/50.81 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 50.59/50.81 Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 50.59/50.81 Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 50.59/50.81 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 50.59/50.81 Found x2:(X4 Xx0)
% 50.59/50.81 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 51.04/51.30 Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 51.04/51.30 Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 51.04/51.30 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 51.04/51.30 Found x2:(X4 Xx0)
% 51.04/51.30 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 51.04/51.30 Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 51.04/51.30 Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 51.04/51.30 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 51.04/51.30 Found x2:(X4 Xx0)
% 51.04/51.30 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 51.04/51.30 Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 51.04/51.30 Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 51.04/51.30 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 51.04/51.30 Found x4:(X4 Xx0)
% 51.04/51.30 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 51.04/51.30 Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 51.04/51.30 Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 51.04/51.30 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 51.04/51.30 Found x4:(X4 Xx0)
% 51.04/51.30 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 51.04/51.30 Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 51.04/51.30 Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 51.04/51.30 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 51.04/51.30 Found x4:(X4 Xx0)
% 51.04/51.30 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 51.04/51.30 Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 51.04/51.30 Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 51.04/51.30 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 51.04/51.30 Found x4:(X4 Xx0)
% 51.04/51.30 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 51.04/51.30 Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 51.04/51.30 Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 51.04/51.30 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 51.33/51.55 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 51.33/51.55 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 51.33/51.55 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 51.33/51.55 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 51.33/51.55 Found (fun (x4:(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)))
% 51.33/51.55 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 51.33/51.55 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 51.33/51.55 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 51.33/51.55 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 51.33/51.55 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 51.33/51.55 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 51.33/51.55 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 51.33/51.55 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 51.33/51.55 Found (fun (x4:(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)))
% 51.33/51.55 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 51.33/51.55 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 51.33/51.55 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 51.33/51.55 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 51.33/51.55 Found x2:(X4 Xx0)
% 51.33/51.55 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 51.33/51.55 Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 51.33/51.55 Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 51.33/51.55 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 51.33/51.55 Found x2:(X4 Xx0)
% 51.33/51.55 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 51.33/51.55 Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 51.33/51.55 Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 51.33/51.55 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 51.33/51.55 Found x2:(X4 Xx0)
% 51.33/51.55 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 51.33/51.55 Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 51.33/51.55 Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 51.51/51.72 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 51.51/51.72 Found x2:(X4 Xx0)
% 51.51/51.72 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 51.51/51.72 Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 51.51/51.72 Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 51.51/51.72 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 51.51/51.72 Found x2:(X4 Xx0)
% 51.51/51.72 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 51.51/51.72 Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 51.51/51.72 Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 51.51/51.72 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 51.51/51.72 Found x2:(X4 Xx0)
% 51.51/51.72 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 51.51/51.72 Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 51.51/51.72 Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 51.51/51.72 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 51.51/51.72 Found x2:(X4 Xx0)
% 51.51/51.72 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 51.51/51.72 Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 51.51/51.72 Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 51.51/51.72 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 51.51/51.72 Found x2:(X4 Xx0)
% 51.51/51.72 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 51.51/51.72 Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 51.51/51.72 Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 51.51/51.72 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 51.51/51.72 Found x2:(X4 Xx0)
% 51.51/51.72 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 51.51/51.72 Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 51.51/51.72 Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 51.51/51.72 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 51.51/51.72 Found x2:(X4 Xx0)
% 51.51/51.72 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 51.61/51.80 Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 51.61/51.80 Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 51.61/51.80 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 51.61/51.80 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 51.61/51.80 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 51.61/51.80 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 51.61/51.80 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 51.61/51.80 Found (fun (x4:(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)))
% 51.61/51.80 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 51.61/51.80 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 51.61/51.80 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 51.61/51.80 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 51.61/51.80 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 51.61/51.80 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 51.61/51.80 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 51.61/51.80 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 51.61/51.80 Found (fun (x4:(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)))
% 51.61/51.80 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 51.61/51.80 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 51.61/51.80 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 51.61/51.80 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 51.61/51.80 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 51.61/51.80 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 51.61/51.80 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 51.61/51.80 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 51.61/51.80 Found (fun (x4:(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)))
% 51.61/51.80 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 51.61/51.80 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 51.61/51.80 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 51.61/51.80 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 51.61/51.80 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 51.81/52.03 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 51.81/52.03 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 51.81/52.03 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 51.81/52.03 Found (fun (x4:(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)))
% 51.81/52.03 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 51.81/52.03 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 51.81/52.03 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 51.81/52.03 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 51.81/52.03 Found x4:(X4 Xx0)
% 51.81/52.03 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 51.81/52.03 Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 51.81/52.03 Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 51.81/52.03 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 51.81/52.03 Found x4:(X4 Xx0)
% 51.81/52.03 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 51.81/52.03 Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 51.81/52.03 Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 51.81/52.03 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 51.81/52.03 Found x4:(X4 Xx0)
% 51.81/52.03 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 51.81/52.03 Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 51.81/52.03 Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 51.81/52.03 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 51.81/52.03 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 51.81/52.03 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 51.81/52.03 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 51.81/52.03 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 51.81/52.03 Found (fun (x4:(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)))
% 51.81/52.03 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 51.81/52.03 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 51.81/52.03 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 51.81/52.03 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 51.91/52.09 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 51.91/52.09 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 51.91/52.09 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 51.91/52.09 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 51.91/52.09 Found (fun (x4:(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)))
% 51.91/52.09 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 51.91/52.09 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 51.91/52.09 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 51.91/52.09 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 51.91/52.09 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 51.91/52.09 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 51.91/52.09 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 51.91/52.09 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 51.91/52.09 Found (fun (x4:(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)))
% 51.91/52.09 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 51.91/52.09 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 51.91/52.09 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 51.91/52.09 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 51.91/52.09 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 51.91/52.09 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 51.91/52.09 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 51.91/52.09 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 51.91/52.09 Found (fun (x4:(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)))
% 51.91/52.09 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 51.91/52.09 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 51.91/52.09 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 51.91/52.09 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 51.91/52.09 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 51.91/52.09 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 51.91/52.09 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 51.91/52.09 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 51.91/52.09 Found (fun (x4:(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)))
% 51.91/52.09 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 51.94/52.13 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 51.94/52.13 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 51.94/52.13 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 51.94/52.13 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 51.94/52.13 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 51.94/52.13 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 51.94/52.13 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 51.94/52.13 Found (fun (x4:(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)))
% 51.94/52.13 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 51.94/52.13 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 51.94/52.13 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 51.94/52.13 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 51.94/52.13 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 51.94/52.13 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 51.94/52.13 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 51.94/52.13 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 51.94/52.13 Found (fun (x4:(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)))
% 51.94/52.13 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 51.94/52.13 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 51.94/52.13 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 51.94/52.13 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 51.94/52.13 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 51.94/52.13 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 51.94/52.13 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 51.94/52.13 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 51.94/52.13 Found (fun (x4:(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)))
% 51.94/52.13 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 51.94/52.13 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 51.94/52.13 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 51.94/52.13 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 52.34/52.59 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 52.34/52.59 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 52.34/52.59 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 52.34/52.59 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 52.34/52.59 Found (fun (x4:(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)))
% 52.34/52.59 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 52.34/52.59 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 52.34/52.59 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 52.34/52.59 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 52.34/52.59 Found x4:(X4 Xx0)
% 52.34/52.59 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 52.34/52.59 Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 52.34/52.59 Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 52.34/52.59 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 52.34/52.59 Found x4:(X4 Xx0)
% 52.34/52.59 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 52.34/52.59 Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 52.34/52.59 Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 52.34/52.59 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 52.34/52.59 Found x4:(X4 Xx0)
% 52.34/52.59 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 52.34/52.59 Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 52.34/52.59 Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 52.34/52.59 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 52.34/52.59 Found x4:(X4 Xx0)
% 52.34/52.59 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 52.34/52.59 Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 52.34/52.59 Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 52.34/52.59 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 52.34/52.59 Found x2:(X4 Xx0)
% 52.34/52.59 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 52.34/52.59 Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 52.51/52.73 Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 52.51/52.73 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 52.51/52.73 Found x2:(X4 Xx0)
% 52.51/52.73 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 52.51/52.73 Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 52.51/52.73 Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 52.51/52.73 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 52.51/52.73 Found x2:(X4 Xx0)
% 52.51/52.73 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 52.51/52.73 Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 52.51/52.73 Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 52.51/52.73 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 52.51/52.73 Found x2:(X4 Xx0)
% 52.51/52.73 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 52.51/52.73 Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 52.51/52.73 Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 52.51/52.73 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 52.51/52.73 Found x2:(X4 Xx0)
% 52.51/52.73 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 52.51/52.73 Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 52.51/52.73 Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 52.51/52.73 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 52.51/52.73 Found x2:(X4 Xx0)
% 52.51/52.73 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 52.51/52.73 Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 52.51/52.73 Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 52.51/52.73 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 52.51/52.73 Found x2:(X4 Xx0)
% 52.51/52.73 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 52.51/52.73 Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 52.51/52.73 Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 52.51/52.73 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 52.95/53.21 Found x2:(X4 Xx0)
% 52.95/53.21 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 52.95/53.21 Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 52.95/53.21 Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 52.95/53.21 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 52.95/53.21 Found x2:(X4 Xx0)
% 52.95/53.21 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 52.95/53.21 Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 52.95/53.21 Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 52.95/53.21 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 52.95/53.21 Found x2:(X4 Xx0)
% 52.95/53.21 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 52.95/53.21 Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 52.95/53.21 Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 52.95/53.21 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 52.95/53.21 Found x4:(X4 Xx0)
% 52.95/53.21 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 52.95/53.21 Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 52.95/53.21 Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 52.95/53.21 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 52.95/53.21 Found x6:(X4 Xx0)
% 52.95/53.21 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 52.95/53.21 Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 52.95/53.21 Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 52.95/53.21 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 52.95/53.21 Found x400:=(x40 x5):((cK x2) Xx)
% 52.95/53.21 Found (x40 x5) as proof of ((cK X4) Xx)
% 52.95/53.21 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 52.95/53.21 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 52.95/53.21 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 52.95/53.21 Found x6:(X4 Xx0)
% 52.95/53.21 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 52.95/53.21 Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 52.95/53.21 Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 52.95/53.21 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 52.95/53.21 Found x400:=(x40 x5):((cK x2) Xx)
% 52.95/53.21 Found (x40 x5) as proof of ((cK X4) Xx)
% 52.95/53.21 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 52.95/53.21 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 53.35/53.57 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 53.35/53.57 Found x6:(X4 Xx0)
% 53.35/53.57 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 53.35/53.57 Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 53.35/53.57 Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 53.35/53.57 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 53.35/53.57 Found x400:=(x40 x5):((cK x2) Xx)
% 53.35/53.57 Found (x40 x5) as proof of ((cK X4) Xx)
% 53.35/53.57 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 53.35/53.57 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 53.35/53.57 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 53.35/53.57 Found x6:(X4 Xx0)
% 53.35/53.57 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 53.35/53.57 Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 53.35/53.57 Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 53.35/53.57 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 53.35/53.57 Found x400:=(x40 x5):((cK x2) Xx)
% 53.35/53.57 Found (x40 x5) as proof of ((cK X4) Xx)
% 53.35/53.57 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 53.35/53.57 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 53.35/53.57 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 53.35/53.57 Found x4:(X4 Xx0)
% 53.35/53.57 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 53.35/53.57 Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 53.35/53.57 Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 53.35/53.57 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 53.35/53.57 Found x4:(X4 Xx0)
% 53.35/53.57 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 53.35/53.57 Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 53.35/53.57 Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 53.35/53.57 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 53.35/53.57 Found x2:(X4 Xx0)
% 53.35/53.57 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 53.35/53.57 Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 53.35/53.57 Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 53.35/53.57 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 53.35/53.57 Found x2:(X4 Xx0)
% 53.35/53.57 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 53.35/53.57 Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 53.35/53.57 Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 53.35/53.57 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 53.79/54.00 Found x4:(X4 Xx0)
% 53.79/54.00 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 53.79/54.00 Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 53.79/54.00 Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 53.79/54.00 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 53.79/54.00 Found x6:(X4 Xx0)
% 53.79/54.00 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 53.79/54.00 Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 53.79/54.00 Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 53.79/54.00 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 53.79/54.00 Found x400:=(x40 x5):((cK x2) Xx)
% 53.79/54.00 Found (x40 x5) as proof of ((cK X4) Xx)
% 53.79/54.00 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 53.79/54.00 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 53.79/54.00 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 53.79/54.00 Found x2:(X4 Xx0)
% 53.79/54.00 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 53.79/54.00 Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 53.79/54.00 Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 53.79/54.00 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 53.79/54.00 Found x2:(X4 Xx0)
% 53.79/54.00 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 53.79/54.00 Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 53.79/54.00 Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 53.79/54.00 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 53.79/54.00 Found x4:(X4 Xx0)
% 53.79/54.00 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 53.79/54.00 Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 53.79/54.00 Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 53.79/54.00 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 53.79/54.00 Found x4:(X4 Xx0)
% 53.79/54.00 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 53.79/54.00 Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 53.79/54.00 Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 53.79/54.00 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 53.79/54.00 Found x2:(X4 Xx0)
% 53.79/54.00 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 54.24/54.44 Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 54.24/54.44 Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 54.24/54.44 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 54.24/54.44 Found x4:(X4 Xx0)
% 54.24/54.44 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 54.24/54.44 Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 54.24/54.44 Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 54.24/54.44 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 54.24/54.44 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 54.24/54.44 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 54.24/54.44 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 54.24/54.44 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 54.24/54.44 Found (fun (x4:(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)))
% 54.24/54.44 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 54.24/54.44 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 54.24/54.44 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 54.24/54.44 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 54.24/54.44 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 54.24/54.44 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 54.24/54.44 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 54.24/54.44 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 54.24/54.44 Found (fun (x4:(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)))
% 54.24/54.44 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 54.24/54.44 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 54.24/54.44 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 54.24/54.44 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 54.24/54.44 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 54.24/54.44 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 54.24/54.44 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 54.24/54.44 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 54.24/54.44 Found (fun (x4:(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)))
% 54.24/54.44 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 54.24/54.44 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 54.31/54.54 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 54.31/54.54 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 54.31/54.54 Found x4:(X4 Xx0)
% 54.31/54.54 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 54.31/54.54 Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 54.31/54.54 Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 54.31/54.54 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 54.31/54.54 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 54.31/54.54 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 54.31/54.54 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 54.31/54.54 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 54.31/54.54 Found (fun (x4:(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)))
% 54.31/54.54 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 54.31/54.54 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 54.31/54.54 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 54.31/54.54 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 54.31/54.54 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 54.31/54.54 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 54.31/54.54 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 54.31/54.54 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 54.31/54.54 Found (fun (x4:(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)))
% 54.31/54.54 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 54.31/54.54 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 54.31/54.54 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 54.31/54.54 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 54.31/54.54 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 54.31/54.54 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 54.31/54.54 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 54.31/54.54 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 54.31/54.54 Found (fun (x4:(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)))
% 54.31/54.54 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 54.40/54.59 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 54.40/54.59 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 54.40/54.59 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 54.40/54.59 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 54.40/54.59 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 54.40/54.59 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 54.40/54.59 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 54.40/54.59 Found (fun (x4:(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)))
% 54.40/54.59 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 54.40/54.59 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 54.40/54.59 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 54.40/54.59 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 54.40/54.59 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 54.40/54.59 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 54.40/54.59 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 54.40/54.59 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 54.40/54.59 Found (fun (x4:(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)))
% 54.40/54.59 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 54.40/54.59 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 54.40/54.59 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 54.40/54.59 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 54.40/54.59 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 54.40/54.59 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 54.40/54.59 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 54.40/54.59 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 54.40/54.59 Found (fun (x4:(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)))
% 54.40/54.59 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 54.40/54.59 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 54.40/54.59 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 54.40/54.59 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 54.43/54.70 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 54.43/54.70 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 54.43/54.70 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 54.43/54.70 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 54.43/54.70 Found (fun (x4:(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)))
% 54.43/54.70 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 54.43/54.70 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 54.43/54.70 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 54.43/54.70 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 54.43/54.70 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 54.43/54.70 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 54.43/54.70 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 54.43/54.70 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 54.43/54.70 Found (fun (x4:(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)))
% 54.43/54.70 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 54.43/54.70 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 54.43/54.70 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 54.43/54.70 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 54.43/54.70 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 54.43/54.70 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 54.43/54.70 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 54.43/54.70 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 54.43/54.70 Found (fun (x4:(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)))
% 54.43/54.70 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 54.43/54.70 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 54.43/54.70 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 54.43/54.70 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 54.43/54.70 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 54.43/54.70 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 54.43/54.70 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 54.43/54.70 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 54.43/54.70 Found (fun (x4:(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)))
% 54.60/54.79 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 54.60/54.79 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 54.60/54.79 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 54.60/54.79 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 54.60/54.79 Found x2:(X4 Xx0)
% 54.60/54.79 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 54.60/54.79 Found (fun (x2:(X4 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 54.60/54.79 Found (fun (Xx0:a) (x2:(X4 Xx0))=> x2) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 54.60/54.79 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 54.60/54.79 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 54.60/54.79 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 54.60/54.79 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 54.60/54.79 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 54.60/54.79 Found (fun (x4:(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)))
% 54.60/54.79 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 54.60/54.79 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 54.60/54.79 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 54.60/54.79 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 54.60/54.79 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 54.60/54.79 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 54.60/54.79 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 54.60/54.79 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 54.60/54.79 Found (fun (x4:(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)))
% 54.60/54.79 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 54.60/54.79 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 54.60/54.79 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 54.60/54.79 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 54.60/54.79 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 54.60/54.79 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 54.60/54.79 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 54.60/54.79 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 54.60/54.79 Found (fun (x4:(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)))
% 54.60/54.80 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 54.60/54.80 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 54.60/54.80 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 54.60/54.80 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 54.60/54.80 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 54.60/54.80 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 54.60/54.80 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 54.60/54.80 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 54.60/54.80 Found (fun (x4:(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)))
% 54.60/54.80 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 54.60/54.80 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 54.60/54.80 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 54.60/54.80 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 54.60/54.80 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 54.60/54.80 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 54.60/54.80 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 54.60/54.80 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 54.60/54.80 Found (fun (x4:(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)))
% 54.60/54.80 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 54.60/54.80 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 54.60/54.80 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 54.60/54.80 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 54.60/54.80 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 54.60/54.80 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 54.60/54.80 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 54.60/54.80 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 54.60/54.80 Found (fun (x4:(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)))
% 54.60/54.80 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 54.60/54.80 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 54.60/54.80 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 55.00/55.19 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 55.00/55.19 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 55.00/55.19 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 55.00/55.19 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 55.00/55.19 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 55.00/55.19 Found (fun (x4:(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)))
% 55.00/55.19 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 55.00/55.19 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 55.00/55.19 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 55.00/55.19 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 55.00/55.19 Found x4:(X4 Xx0)
% 55.00/55.19 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 55.00/55.19 Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 55.00/55.19 Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 55.00/55.19 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 55.00/55.19 Found x4:(X4 Xx0)
% 55.00/55.19 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 55.00/55.19 Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 55.00/55.19 Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 55.00/55.19 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 55.00/55.19 Found x4:(X4 Xx0)
% 55.00/55.19 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 55.00/55.19 Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 55.00/55.19 Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 55.00/55.19 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 55.00/55.19 Found x4:(X4 Xx0)
% 55.00/55.19 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 55.00/55.19 Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 55.00/55.19 Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 55.00/55.19 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 55.00/55.19 Found x4:(X4 Xx0)
% 55.00/55.19 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 56.35/56.60 Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 56.35/56.60 Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 56.35/56.60 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 56.35/56.60 Found x4:(X4 Xx0)
% 56.35/56.60 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 56.35/56.60 Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 56.35/56.60 Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 56.35/56.60 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 56.35/56.60 Found x4:(X4 Xx0)
% 56.35/56.60 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 56.35/56.60 Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 56.35/56.60 Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 56.35/56.60 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 56.35/56.60 Found x4:(X4 Xx0)
% 56.35/56.60 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 56.35/56.60 Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 56.35/56.60 Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 56.35/56.60 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 56.35/56.60 Found x4:(X4 Xx0)
% 56.35/56.60 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 56.35/56.60 Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 56.35/56.60 Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 56.35/56.60 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 56.35/56.60 Found x4:(X4 Xx0)
% 56.35/56.60 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 56.35/56.60 Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 56.35/56.60 Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 56.35/56.60 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 56.35/56.60 Found x6:(X4 Xx0)
% 56.35/56.60 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 56.35/56.60 Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 56.35/56.60 Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 56.35/56.60 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 56.61/56.82 Found x400:=(x40 x5):((cK x2) Xx)
% 56.61/56.82 Found (x40 x5) as proof of ((cK X4) Xx)
% 56.61/56.82 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 56.61/56.82 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 56.61/56.82 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 56.61/56.82 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 56.61/56.82 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 56.61/56.82 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 56.61/56.82 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 56.61/56.82 Found (fun (x4:(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)))
% 56.61/56.82 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 56.61/56.82 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 56.61/56.82 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 56.61/56.82 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 56.61/56.82 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 56.61/56.82 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 56.61/56.82 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 56.61/56.82 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 56.61/56.82 Found (fun (x4:(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)))
% 56.61/56.82 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 56.61/56.82 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 56.61/56.82 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 56.61/56.82 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 56.61/56.82 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 56.61/56.82 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 56.61/56.82 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 56.61/56.82 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 56.61/56.82 Found (fun (x4:(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)))
% 56.61/56.82 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 56.61/56.82 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 56.61/56.82 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 56.61/56.82 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 56.61/56.82 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 56.61/56.82 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 56.61/56.82 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 56.61/56.82 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 56.75/56.95 Found (fun (x4:(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)))
% 56.75/56.95 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 56.75/56.95 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 56.75/56.95 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 56.75/56.95 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 56.75/56.95 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 56.75/56.95 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 56.75/56.95 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 56.75/56.95 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 56.75/56.95 Found (fun (x4:(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)))
% 56.75/56.95 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 56.75/56.95 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 56.75/56.95 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 56.75/56.95 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 56.75/56.95 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 56.75/56.95 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 56.75/56.95 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 56.75/56.95 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 56.75/56.95 Found (fun (x4:(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)))
% 56.75/56.95 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 56.75/56.95 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 56.75/56.95 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 56.75/56.95 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 56.75/56.95 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 56.75/56.95 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 56.75/56.95 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 56.75/56.95 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 56.75/56.95 Found (fun (x4:(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)))
% 56.75/56.95 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 56.75/56.95 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 56.75/56.95 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 56.75/56.97 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 56.75/56.97 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 56.75/56.97 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 56.75/56.97 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 56.75/56.97 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 56.75/56.97 Found (fun (x4:(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)))
% 56.75/56.97 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 56.75/56.97 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 56.75/56.97 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 56.75/56.97 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 56.75/56.97 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 56.75/56.97 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 56.75/56.97 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 56.75/56.97 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 56.75/56.97 Found (fun (x4:(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)))
% 56.75/56.97 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 56.75/56.97 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 56.75/56.97 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 56.75/56.97 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 56.75/56.97 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 56.75/56.97 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 56.75/56.97 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 56.75/56.97 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 56.75/56.97 Found (fun (x4:(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)))
% 56.75/56.97 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 56.75/56.97 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 56.75/56.97 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 56.75/56.97 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 56.75/56.97 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 56.75/56.97 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 56.75/56.97 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 56.81/57.03 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 56.81/57.03 Found (fun (x4:(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)))
% 56.81/57.03 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 56.81/57.03 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 56.81/57.03 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 56.81/57.03 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 56.81/57.03 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 56.81/57.03 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 56.81/57.03 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 56.81/57.03 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 56.81/57.03 Found (fun (x4:(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)))
% 56.81/57.03 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 56.81/57.03 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 56.81/57.03 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 56.81/57.03 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 56.81/57.03 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 56.81/57.03 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 56.81/57.03 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 56.81/57.03 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 56.81/57.03 Found (fun (x4:(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)))
% 56.81/57.03 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 56.81/57.03 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 56.81/57.03 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 56.81/57.03 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 56.81/57.03 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 56.81/57.03 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 56.81/57.03 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 56.81/57.03 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 56.81/57.03 Found (fun (x4:(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)))
% 56.81/57.03 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 56.81/57.03 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 56.81/57.03 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 57.05/57.27 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 57.05/57.27 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 57.05/57.27 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 57.05/57.27 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 57.05/57.27 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 57.05/57.27 Found (fun (x4:(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)))
% 57.05/57.27 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 57.05/57.27 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 57.05/57.27 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 57.05/57.27 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 57.05/57.27 Found x4:(X4 Xx0)
% 57.05/57.27 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 57.05/57.27 Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 57.05/57.27 Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 57.05/57.27 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 57.05/57.27 Found x4:(X4 Xx0)
% 57.05/57.27 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 57.05/57.27 Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 57.05/57.27 Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 57.05/57.27 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 57.05/57.27 Found x4:(X4 Xx0)
% 57.05/57.27 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 57.05/57.27 Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 57.05/57.27 Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 57.05/57.27 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 57.05/57.27 Found x4:(X4 Xx0)
% 57.05/57.27 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 57.05/57.27 Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 57.05/57.27 Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 57.05/57.27 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 58.14/58.39 Found x4:(X4 Xx0)
% 58.14/58.39 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 58.14/58.39 Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 58.14/58.39 Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 58.14/58.39 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 58.14/58.39 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 58.14/58.39 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 58.14/58.39 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 58.14/58.39 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 58.14/58.39 Found (fun (x4:(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)))
% 58.14/58.39 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 58.14/58.39 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 58.14/58.39 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 58.14/58.39 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 58.14/58.39 Found x4:(X4 Xx0)
% 58.14/58.39 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 58.14/58.39 Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 58.14/58.39 Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 58.14/58.39 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 58.14/58.39 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 58.14/58.39 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 58.14/58.39 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 58.14/58.39 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 58.14/58.39 Found (fun (x4:(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)))
% 58.14/58.39 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 58.14/58.39 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 58.14/58.39 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 58.14/58.39 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 58.14/58.39 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 58.14/58.39 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 58.14/58.39 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 58.14/58.39 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 58.14/58.39 Found (fun (x4:(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)))
% 58.24/58.44 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 58.24/58.44 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 58.24/58.44 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 58.24/58.44 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 58.24/58.44 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 58.24/58.44 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 58.24/58.44 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 58.24/58.44 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 58.24/58.44 Found (fun (x4:(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)))
% 58.24/58.44 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 58.24/58.44 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 58.24/58.44 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 58.24/58.44 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 58.24/58.44 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 58.24/58.44 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 58.24/58.44 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 58.24/58.44 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 58.24/58.44 Found (fun (x4:(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)))
% 58.24/58.44 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 58.24/58.44 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 58.24/58.44 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 58.24/58.44 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 58.24/58.44 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 58.24/58.44 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 58.24/58.44 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 58.24/58.44 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 58.24/58.44 Found (fun (x4:(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)))
% 58.24/58.44 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 58.24/58.44 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 58.24/58.44 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 58.24/58.44 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 63.85/64.04 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 63.85/64.04 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 63.85/64.04 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 63.85/64.04 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 63.85/64.04 Found (fun (x4:(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)))
% 63.85/64.04 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 63.85/64.04 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 63.85/64.04 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 63.85/64.04 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 63.85/64.04 Found x6:(X4 Xx0)
% 63.85/64.04 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 63.85/64.04 Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 63.85/64.04 Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 63.85/64.04 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 63.85/64.04 Found x400:=(x40 x5):((cK x1) Xx)
% 63.85/64.04 Found (x40 x5) as proof of ((cK X4) Xx)
% 63.85/64.04 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 63.85/64.04 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 63.85/64.04 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 63.85/64.04 Found x6:(X4 Xx0)
% 63.85/64.04 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 63.85/64.04 Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 63.85/64.04 Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 63.85/64.04 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 63.85/64.04 Found x400:=(x40 x5):((cK x2) Xx)
% 63.85/64.04 Found (x40 x5) as proof of ((cK X4) Xx)
% 63.85/64.04 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 63.85/64.04 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 63.85/64.04 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 63.85/64.04 Found x4:(X4 Xx0)
% 63.85/64.04 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 63.85/64.04 Found (fun (x4:(X4 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 63.85/64.04 Found (fun (Xx0:a) (x4:(X4 Xx0))=> x4) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 63.85/64.04 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 63.85/64.04 Found x6:(X4 Xx0)
% 63.85/64.04 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 63.85/64.04 Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 63.85/64.04 Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 66.10/66.35 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 66.10/66.35 Found x400:=(x40 x5):((cK x1) Xx)
% 66.10/66.35 Found (x40 x5) as proof of ((cK X4) Xx)
% 66.10/66.35 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 66.10/66.35 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 66.10/66.35 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 66.10/66.35 Found x6:(X4 Xx0)
% 66.10/66.35 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 66.10/66.35 Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 66.10/66.35 Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 66.10/66.35 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 66.10/66.35 Found x400:=(x40 x5):((cK x2) Xx)
% 66.10/66.35 Found (x40 x5) as proof of ((cK X4) Xx)
% 66.10/66.35 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 66.10/66.35 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 66.10/66.35 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 66.10/66.35 Found x6:(X4 Xx0)
% 66.10/66.35 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 66.10/66.35 Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 66.10/66.35 Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 66.10/66.35 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 66.10/66.35 Found x400:=(x40 x5):((cK x2) Xx)
% 66.10/66.35 Found (x40 x5) as proof of ((cK X4) Xx)
% 66.10/66.35 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 66.10/66.35 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 66.10/66.35 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 66.10/66.35 Found x6:(X4 Xx0)
% 66.10/66.35 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 66.10/66.35 Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 66.10/66.35 Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 66.10/66.35 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 66.10/66.35 Found x400:=(x40 x5):((cK x1) Xx)
% 66.10/66.35 Found (x40 x5) as proof of ((cK X4) Xx)
% 66.10/66.35 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 66.10/66.35 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 66.10/66.35 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 66.10/66.35 Found x6:(X4 Xx0)
% 66.10/66.35 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 66.10/66.35 Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 66.10/66.35 Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 66.10/66.35 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 66.10/66.35 Found x400:=(x40 x5):((cK x2) Xx)
% 66.10/66.35 Found (x40 x5) as proof of ((cK X4) Xx)
% 66.10/66.35 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 66.10/66.35 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 66.10/66.35 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 66.10/66.35 Found x6:(X4 Xx0)
% 66.10/66.35 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 66.10/66.35 Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 66.10/66.35 Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 66.67/66.94 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 66.67/66.94 Found x400:=(x40 x5):((cK x1) Xx)
% 66.67/66.94 Found (x40 x5) as proof of ((cK X4) Xx)
% 66.67/66.94 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 66.67/66.94 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 66.67/66.94 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 66.67/66.94 Found x6:(X4 Xx0)
% 66.67/66.94 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 66.67/66.94 Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 66.67/66.94 Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 66.67/66.94 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 66.67/66.94 Found x400:=(x40 x5):((cK x2) Xx)
% 66.67/66.94 Found (x40 x5) as proof of ((cK X4) Xx)
% 66.67/66.94 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 66.67/66.94 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 66.67/66.94 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 66.67/66.94 Found x6:(X4 Xx0)
% 66.67/66.94 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 66.67/66.94 Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 66.67/66.94 Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 66.67/66.94 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 66.67/66.94 Found x400:=(x40 x5):((cK x2) Xx)
% 66.67/66.94 Found (x40 x5) as proof of ((cK X4) Xx)
% 66.67/66.94 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 66.67/66.94 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 66.67/66.94 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 66.67/66.94 Found x6:(X4 Xx0)
% 66.67/66.94 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 66.67/66.94 Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 66.67/66.94 Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 66.67/66.94 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 66.67/66.94 Found x400:=(x40 x5):((cK x2) Xx)
% 66.67/66.94 Found (x40 x5) as proof of ((cK X4) Xx)
% 66.67/66.94 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 66.67/66.94 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 66.67/66.94 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 66.67/66.94 Found x6:(X4 Xx0)
% 66.67/66.94 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 66.67/66.94 Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 66.67/66.94 Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 66.67/66.94 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 66.67/66.94 Found x400:=(x40 x5):((cK x1) Xx)
% 66.67/66.94 Found (x40 x5) as proof of ((cK X4) Xx)
% 66.67/66.94 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 66.67/66.94 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 66.67/66.94 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 66.67/66.94 Found x6:(X4 Xx0)
% 66.67/66.94 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 66.67/66.94 Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 66.67/66.94 Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 67.30/67.55 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 67.30/67.55 Found x400:=(x40 x5):((cK x2) Xx)
% 67.30/67.55 Found (x40 x5) as proof of ((cK X4) Xx)
% 67.30/67.55 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 67.30/67.55 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 67.30/67.55 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 67.30/67.55 Found x6:(X4 Xx0)
% 67.30/67.55 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 67.30/67.55 Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 67.30/67.55 Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 67.30/67.55 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 67.30/67.55 Found x400:=(x40 x5):((cK x2) Xx)
% 67.30/67.55 Found (x40 x5) as proof of ((cK X4) Xx)
% 67.30/67.55 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 67.30/67.55 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 67.30/67.55 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 67.30/67.55 Found x6:(X4 Xx0)
% 67.30/67.55 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 67.30/67.55 Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 67.30/67.55 Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 67.30/67.55 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 67.30/67.55 Found x400:=(x40 x5):((cK x2) Xx)
% 67.30/67.55 Found (x40 x5) as proof of ((cK X4) Xx)
% 67.30/67.55 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 67.30/67.55 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 67.30/67.55 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 67.30/67.55 Found x6:(X4 Xx0)
% 67.30/67.55 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 67.30/67.55 Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 67.30/67.55 Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 67.30/67.55 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 67.30/67.55 Found x400:=(x40 x5):((cK x2) Xx)
% 67.30/67.55 Found (x40 x5) as proof of ((cK X4) Xx)
% 67.30/67.55 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 67.30/67.55 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 67.30/67.55 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 67.30/67.55 Found x6:(X4 Xx0)
% 67.30/67.55 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 67.30/67.55 Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 67.30/67.55 Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 67.30/67.55 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 67.30/67.55 Found x400:=(x40 x5):((cK x2) Xx)
% 67.30/67.55 Found (x40 x5) as proof of ((cK X4) Xx)
% 67.30/67.55 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 67.30/67.55 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 67.30/67.55 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 67.30/67.55 Found x6:(X4 Xx0)
% 67.30/67.55 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 67.30/67.55 Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 67.30/67.55 Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 67.58/67.82 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 67.58/67.82 Found x400:=(x40 x5):((cK x2) Xx)
% 67.58/67.82 Found (x40 x5) as proof of ((cK X4) Xx)
% 67.58/67.82 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 67.58/67.82 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 67.58/67.82 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 67.58/67.82 Found x6:(X4 Xx0)
% 67.58/67.82 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 67.58/67.82 Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 67.58/67.82 Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 67.58/67.82 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 67.58/67.82 Found x400:=(x40 x5):((cK x2) Xx)
% 67.58/67.82 Found (x40 x5) as proof of ((cK X4) Xx)
% 67.58/67.82 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 67.58/67.82 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 67.58/67.82 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 67.58/67.82 Found x6:(X4 Xx0)
% 67.58/67.82 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 67.58/67.82 Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 67.58/67.82 Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 67.58/67.82 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 67.58/67.82 Found x400:=(x40 x5):((cK x2) Xx)
% 67.58/67.82 Found (x40 x5) as proof of ((cK X4) Xx)
% 67.58/67.82 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 67.58/67.82 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 67.58/67.82 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 67.58/67.82 Found x6:(X4 Xx0)
% 67.58/67.82 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 67.58/67.82 Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 67.58/67.82 Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 67.58/67.82 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 67.58/67.82 Found x400:=(x40 x5):((cK x2) Xx)
% 67.58/67.82 Found (x40 x5) as proof of ((cK X4) Xx)
% 67.58/67.82 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 67.58/67.82 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 67.58/67.82 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 67.58/67.82 Found x6:(X4 Xx0)
% 67.58/67.82 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 67.58/67.82 Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 67.58/67.82 Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 67.58/67.82 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 67.58/67.82 Found x400:=(x40 x5):((cK x2) Xx)
% 67.58/67.82 Found (x40 x5) as proof of ((cK X4) Xx)
% 67.58/67.82 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 67.58/67.82 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 67.58/67.82 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 67.58/67.82 Found x6:(X4 Xx0)
% 67.58/67.82 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 67.58/67.82 Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 68.28/68.48 Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 68.28/68.48 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 68.28/68.48 Found x400:=(x40 x5):((cK x2) Xx)
% 68.28/68.48 Found (x40 x5) as proof of ((cK X4) Xx)
% 68.28/68.48 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 68.28/68.48 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 68.28/68.48 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 68.28/68.48 Found x6:(X4 Xx0)
% 68.28/68.48 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 68.28/68.48 Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 68.28/68.48 Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 68.28/68.48 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 68.28/68.48 Found x400:=(x40 x5):((cK x2) Xx)
% 68.28/68.48 Found (x40 x5) as proof of ((cK X4) Xx)
% 68.28/68.48 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 68.28/68.48 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 68.28/68.48 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 68.28/68.48 Found x40:=(x4 Xx):((x1 Xx)->((cK x1) Xx))
% 68.28/68.48 Found (x4 Xx) as proof of ((x1 Xx)->((cK X4) Xx))
% 68.28/68.48 Found (x4 Xx) as proof of ((x1 Xx)->((cK X4) Xx))
% 68.28/68.48 Found (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx)) as proof of ((x1 Xx)->((cK X4) Xx))
% 68.28/68.48 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)))
% 68.28/68.48 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 68.28/68.48 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 68.28/68.48 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)
% 68.28/68.48 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)
% 68.28/68.48 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 68.28/68.48 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 68.28/68.48 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 68.28/68.48 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 68.28/68.48 Found (fun (x4:(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)))
% 68.28/68.48 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 68.28/68.48 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 68.28/68.48 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 68.28/68.48 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)
% 68.28/68.48 Found x6:(X4 Xx0)
% 68.28/68.48 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 68.28/68.48 Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 68.44/68.64 Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 68.44/68.64 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 68.44/68.64 Found x400:=(x40 x5):((cK x2) Xx)
% 68.44/68.64 Found (x40 x5) as proof of ((cK X4) Xx)
% 68.44/68.64 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 68.44/68.64 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 68.44/68.64 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 68.44/68.64 Found x6:(X4 Xx0)
% 68.44/68.64 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 68.44/68.64 Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 68.44/68.64 Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 68.44/68.64 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 68.44/68.64 Found x400:=(x40 x5):((cK x2) Xx)
% 68.44/68.64 Found (x40 x5) as proof of ((cK X4) Xx)
% 68.44/68.64 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 68.44/68.64 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 68.44/68.64 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 68.44/68.64 Found x6:(X4 Xx0)
% 68.44/68.64 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 68.44/68.64 Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 68.44/68.64 Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 68.44/68.64 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 68.44/68.64 Found x400:=(x40 x5):((cK x2) Xx)
% 68.44/68.64 Found (x40 x5) as proof of ((cK X4) Xx)
% 68.44/68.64 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 68.44/68.64 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 68.44/68.64 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 68.44/68.64 Found x6:(X4 Xx0)
% 68.44/68.64 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 68.44/68.64 Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 68.44/68.64 Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 68.44/68.64 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 68.44/68.64 Found x400:=(x40 x5):((cK x2) Xx)
% 68.44/68.64 Found (x40 x5) as proof of ((cK X4) Xx)
% 68.44/68.64 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 68.44/68.64 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 68.44/68.64 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 68.44/68.64 Found x6:(X4 Xx0)
% 68.44/68.64 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 68.44/68.64 Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 68.44/68.64 Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 68.44/68.64 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 68.44/68.64 Found x400:=(x40 x5):((cK x2) Xx)
% 68.44/68.64 Found (x40 x5) as proof of ((cK X4) Xx)
% 68.44/68.64 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 68.44/68.64 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 68.44/68.64 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 68.44/68.64 Found x6:(X4 Xx0)
% 68.44/68.64 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 68.44/68.64 Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 68.95/69.14 Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 68.95/69.14 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 68.95/69.14 Found x400:=(x40 x5):((cK x2) Xx)
% 68.95/69.14 Found (x40 x5) as proof of ((cK X4) Xx)
% 68.95/69.14 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 68.95/69.14 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 68.95/69.14 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 68.95/69.14 Found x6:(X4 Xx0)
% 68.95/69.14 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 68.95/69.14 Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 68.95/69.14 Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 68.95/69.14 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 68.95/69.14 Found x400:=(x40 x5):((cK x2) Xx)
% 68.95/69.14 Found (x40 x5) as proof of ((cK X4) Xx)
% 68.95/69.14 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 68.95/69.14 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 68.95/69.14 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 68.95/69.14 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 68.95/69.14 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 68.95/69.14 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 68.95/69.14 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 68.95/69.14 Found (fun (x4:(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)))
% 68.95/69.14 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 68.95/69.14 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 68.95/69.14 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 68.95/69.14 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)
% 68.95/69.14 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 68.95/69.14 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 68.95/69.14 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 68.95/69.14 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 68.95/69.14 Found (fun (x4:(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)))
% 68.95/69.14 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 68.95/69.14 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 68.95/69.14 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 68.95/69.14 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)
% 68.95/69.14 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 68.95/69.14 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 68.95/69.14 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 68.95/69.14 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 69.19/69.46 Found (fun (x4:(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)))
% 69.19/69.46 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 69.19/69.46 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 69.19/69.46 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 69.19/69.46 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)
% 69.19/69.46 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 69.19/69.46 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 69.19/69.46 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 69.19/69.46 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 69.19/69.46 Found (fun (x4:(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)))
% 69.19/69.46 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 69.19/69.46 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 69.19/69.46 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 69.19/69.46 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)
% 69.19/69.46 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 69.19/69.46 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 69.19/69.46 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 69.19/69.46 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 69.19/69.46 Found (fun (x4:(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)))
% 69.19/69.46 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 69.19/69.46 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 69.19/69.46 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 69.19/69.46 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)
% 69.19/69.46 Found x6:(X4 Xx0)
% 69.19/69.46 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 69.19/69.46 Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 69.19/69.46 Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 69.19/69.46 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 69.77/70.00 Found x400:=(x40 x5):((cK x2) Xx)
% 69.77/70.00 Found (x40 x5) as proof of ((cK X4) Xx)
% 69.77/70.00 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 69.77/70.00 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 69.77/70.00 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 69.77/70.00 Found x6:(X4 Xx0)
% 69.77/70.00 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 69.77/70.00 Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 69.77/70.00 Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 69.77/70.00 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 69.77/70.00 Found x400:=(x40 x5):((cK x2) Xx)
% 69.77/70.00 Found (x40 x5) as proof of ((cK X4) Xx)
% 69.77/70.00 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 69.77/70.00 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 69.77/70.00 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 69.77/70.00 Found x6:(X4 Xx0)
% 69.77/70.00 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 69.77/70.00 Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 69.77/70.00 Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 69.77/70.00 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 69.77/70.00 Found x400:=(x40 x5):((cK x2) Xx)
% 69.77/70.00 Found (x40 x5) as proof of ((cK X4) Xx)
% 69.77/70.00 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 69.77/70.00 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 69.77/70.00 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 69.77/70.00 Found x6:(X4 Xx0)
% 69.77/70.00 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 69.77/70.00 Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 69.77/70.00 Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 69.77/70.00 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 69.77/70.00 Found x400:=(x40 x5):((cK x2) Xx)
% 69.77/70.00 Found (x40 x5) as proof of ((cK X4) Xx)
% 69.77/70.00 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 69.77/70.00 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 69.77/70.00 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 69.77/70.00 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 69.77/70.00 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 69.77/70.00 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 69.77/70.00 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 69.77/70.00 Found (fun (x4:(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)))
% 69.77/70.00 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 69.77/70.00 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 69.77/70.00 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 69.77/70.00 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)
% 69.77/70.00 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 69.77/70.01 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 69.77/70.01 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 69.77/70.01 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 69.77/70.01 Found (fun (x4:(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)))
% 69.77/70.01 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 69.77/70.01 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 69.77/70.01 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 69.77/70.01 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)
% 69.77/70.01 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 69.77/70.01 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 69.77/70.01 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 69.77/70.01 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 69.77/70.01 Found (fun (x4:(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)))
% 69.77/70.01 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 69.77/70.01 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 69.77/70.01 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 69.77/70.01 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)
% 69.77/70.01 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 69.77/70.01 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 69.77/70.01 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 69.77/70.01 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 69.77/70.01 Found (fun (x4:(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)))
% 69.77/70.01 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 69.77/70.01 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 69.77/70.01 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 69.77/70.01 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)
% 69.77/70.01 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 69.77/70.01 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 69.77/70.01 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 69.77/70.01 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 69.77/70.01 Found (fun (x4:(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)))
% 69.77/70.02 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 69.77/70.02 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 69.77/70.02 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 69.77/70.02 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)
% 69.77/70.02 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 69.77/70.02 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 69.77/70.02 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 69.77/70.02 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 69.77/70.02 Found (fun (x4:(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)))
% 69.77/70.02 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 69.77/70.02 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 69.77/70.02 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 69.77/70.02 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)
% 69.77/70.02 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 69.77/70.02 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 69.77/70.02 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 69.77/70.02 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 69.77/70.02 Found (fun (x4:(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)))
% 69.77/70.02 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 69.77/70.02 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 69.77/70.02 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 69.77/70.02 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)
% 69.77/70.02 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 69.77/70.02 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 69.77/70.02 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 69.77/70.02 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 69.77/70.02 Found (fun (x4:(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)))
% 69.77/70.02 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 69.77/70.02 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 69.77/70.02 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 70.35/70.56 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)
% 70.35/70.56 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 70.35/70.56 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 70.35/70.56 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 70.35/70.56 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 70.35/70.56 Found (fun (x4:(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)))
% 70.35/70.56 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 70.35/70.56 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 70.35/70.56 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 70.35/70.56 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)
% 70.35/70.56 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 70.35/70.56 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 70.35/70.56 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 70.35/70.56 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 70.35/70.56 Found (fun (x4:(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)))
% 70.35/70.56 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 70.35/70.56 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 70.35/70.56 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 70.35/70.56 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)
% 70.35/70.56 Found x6:(X4 Xx0)
% 70.35/70.56 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 70.35/70.56 Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 70.35/70.56 Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 70.35/70.56 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 70.35/70.56 Found x300:=(x30 x4):((cK x1) Xx)
% 70.35/70.56 Found (x30 x4) as proof of ((cK X4) Xx)
% 70.35/70.56 Found ((x3 Xx) x4) as proof of ((cK X4) Xx)
% 70.35/70.56 Found ((x3 Xx) x4) as proof of ((cK X4) Xx)
% 70.35/70.56 Found ((x3 Xx) x4) as proof of ((cK X4) Xx)
% 70.35/70.56 Found x6:(X4 Xx0)
% 70.35/70.56 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 70.35/70.56 Found (fun (x6:(X4 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 70.51/70.72 Found (fun (Xx0:a) (x6:(X4 Xx0))=> x6) as proof of ((X4 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 70.51/70.72 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 (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 70.51/70.72 Found x400:=(x40 x5):((cK x2) Xx)
% 70.51/70.72 Found (x40 x5) as proof of ((cK X4) Xx)
% 70.51/70.72 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 70.51/70.72 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 70.51/70.72 Found ((x4 Xx) x5) as proof of ((cK X4) Xx)
% 70.51/70.72 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 70.51/70.72 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 70.51/70.72 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 70.51/70.72 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 70.51/70.72 Found (fun (x4:(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)))
% 70.51/70.72 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 70.51/70.72 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 70.51/70.72 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 70.51/70.72 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)
% 70.51/70.72 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 70.51/70.72 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 70.51/70.72 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 70.51/70.72 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 70.51/70.72 Found (fun (x4:(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)))
% 70.51/70.72 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 70.51/70.72 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 70.51/70.72 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 70.51/70.72 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)
% 70.51/70.72 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 70.51/70.72 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 70.51/70.72 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 70.51/70.72 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 70.51/70.72 Found (fun (x4:(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)))
% 70.51/70.72 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 70.51/70.72 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 70.51/70.72 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 70.51/70.72 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)
% 70.56/70.78 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 70.56/70.78 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 70.56/70.78 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 70.56/70.78 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 70.56/70.78 Found (fun (x4:(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)))
% 70.56/70.78 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 70.56/70.78 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 70.56/70.78 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 70.56/70.78 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)
% 70.56/70.78 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 70.56/70.78 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 70.56/70.78 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 70.56/70.78 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 70.56/70.78 Found (fun (x4:(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)))
% 70.56/70.78 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 70.56/70.78 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 70.56/70.78 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 70.56/70.78 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)
% 70.56/70.78 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 70.56/70.78 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 70.56/70.78 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 70.56/70.78 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 70.56/70.78 Found (fun (x4:(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)))
% 70.56/70.78 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 70.56/70.78 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 70.56/70.78 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 70.56/70.78 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)
% 70.56/70.82 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 70.56/70.82 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 70.56/70.82 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 70.56/70.82 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 70.56/70.82 Found (fun (x4:(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)))
% 70.56/70.82 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 70.56/70.82 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 70.56/70.82 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 70.56/70.82 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)
% 70.56/70.82 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 70.56/70.82 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 70.56/70.82 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 70.56/70.82 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 70.56/70.82 Found (fun (x4:(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)))
% 70.56/70.82 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 70.56/70.82 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 70.56/70.82 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 70.56/70.82 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)
% 70.56/70.82 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 70.56/70.82 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 70.56/70.82 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 70.56/70.82 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 70.56/70.82 Found (fun (x4:(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)))
% 70.56/70.82 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 70.56/70.82 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 70.56/70.82 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 70.56/70.82 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)
% 70.56/70.82 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 70.56/70.82 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 70.56/70.82 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 70.56/70.82 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 70.56/70.82 Found (fun (x4:(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)))
% 71.09/71.31 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 71.09/71.31 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 71.09/71.31 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 71.09/71.31 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)
% 71.09/71.31 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 71.09/71.31 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 71.09/71.31 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 71.09/71.31 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 71.09/71.31 Found (fun (x4:(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)))
% 71.09/71.31 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 71.09/71.31 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 71.09/71.31 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 71.09/71.31 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)
% 71.09/71.31 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 71.09/71.31 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 71.09/71.31 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 71.09/71.31 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 71.09/71.31 Found (fun (x4:(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)))
% 71.09/71.31 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 71.09/71.31 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 71.09/71.31 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 71.09/71.31 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)
% 71.09/71.31 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 71.09/71.31 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 71.09/71.31 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 71.09/71.31 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 71.09/71.31 Found (fun (x4:(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)))
% 71.09/71.31 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 71.09/71.31 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 71.09/71.31 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 71.31/71.50 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)
% 71.31/71.50 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 71.31/71.50 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 71.31/71.50 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 71.31/71.50 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 71.31/71.50 Found (fun (x4:(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)))
% 71.31/71.50 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 71.31/71.50 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 71.31/71.50 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 71.31/71.50 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)
% 71.31/71.50 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 71.31/71.50 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 71.31/71.50 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 71.31/71.50 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 71.31/71.50 Found (fun (x4:(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)))
% 71.31/71.50 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 71.31/71.50 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 71.31/71.50 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 71.31/71.50 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)
% 71.31/71.50 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 71.31/71.50 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 71.31/71.50 Found (x4 Xx) as proof of ((x2 Xx)->((cK X4) Xx))
% 71.31/71.50 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X4) Xx))
% 71.31/71.50 Found (fun (x4:(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)))
% 71.31/71.50 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 71.31/71.50 Found ((and_rect0 ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 71.31/71.50 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X4) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X4) Xx)
% 71.31/71.50 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)
% 91.92/92.16 Found x4:(X5 Xx0)
% 91.92/92.16 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 91.92/92.16 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 91.92/92.16 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 91.92/92.16 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 91.92/92.16 Found x6:(X5 Xx0)
% 91.92/92.16 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 91.92/92.17 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 91.92/92.17 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 91.92/92.17 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 91.92/92.17 Found x400:=(x40 x5):((cK x2) Xx)
% 91.92/92.17 Found (x40 x5) as proof of ((cK X5) Xx)
% 91.92/92.17 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 91.92/92.17 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 91.92/92.17 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 91.92/92.17 Found x4:(X5 Xx0)
% 91.92/92.17 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 91.92/92.17 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 91.92/92.17 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 91.92/92.17 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 91.92/92.17 Found x4:(X5 Xx0)
% 91.92/92.17 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 91.92/92.17 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 91.92/92.17 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 91.92/92.17 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 91.92/92.17 Found x6:(X5 Xx0)
% 91.92/92.17 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 91.92/92.17 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 91.92/92.17 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 91.92/92.17 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 91.92/92.17 Found x400:=(x40 x5):((cK x2) Xx)
% 91.92/92.17 Found (x40 x5) as proof of ((cK X5) Xx)
% 91.92/92.17 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 91.92/92.17 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 91.92/92.17 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 91.92/92.17 Found x6:(X5 Xx0)
% 91.92/92.17 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 91.92/92.17 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 91.92/92.17 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 97.71/97.93 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 97.71/97.93 Found x400:=(x40 x5):((cK x2) Xx)
% 97.71/97.93 Found (x40 x5) as proof of ((cK X5) Xx)
% 97.71/97.93 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 97.71/97.93 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 97.71/97.93 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 97.71/97.93 Found x6:(X5 Xx0)
% 97.71/97.93 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 97.71/97.93 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 97.71/97.93 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 97.71/97.93 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 97.71/97.93 Found x400:=(x40 x5):((cK x2) Xx)
% 97.71/97.93 Found (x40 x5) as proof of ((cK X5) Xx)
% 97.71/97.93 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 97.71/97.93 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 97.71/97.93 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 97.71/97.93 Found x4:(X5 Xx0)
% 97.71/97.93 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 97.71/97.93 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 97.71/97.93 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 97.71/97.93 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 97.71/97.93 Found x4:(X5 Xx0)
% 97.71/97.93 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 97.71/97.93 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 97.71/97.93 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 97.71/97.93 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 97.71/97.93 Found x4:(X5 Xx0)
% 97.71/97.93 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 97.71/97.93 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 97.71/97.93 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 97.71/97.93 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 97.71/97.93 Found x6:(X5 Xx0)
% 97.71/97.93 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 97.71/97.93 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 97.71/97.93 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 97.71/97.93 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 97.71/97.93 Found x400:=(x40 x5):((cK x2) Xx)
% 97.71/97.93 Found (x40 x5) as proof of ((cK X5) Xx)
% 97.71/97.93 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 97.71/97.93 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 97.71/97.93 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 97.71/97.93 Found x6:(X5 Xx0)
% 97.71/97.93 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 98.71/98.95 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 98.71/98.95 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 98.71/98.95 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 98.71/98.95 Found x400:=(x40 x5):((cK x2) Xx)
% 98.71/98.95 Found (x40 x5) as proof of ((cK X5) Xx)
% 98.71/98.95 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 98.71/98.95 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 98.71/98.95 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 98.71/98.95 Found x6:(X5 Xx0)
% 98.71/98.95 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 98.71/98.95 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 98.71/98.95 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 98.71/98.95 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 98.71/98.95 Found x400:=(x40 x5):((cK x2) Xx)
% 98.71/98.95 Found (x40 x5) as proof of ((cK X5) Xx)
% 98.71/98.95 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 98.71/98.95 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 98.71/98.95 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 98.71/98.95 Found x6:(X5 Xx0)
% 98.71/98.95 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 98.71/98.95 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 98.71/98.95 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 98.71/98.95 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 98.71/98.95 Found x400:=(x40 x5):((cK x2) Xx)
% 98.71/98.95 Found (x40 x5) as proof of ((cK X5) Xx)
% 98.71/98.95 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 98.71/98.95 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 98.71/98.95 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 98.71/98.95 Found x6:(X5 Xx0)
% 98.71/98.95 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 98.71/98.95 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 98.71/98.95 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 98.71/98.95 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 98.71/98.95 Found x400:=(x40 x5):((cK x2) Xx)
% 98.71/98.95 Found (x40 x5) as proof of ((cK X5) Xx)
% 98.71/98.95 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 98.71/98.95 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 98.71/98.95 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 98.71/98.95 Found x6:(X5 Xx0)
% 98.71/98.95 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 98.71/98.95 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 98.71/98.95 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 98.71/98.95 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 98.71/98.95 Found x400:=(x40 x5):((cK x2) Xx)
% 98.71/98.95 Found (x40 x5) as proof of ((cK X5) Xx)
% 98.71/98.95 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 98.71/98.95 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 98.71/98.95 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 98.71/98.95 Found x4:(X5 Xx0)
% 102.34/102.61 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 102.34/102.61 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 102.34/102.61 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 102.34/102.61 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 102.34/102.61 Found x4:(X5 Xx0)
% 102.34/102.61 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 102.34/102.61 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 102.34/102.61 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 102.34/102.61 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 102.34/102.61 Found x4:(X5 Xx0)
% 102.34/102.61 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 102.34/102.61 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 102.34/102.61 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 102.34/102.61 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 102.34/102.61 Found x4:(X5 Xx0)
% 102.34/102.61 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 102.34/102.61 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 102.34/102.61 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 102.34/102.61 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 102.34/102.61 Found x4:(X5 Xx0)
% 102.34/102.61 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 102.34/102.61 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 102.34/102.61 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 102.34/102.61 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 102.34/102.61 Found x6:(X5 Xx0)
% 102.34/102.61 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 102.34/102.61 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 102.34/102.61 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 102.34/102.61 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 102.34/102.61 Found x400:=(x40 x5):((cK x2) Xx)
% 102.34/102.61 Found (x40 x5) as proof of ((cK X5) Xx)
% 102.34/102.61 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 102.34/102.61 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 102.34/102.61 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 102.34/102.61 Found x6:(X5 Xx0)
% 102.34/102.61 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 102.34/102.61 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 102.63/102.85 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 102.63/102.85 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 102.63/102.85 Found x400:=(x40 x5):((cK x2) Xx)
% 102.63/102.85 Found (x40 x5) as proof of ((cK X5) Xx)
% 102.63/102.85 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 102.63/102.85 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 102.63/102.85 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 102.63/102.85 Found x6:(X5 Xx0)
% 102.63/102.85 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 102.63/102.85 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 102.63/102.85 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 102.63/102.85 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 102.63/102.85 Found x400:=(x40 x5):((cK x2) Xx)
% 102.63/102.85 Found (x40 x5) as proof of ((cK X5) Xx)
% 102.63/102.85 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 102.63/102.85 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 102.63/102.85 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 102.63/102.85 Found x6:(X5 Xx0)
% 102.63/102.85 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 102.63/102.85 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 102.63/102.85 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 102.63/102.85 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 102.63/102.85 Found x400:=(x40 x5):((cK x2) Xx)
% 102.63/102.85 Found (x40 x5) as proof of ((cK X5) Xx)
% 102.63/102.85 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 102.63/102.85 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 102.63/102.85 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 102.63/102.85 Found x6:(X5 Xx0)
% 102.63/102.85 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 102.63/102.85 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 102.63/102.85 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 102.63/102.85 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 102.63/102.85 Found x400:=(x40 x5):((cK x2) Xx)
% 102.63/102.85 Found (x40 x5) as proof of ((cK X5) Xx)
% 102.63/102.85 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 102.63/102.85 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 102.63/102.85 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 102.63/102.85 Found x6:(X5 Xx0)
% 102.63/102.85 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 102.63/102.85 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 102.63/102.85 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 102.63/102.85 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 102.63/102.85 Found x400:=(x40 x5):((cK x2) Xx)
% 102.63/102.85 Found (x40 x5) as proof of ((cK X5) Xx)
% 102.63/102.85 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 102.63/102.85 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 102.63/102.85 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 102.63/102.85 Found x6:(X5 Xx0)
% 102.63/102.85 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 102.63/102.85 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 103.76/103.97 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 103.76/103.97 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 103.76/103.97 Found x400:=(x40 x5):((cK x2) Xx)
% 103.76/103.97 Found (x40 x5) as proof of ((cK X5) Xx)
% 103.76/103.97 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 103.76/103.97 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 103.76/103.97 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 103.76/103.97 Found x6:(X5 Xx0)
% 103.76/103.97 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 103.76/103.97 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 103.76/103.97 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 103.76/103.97 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 103.76/103.97 Found x400:=(x40 x5):((cK x2) Xx)
% 103.76/103.97 Found (x40 x5) as proof of ((cK X5) Xx)
% 103.76/103.97 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 103.76/103.97 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 103.76/103.97 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 103.76/103.97 Found x6:(X5 Xx0)
% 103.76/103.97 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 103.76/103.97 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 103.76/103.97 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 103.76/103.97 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 103.76/103.97 Found x400:=(x40 x5):((cK x2) Xx)
% 103.76/103.97 Found (x40 x5) as proof of ((cK X5) Xx)
% 103.76/103.97 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 103.76/103.97 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 103.76/103.97 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 103.76/103.97 Found x6:(X5 Xx0)
% 103.76/103.97 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 103.76/103.97 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 103.76/103.97 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 103.76/103.97 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 103.76/103.97 Found x400:=(x40 x5):((cK x2) Xx)
% 103.76/103.97 Found (x40 x5) as proof of ((cK X5) Xx)
% 103.76/103.97 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 103.76/103.97 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 103.76/103.97 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 103.76/103.97 Found x6:(X5 Xx0)
% 103.76/103.97 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 103.76/103.97 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 103.76/103.97 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 103.76/103.97 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 103.76/103.97 Found x400:=(x40 x5):((cK x2) Xx)
% 103.76/103.97 Found (x40 x5) as proof of ((cK X5) Xx)
% 103.76/103.97 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 103.76/103.97 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 103.76/103.97 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 103.76/103.97 Found x4:(X5 Xx0)
% 103.76/103.97 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 105.29/105.56 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 105.29/105.56 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 105.29/105.56 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 105.29/105.56 Found x4:(X5 Xx0)
% 105.29/105.56 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 105.29/105.56 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 105.29/105.56 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 105.29/105.56 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 105.29/105.56 Found x4:(X5 Xx0)
% 105.29/105.56 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 105.29/105.56 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 105.29/105.56 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 105.29/105.56 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 105.29/105.56 Found x4:(X5 Xx0)
% 105.29/105.56 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 105.29/105.56 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 105.29/105.56 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 105.29/105.56 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 105.29/105.56 Found x4:(X5 Xx0)
% 105.29/105.56 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 105.29/105.56 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 105.29/105.56 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 105.29/105.56 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 105.29/105.56 Found x4:(X5 Xx0)
% 105.29/105.56 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 105.29/105.56 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 105.29/105.56 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 105.29/105.56 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 105.29/105.56 Found x4:(X5 Xx0)
% 105.29/105.56 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 105.29/105.56 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 105.29/105.56 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 105.29/105.56 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 106.72/106.94 Found x2:(X5 Xx0)
% 106.72/106.94 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 106.72/106.94 Found (fun (x2:(X5 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 106.72/106.94 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 106.72/106.94 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 106.72/106.94 Found x4:(X5 Xx0)
% 106.72/106.94 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 106.72/106.94 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 106.72/106.94 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 106.72/106.94 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 106.72/106.94 Found x6:(X5 Xx0)
% 106.72/106.94 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 106.72/106.94 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 106.72/106.94 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 106.72/106.94 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 106.72/106.94 Found x400:=(x40 x5):((cK x2) Xx)
% 106.72/106.94 Found (x40 x5) as proof of ((cK X5) Xx)
% 106.72/106.94 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 106.72/106.94 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 106.72/106.94 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 106.72/106.94 Found x6:(X5 Xx0)
% 106.72/106.94 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 106.72/106.94 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 106.72/106.94 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 106.72/106.94 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 106.72/106.94 Found x400:=(x40 x5):((cK x2) Xx)
% 106.72/106.94 Found (x40 x5) as proof of ((cK X5) Xx)
% 106.72/106.94 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 106.72/106.94 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 106.72/106.94 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 106.72/106.94 Found x6:(X5 Xx0)
% 106.72/106.94 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 106.72/106.94 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 106.72/106.94 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 106.72/106.94 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 106.72/106.94 Found x400:=(x40 x5):((cK x2) Xx)
% 106.72/106.94 Found (x40 x5) as proof of ((cK X5) Xx)
% 106.72/106.94 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 106.72/106.94 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 106.72/106.94 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 106.72/106.94 Found x6:(X5 Xx0)
% 106.72/106.94 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 106.72/106.94 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 107.05/107.25 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 107.05/107.25 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 107.05/107.25 Found x400:=(x40 x5):((cK x2) Xx)
% 107.05/107.25 Found (x40 x5) as proof of ((cK X5) Xx)
% 107.05/107.25 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 107.05/107.25 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 107.05/107.25 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 107.05/107.25 Found x6:(X5 Xx0)
% 107.05/107.25 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 107.05/107.25 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 107.05/107.25 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 107.05/107.25 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 107.05/107.25 Found x400:=(x40 x5):((cK x2) Xx)
% 107.05/107.25 Found (x40 x5) as proof of ((cK X5) Xx)
% 107.05/107.25 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 107.05/107.25 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 107.05/107.25 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 107.05/107.25 Found x6:(X5 Xx0)
% 107.05/107.25 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 107.05/107.25 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 107.05/107.25 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 107.05/107.25 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 107.05/107.25 Found x400:=(x40 x5):((cK x2) Xx)
% 107.05/107.25 Found (x40 x5) as proof of ((cK X5) Xx)
% 107.05/107.25 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 107.05/107.25 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 107.05/107.25 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 107.05/107.25 Found x6:(X5 Xx0)
% 107.05/107.25 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 107.05/107.25 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 107.05/107.25 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 107.05/107.25 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 107.05/107.25 Found x400:=(x40 x5):((cK x2) Xx)
% 107.05/107.25 Found (x40 x5) as proof of ((cK X5) Xx)
% 107.05/107.25 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 107.05/107.25 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 107.05/107.25 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 107.05/107.25 Found x6:(X5 Xx0)
% 107.05/107.25 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 107.05/107.25 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 107.05/107.25 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 107.05/107.25 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 107.05/107.25 Found x400:=(x40 x5):((cK x2) Xx)
% 107.05/107.25 Found (x40 x5) as proof of ((cK X5) Xx)
% 107.05/107.25 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 107.05/107.25 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 107.05/107.25 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 107.05/107.25 Found x6:(X5 Xx0)
% 107.05/107.25 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 107.05/107.25 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 107.26/107.46 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 107.26/107.46 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 107.26/107.46 Found x400:=(x40 x5):((cK x2) Xx)
% 107.26/107.46 Found (x40 x5) as proof of ((cK X5) Xx)
% 107.26/107.46 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 107.26/107.46 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 107.26/107.46 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 107.26/107.46 Found x6:(X5 Xx0)
% 107.26/107.46 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 107.26/107.46 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 107.26/107.46 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 107.26/107.46 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 107.26/107.46 Found x400:=(x40 x5):((cK x2) Xx)
% 107.26/107.46 Found (x40 x5) as proof of ((cK X5) Xx)
% 107.26/107.46 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 107.26/107.46 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 107.26/107.46 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 107.26/107.46 Found x6:(X5 Xx0)
% 107.26/107.46 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 107.26/107.46 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 107.26/107.46 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 107.26/107.46 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 107.26/107.46 Found x400:=(x40 x5):((cK x2) Xx)
% 107.26/107.46 Found (x40 x5) as proof of ((cK X5) Xx)
% 107.26/107.46 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 107.26/107.46 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 107.26/107.46 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 107.26/107.46 Found x6:(X5 Xx0)
% 107.26/107.46 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 107.26/107.46 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 107.26/107.46 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 107.26/107.46 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 107.26/107.46 Found x400:=(x40 x5):((cK x2) Xx)
% 107.26/107.46 Found (x40 x5) as proof of ((cK X5) Xx)
% 107.26/107.46 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 107.26/107.46 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 107.26/107.46 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 107.26/107.46 Found x6:(X5 Xx0)
% 107.26/107.46 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 107.26/107.46 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 107.26/107.46 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 107.26/107.46 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 107.26/107.46 Found x400:=(x40 x5):((cK x2) Xx)
% 107.26/107.46 Found (x40 x5) as proof of ((cK X5) Xx)
% 107.26/107.46 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 107.26/107.46 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 107.26/107.46 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 107.26/107.46 Found x2:(X5 Xx0)
% 107.26/107.46 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 107.26/107.46 Found (fun (x2:(X5 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 107.41/107.63 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 107.41/107.63 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 107.41/107.63 Found x6:(X5 Xx0)
% 107.41/107.63 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 107.41/107.63 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 107.41/107.63 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 107.41/107.63 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 107.41/107.63 Found x400:=(x40 x5):((cK x2) Xx)
% 107.41/107.63 Found (x40 x5) as proof of ((cK X5) Xx)
% 107.41/107.63 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 107.41/107.63 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 107.41/107.63 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 107.41/107.63 Found x2:(X5 Xx0)
% 107.41/107.63 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 107.41/107.63 Found (fun (x2:(X5 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 107.41/107.63 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 107.41/107.63 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 107.41/107.63 Found x2:(X5 Xx0)
% 107.41/107.63 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 107.41/107.63 Found (fun (x2:(X5 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 107.41/107.63 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 107.41/107.63 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 107.41/107.63 Found x2:(X5 Xx0)
% 107.41/107.63 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 107.41/107.63 Found (fun (x2:(X5 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 107.41/107.63 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 107.41/107.63 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 107.41/107.63 Found x6:(X5 Xx0)
% 107.41/107.63 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 107.41/107.63 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 107.41/107.63 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 107.41/107.63 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 107.41/107.63 Found x400:=(x40 x5):((cK x2) Xx)
% 107.41/107.63 Found (x40 x5) as proof of ((cK X5) Xx)
% 107.41/107.63 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 107.41/107.63 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 107.41/107.63 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 107.41/107.63 Found x2:(X5 Xx0)
% 107.41/107.63 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 107.41/107.63 Found (fun (x2:(X5 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 107.57/107.80 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 107.57/107.80 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 107.57/107.80 Found x6:(X5 Xx0)
% 107.57/107.80 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 107.57/107.80 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 107.57/107.80 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 107.57/107.80 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 107.57/107.80 Found x400:=(x40 x5):((cK x2) Xx)
% 107.57/107.80 Found (x40 x5) as proof of ((cK X5) Xx)
% 107.57/107.80 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 107.57/107.80 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 107.57/107.80 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 107.57/107.80 Found x6:(X5 Xx0)
% 107.57/107.80 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 107.57/107.80 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 107.57/107.80 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 107.57/107.80 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 107.57/107.80 Found x400:=(x40 x5):((cK x2) Xx)
% 107.57/107.80 Found (x40 x5) as proof of ((cK X5) Xx)
% 107.57/107.80 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 107.57/107.80 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 107.57/107.80 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 107.57/107.80 Found x6:(X5 Xx0)
% 107.57/107.80 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 107.57/107.80 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 107.57/107.80 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 107.57/107.80 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 107.57/107.80 Found x400:=(x40 x5):((cK x2) Xx)
% 107.57/107.80 Found (x40 x5) as proof of ((cK X5) Xx)
% 107.57/107.80 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 107.57/107.80 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 107.57/107.80 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 107.57/107.80 Found x2:(X5 Xx0)
% 107.57/107.80 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 107.57/107.80 Found (fun (x2:(X5 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 107.57/107.80 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 107.57/107.80 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 107.57/107.80 Found x6:(X5 Xx0)
% 107.57/107.80 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 107.57/107.80 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 107.57/107.80 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 107.57/107.80 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 108.62/108.87 Found x400:=(x40 x5):((cK x2) Xx)
% 108.62/108.87 Found (x40 x5) as proof of ((cK X5) Xx)
% 108.62/108.87 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 108.62/108.87 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 108.62/108.87 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 108.62/108.87 Found x4:(X5 Xx0)
% 108.62/108.87 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 108.62/108.87 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 108.62/108.87 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 108.62/108.87 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 108.62/108.87 Found x4:(X5 Xx0)
% 108.62/108.87 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 108.62/108.87 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 108.62/108.87 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 108.62/108.87 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 108.62/108.87 Found x4:(X5 Xx0)
% 108.62/108.87 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 108.62/108.87 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 108.62/108.87 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 108.62/108.87 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 108.62/108.87 Found x4:(X5 Xx0)
% 108.62/108.87 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 108.62/108.87 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 108.62/108.87 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 108.62/108.87 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 108.62/108.87 Found x4:(X5 Xx0)
% 108.62/108.87 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 108.62/108.87 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 108.62/108.87 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 108.62/108.87 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 108.62/108.87 Found x2:(X5 Xx0)
% 108.62/108.87 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 108.62/108.87 Found (fun (x2:(X5 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 108.62/108.87 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 108.62/108.87 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 108.62/108.87 Found x2:(X5 Xx0)
% 108.62/108.87 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 108.83/109.03 Found (fun (x2:(X5 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 108.83/109.03 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 108.83/109.03 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 108.83/109.03 Found x2:(X5 Xx0)
% 108.83/109.03 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 108.83/109.03 Found (fun (x2:(X5 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 108.83/109.03 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 108.83/109.03 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 108.83/109.03 Found x2:(X5 Xx0)
% 108.83/109.03 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 108.83/109.03 Found (fun (x2:(X5 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 108.83/109.03 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 108.83/109.03 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 108.83/109.03 Found x2:(X5 Xx0)
% 108.83/109.03 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 108.83/109.03 Found (fun (x2:(X5 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 108.83/109.03 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 108.83/109.03 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 108.83/109.03 Found x2:(X5 Xx0)
% 108.83/109.03 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 108.83/109.03 Found (fun (x2:(X5 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 108.83/109.03 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 108.83/109.03 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 108.83/109.03 Found x2:(X5 Xx0)
% 108.83/109.03 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 108.83/109.03 Found (fun (x2:(X5 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 108.83/109.03 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 108.83/109.03 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 108.83/109.03 Found x2:(X5 Xx0)
% 108.83/109.03 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 108.83/109.03 Found (fun (x2:(X5 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 108.83/109.03 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 108.83/109.03 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 108.98/109.20 Found x2:(X5 Xx0)
% 108.98/109.20 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 108.98/109.20 Found (fun (x2:(X5 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 108.98/109.20 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 108.98/109.20 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 108.98/109.20 Found x2:(X5 Xx0)
% 108.98/109.20 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 108.98/109.20 Found (fun (x2:(X5 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 108.98/109.20 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 108.98/109.20 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 108.98/109.20 Found x2:(X5 Xx0)
% 108.98/109.20 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 108.98/109.20 Found (fun (x2:(X5 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 108.98/109.20 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 108.98/109.20 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 108.98/109.20 Found x2:(X5 Xx0)
% 108.98/109.20 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 108.98/109.20 Found (fun (x2:(X5 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 108.98/109.20 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 108.98/109.20 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 108.98/109.20 Found x2:(X5 Xx0)
% 108.98/109.20 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 108.98/109.20 Found (fun (x2:(X5 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 108.98/109.20 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 108.98/109.20 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 108.98/109.20 Found x2:(X5 Xx0)
% 108.98/109.20 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 108.98/109.20 Found (fun (x2:(X5 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 108.98/109.20 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 108.98/109.20 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 108.98/109.20 Found x2:(X5 Xx0)
% 108.98/109.20 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 108.98/109.20 Found (fun (x2:(X5 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 109.59/109.83 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 109.59/109.83 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 109.59/109.83 Found x4:(X5 Xx0)
% 109.59/109.83 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 109.59/109.83 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 109.59/109.83 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 109.59/109.83 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 109.59/109.83 Found x4:(X5 Xx0)
% 109.59/109.83 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 109.59/109.83 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 109.59/109.83 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 109.59/109.83 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 109.59/109.83 Found x4:(X5 Xx0)
% 109.59/109.83 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 109.59/109.83 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 109.59/109.83 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 109.59/109.83 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 109.59/109.83 Found x4:(X5 Xx0)
% 109.59/109.83 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 109.59/109.83 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 109.59/109.83 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 109.59/109.83 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 109.59/109.83 Found x4:(X5 Xx0)
% 109.59/109.83 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 109.59/109.83 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 109.59/109.83 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 109.59/109.83 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 109.59/109.83 Found x4:(X5 Xx0)
% 109.59/109.83 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 109.59/109.83 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 109.59/109.83 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 109.59/109.83 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 110.20/110.44 Found x4:(X5 Xx0)
% 110.20/110.44 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 110.20/110.44 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 110.20/110.44 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 110.20/110.44 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 110.20/110.44 Found x2:(X5 Xx0)
% 110.20/110.44 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 110.20/110.44 Found (fun (x2:(X5 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 110.20/110.44 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 110.20/110.44 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 110.20/110.44 Found x2:(X5 Xx0)
% 110.20/110.44 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 110.20/110.44 Found (fun (x2:(X5 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 110.20/110.44 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 110.20/110.44 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 110.20/110.44 Found x2:(X5 Xx0)
% 110.20/110.44 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 110.20/110.44 Found (fun (x2:(X5 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 110.20/110.44 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 110.20/110.44 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 110.20/110.44 Found x2:(X5 Xx0)
% 110.20/110.44 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 110.20/110.44 Found (fun (x2:(X5 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 110.20/110.44 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 110.20/110.44 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 110.20/110.44 Found x2:(X5 Xx0)
% 110.20/110.44 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 110.20/110.44 Found (fun (x2:(X5 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 110.20/110.44 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 110.20/110.44 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 110.20/110.44 Found x2:(X5 Xx0)
% 110.20/110.44 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 110.20/110.44 Found (fun (x2:(X5 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 110.20/110.44 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 110.44/110.64 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 110.44/110.64 Found x2:(X5 Xx0)
% 110.44/110.64 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 110.44/110.64 Found (fun (x2:(X5 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 110.44/110.64 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 110.44/110.64 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 110.44/110.64 Found x2:(X5 Xx0)
% 110.44/110.64 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 110.44/110.64 Found (fun (x2:(X5 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 110.44/110.64 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 110.44/110.64 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 110.44/110.64 Found x2:(X5 Xx0)
% 110.44/110.64 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 110.44/110.64 Found (fun (x2:(X5 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 110.44/110.64 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 110.44/110.64 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 110.44/110.64 Found x2:(X5 Xx0)
% 110.44/110.64 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 110.44/110.64 Found (fun (x2:(X5 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 110.44/110.64 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 110.44/110.64 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 110.44/110.64 Found x2:(X5 Xx0)
% 110.44/110.64 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 110.44/110.64 Found (fun (x2:(X5 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 110.44/110.64 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 110.44/110.64 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 110.44/110.64 Found x2:(X5 Xx0)
% 110.44/110.64 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 110.44/110.64 Found (fun (x2:(X5 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 110.44/110.64 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 110.44/110.64 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 110.44/110.64 Found x2:(X5 Xx0)
% 110.44/110.64 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 110.56/110.83 Found (fun (x2:(X5 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 110.56/110.83 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 110.56/110.83 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 110.56/110.83 Found x2:(X5 Xx0)
% 110.56/110.83 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 110.56/110.83 Found (fun (x2:(X5 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 110.56/110.83 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 110.56/110.83 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 110.56/110.83 Found x2:(X5 Xx0)
% 110.56/110.83 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 110.56/110.83 Found (fun (x2:(X5 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 110.56/110.83 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 110.56/110.83 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 110.56/110.83 Found x2:(X5 Xx0)
% 110.56/110.83 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 110.56/110.83 Found (fun (x2:(X5 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 110.56/110.83 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 110.56/110.83 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 110.56/110.83 Found x2:(X5 Xx0)
% 110.56/110.83 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 110.56/110.83 Found (fun (x2:(X5 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 110.56/110.83 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 110.56/110.83 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 110.56/110.83 Found x2:(X5 Xx0)
% 110.56/110.83 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 110.56/110.83 Found (fun (x2:(X5 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 110.56/110.83 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 110.56/110.83 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 110.56/110.83 Found x2:(X5 Xx0)
% 110.56/110.83 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 110.56/110.83 Found (fun (x2:(X5 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 110.56/110.83 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 110.56/110.83 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 111.49/111.71 Found x2:(X5 Xx0)
% 111.49/111.71 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 111.49/111.71 Found (fun (x2:(X5 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 111.49/111.71 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 111.49/111.71 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 111.49/111.71 Found x4:(X5 Xx0)
% 111.49/111.71 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 111.49/111.71 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 111.49/111.71 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 111.49/111.71 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 111.49/111.71 Found x6:(X5 Xx0)
% 111.49/111.71 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 111.49/111.71 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 111.49/111.71 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 111.49/111.71 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 111.49/111.71 Found x400:=(x40 x5):((cK x2) Xx)
% 111.49/111.71 Found (x40 x5) as proof of ((cK X5) Xx)
% 111.49/111.71 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 111.49/111.71 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 111.49/111.71 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 111.49/111.71 Found x6:(X5 Xx0)
% 111.49/111.71 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 111.49/111.71 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 111.49/111.71 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 111.49/111.71 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 111.49/111.71 Found x400:=(x40 x5):((cK x2) Xx)
% 111.49/111.71 Found (x40 x5) as proof of ((cK X5) Xx)
% 111.49/111.71 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 111.49/111.71 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 111.49/111.71 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 111.49/111.71 Found x6:(X5 Xx0)
% 111.49/111.71 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 111.49/111.71 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 111.49/111.71 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 111.49/111.71 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 111.49/111.71 Found x400:=(x40 x5):((cK x2) Xx)
% 111.49/111.71 Found (x40 x5) as proof of ((cK X5) Xx)
% 111.49/111.71 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 111.49/111.71 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 111.49/111.71 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 111.49/111.71 Found x6:(X5 Xx0)
% 111.49/111.71 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 111.49/111.71 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 111.65/111.89 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 111.65/111.89 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 111.65/111.89 Found x400:=(x40 x5):((cK x2) Xx)
% 111.65/111.89 Found (x40 x5) as proof of ((cK X5) Xx)
% 111.65/111.89 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 111.65/111.89 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 111.65/111.89 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 111.65/111.89 Found x6:(X5 Xx0)
% 111.65/111.89 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 111.65/111.89 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 111.65/111.89 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 111.65/111.89 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 111.65/111.89 Found x400:=(x40 x5):((cK x2) Xx)
% 111.65/111.89 Found (x40 x5) as proof of ((cK X5) Xx)
% 111.65/111.89 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 111.65/111.89 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 111.65/111.89 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 111.65/111.89 Found x6:(X5 Xx0)
% 111.65/111.89 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 111.65/111.89 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 111.65/111.89 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 111.65/111.89 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 111.65/111.89 Found x400:=(x40 x5):((cK x2) Xx)
% 111.65/111.89 Found (x40 x5) as proof of ((cK X5) Xx)
% 111.65/111.89 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 111.65/111.89 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 111.65/111.89 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 111.65/111.89 Found x6:(X5 Xx0)
% 111.65/111.89 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 111.65/111.89 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 111.65/111.89 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 111.65/111.89 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 111.65/111.89 Found x400:=(x40 x5):((cK x2) Xx)
% 111.65/111.89 Found (x40 x5) as proof of ((cK X5) Xx)
% 111.65/111.89 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 111.65/111.89 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 111.65/111.89 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 111.65/111.89 Found x6:(X5 Xx0)
% 111.65/111.89 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 111.65/111.89 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 111.65/111.89 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 111.65/111.89 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 111.65/111.89 Found x400:=(x40 x5):((cK x2) Xx)
% 111.65/111.89 Found (x40 x5) as proof of ((cK X5) Xx)
% 111.65/111.89 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 111.65/111.89 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 111.65/111.89 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 111.65/111.89 Found x6:(X5 Xx0)
% 111.65/111.89 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 111.65/111.89 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 111.85/112.07 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 111.85/112.07 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 111.85/112.07 Found x400:=(x40 x5):((cK x2) Xx)
% 111.85/112.07 Found (x40 x5) as proof of ((cK X5) Xx)
% 111.85/112.07 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 111.85/112.07 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 111.85/112.07 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 111.85/112.07 Found x6:(X5 Xx0)
% 111.85/112.07 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 111.85/112.07 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 111.85/112.07 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 111.85/112.07 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 111.85/112.07 Found x400:=(x40 x5):((cK x2) Xx)
% 111.85/112.07 Found (x40 x5) as proof of ((cK X5) Xx)
% 111.85/112.07 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 111.85/112.07 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 111.85/112.07 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 111.85/112.07 Found x6:(X5 Xx0)
% 111.85/112.07 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 111.85/112.07 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 111.85/112.07 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 111.85/112.07 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 111.85/112.07 Found x400:=(x40 x5):((cK x2) Xx)
% 111.85/112.07 Found (x40 x5) as proof of ((cK X5) Xx)
% 111.85/112.07 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 111.85/112.07 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 111.85/112.07 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 111.85/112.07 Found x6:(X5 Xx0)
% 111.85/112.07 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 111.85/112.07 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 111.85/112.07 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 111.85/112.07 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 111.85/112.07 Found x400:=(x40 x5):((cK x2) Xx)
% 111.85/112.07 Found (x40 x5) as proof of ((cK X5) Xx)
% 111.85/112.07 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 111.85/112.07 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 111.85/112.07 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 111.87/112.07 Found x6:(X5 Xx0)
% 111.87/112.07 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 111.87/112.07 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 111.87/112.07 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 111.87/112.07 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 111.87/112.07 Found x400:=(x40 x5):((cK x2) Xx)
% 111.87/112.07 Found (x40 x5) as proof of ((cK X5) Xx)
% 111.87/112.07 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 111.87/112.07 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 111.87/112.07 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 111.87/112.07 Found x6:(X5 Xx0)
% 111.87/112.07 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 111.87/112.07 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 112.03/112.24 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 112.03/112.24 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 112.03/112.24 Found x400:=(x40 x5):((cK x2) Xx)
% 112.03/112.24 Found (x40 x5) as proof of ((cK X5) Xx)
% 112.03/112.24 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 112.03/112.24 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 112.03/112.24 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 112.03/112.24 Found x6:(X5 Xx0)
% 112.03/112.24 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 112.03/112.24 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 112.03/112.24 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 112.03/112.24 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 112.03/112.24 Found x400:=(x40 x5):((cK x2) Xx)
% 112.03/112.24 Found (x40 x5) as proof of ((cK X5) Xx)
% 112.03/112.24 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 112.03/112.24 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 112.03/112.24 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 112.03/112.24 Found x6:(X5 Xx0)
% 112.03/112.24 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 112.03/112.24 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 112.03/112.24 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 112.03/112.24 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 112.03/112.24 Found x400:=(x40 x5):((cK x2) Xx)
% 112.03/112.24 Found (x40 x5) as proof of ((cK X5) Xx)
% 112.03/112.24 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 112.03/112.24 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 112.03/112.24 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 112.03/112.24 Found x6:(X5 Xx0)
% 112.03/112.24 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 112.03/112.24 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 112.03/112.24 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 112.03/112.24 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 112.03/112.24 Found x400:=(x40 x5):((cK x2) Xx)
% 112.03/112.24 Found (x40 x5) as proof of ((cK X5) Xx)
% 112.03/112.24 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 112.03/112.24 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 112.03/112.24 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 112.03/112.24 Found x6:(X5 Xx0)
% 112.03/112.24 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 112.03/112.24 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 112.03/112.24 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 112.03/112.24 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 112.03/112.24 Found x400:=(x40 x5):((cK x2) Xx)
% 112.03/112.24 Found (x40 x5) as proof of ((cK X5) Xx)
% 112.03/112.24 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 112.03/112.24 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 112.03/112.24 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 112.03/112.24 Found x6:(X5 Xx0)
% 112.03/112.24 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 112.24/112.44 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 112.24/112.44 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 112.24/112.44 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 112.24/112.44 Found x400:=(x40 x5):((cK x2) Xx)
% 112.24/112.44 Found (x40 x5) as proof of ((cK X5) Xx)
% 112.24/112.44 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 112.24/112.44 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 112.24/112.44 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 112.24/112.44 Found x6:(X5 Xx0)
% 112.24/112.44 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 112.24/112.44 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 112.24/112.44 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 112.24/112.44 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 112.24/112.44 Found x400:=(x40 x5):((cK x2) Xx)
% 112.24/112.44 Found (x40 x5) as proof of ((cK X5) Xx)
% 112.24/112.44 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 112.24/112.44 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 112.24/112.44 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 112.24/112.44 Found x6:(X5 Xx0)
% 112.24/112.44 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 112.24/112.44 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 112.24/112.44 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 112.24/112.44 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 112.24/112.44 Found x400:=(x40 x5):((cK x2) Xx)
% 112.24/112.44 Found (x40 x5) as proof of ((cK X5) Xx)
% 112.24/112.44 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 112.24/112.44 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 112.24/112.44 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 112.24/112.44 Found x6:(X5 Xx0)
% 112.24/112.44 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 112.24/112.44 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 112.24/112.44 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 112.24/112.44 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 112.24/112.44 Found x400:=(x40 x5):((cK x2) Xx)
% 112.24/112.44 Found (x40 x5) as proof of ((cK X5) Xx)
% 112.24/112.44 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 112.24/112.44 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 112.24/112.44 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 112.24/112.44 Found x4:(X5 Xx0)
% 112.24/112.44 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 112.24/112.44 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 112.24/112.44 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 112.24/112.44 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 112.24/112.44 Found x6:(X5 Xx0)
% 112.24/112.44 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 112.24/112.44 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 112.24/112.44 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 112.48/112.69 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 112.48/112.69 Found x400:=(x40 x5):((cK x2) Xx)
% 112.48/112.69 Found (x40 x5) as proof of ((cK X5) Xx)
% 112.48/112.69 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 112.48/112.69 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 112.48/112.69 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 112.48/112.69 Found x6:(X5 Xx0)
% 112.48/112.69 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 112.48/112.69 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 112.48/112.69 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 112.48/112.69 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 112.48/112.69 Found x400:=(x40 x5):((cK x2) Xx)
% 112.48/112.69 Found (x40 x5) as proof of ((cK X5) Xx)
% 112.48/112.69 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 112.48/112.69 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 112.48/112.69 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 112.48/112.69 Found x4:(X5 Xx0)
% 112.48/112.69 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 112.48/112.69 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 112.48/112.69 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 112.48/112.69 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 112.48/112.69 Found x4:(X5 Xx0)
% 112.48/112.69 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 112.48/112.69 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 112.48/112.69 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 112.48/112.69 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 112.48/112.69 Found x6:(X5 Xx0)
% 112.48/112.69 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 112.48/112.69 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 112.48/112.69 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 112.48/112.69 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 112.48/112.69 Found x400:=(x40 x5):((cK x2) Xx)
% 112.48/112.69 Found (x40 x5) as proof of ((cK X5) Xx)
% 112.48/112.69 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 112.48/112.69 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 112.48/112.69 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 112.48/112.69 Found x6:(X5 Xx0)
% 112.48/112.69 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 112.48/112.69 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 112.48/112.69 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 112.48/112.69 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 112.48/112.69 Found x400:=(x40 x5):((cK x2) Xx)
% 112.48/112.69 Found (x40 x5) as proof of ((cK X5) Xx)
% 112.69/112.96 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 112.69/112.96 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 112.69/112.96 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 112.69/112.96 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 112.69/112.96 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 112.69/112.96 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 112.69/112.96 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 112.69/112.96 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 112.69/112.96 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 112.69/112.96 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 112.69/112.96 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 112.69/112.96 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 112.69/112.96 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 112.69/112.96 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 112.69/112.96 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 112.69/112.96 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 112.69/112.96 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 112.69/112.96 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 112.69/112.96 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 112.69/112.96 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 112.69/112.96 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 112.69/112.96 Found x2:(X5 Xx0)
% 112.69/112.96 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 112.69/112.96 Found (fun (x2:(X5 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 112.69/112.96 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 112.69/112.96 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 112.69/112.96 Found x2:(X5 Xx0)
% 112.69/112.96 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 112.69/112.96 Found (fun (x2:(X5 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 112.69/112.96 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 112.69/112.96 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 112.69/112.96 Found x2:(X5 Xx0)
% 112.69/112.96 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 112.69/112.96 Found (fun (x2:(X5 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 112.69/112.96 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 112.99/113.21 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 112.99/113.21 Found x4:(X5 Xx0)
% 112.99/113.21 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 112.99/113.21 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 112.99/113.21 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 112.99/113.21 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 112.99/113.21 Found x2:(X5 Xx0)
% 112.99/113.21 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 112.99/113.21 Found (fun (x2:(X5 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 112.99/113.21 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 112.99/113.21 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 112.99/113.21 Found x2:(X5 Xx0)
% 112.99/113.21 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 112.99/113.21 Found (fun (x2:(X5 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 112.99/113.21 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 112.99/113.21 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 112.99/113.21 Found x2:(X5 Xx0)
% 112.99/113.21 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 112.99/113.21 Found (fun (x2:(X5 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 112.99/113.21 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 112.99/113.21 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 112.99/113.21 Found x2:(X5 Xx0)
% 112.99/113.21 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 112.99/113.21 Found (fun (x2:(X5 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 112.99/113.21 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 112.99/113.21 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 112.99/113.21 Found x2:(X5 Xx0)
% 112.99/113.21 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 112.99/113.21 Found (fun (x2:(X5 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 112.99/113.21 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 112.99/113.21 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 112.99/113.21 Found x2:(X5 Xx0)
% 112.99/113.21 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 113.14/113.41 Found (fun (x2:(X5 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 113.14/113.41 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 113.14/113.41 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 113.14/113.41 Found x2:(X5 Xx0)
% 113.14/113.41 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 113.14/113.41 Found (fun (x2:(X5 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 113.14/113.41 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 113.14/113.41 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 113.14/113.41 Found x2:(X5 Xx0)
% 113.14/113.41 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 113.14/113.41 Found (fun (x2:(X5 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 113.14/113.41 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 113.14/113.41 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 113.14/113.41 Found x2:(X5 Xx0)
% 113.14/113.41 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 113.14/113.41 Found (fun (x2:(X5 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 113.14/113.41 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 113.14/113.41 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 113.14/113.41 Found x2:(X5 Xx0)
% 113.14/113.41 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 113.14/113.41 Found (fun (x2:(X5 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 113.14/113.41 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 113.14/113.41 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 113.14/113.41 Found x4:(X5 Xx0)
% 113.14/113.41 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 113.14/113.41 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 113.14/113.41 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 113.14/113.41 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 113.14/113.41 Found x2:(X5 Xx0)
% 113.14/113.41 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 113.14/113.41 Found (fun (x2:(X5 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 113.14/113.41 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 113.14/113.41 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 113.76/113.97 Found x4:(X5 Xx0)
% 113.76/113.97 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 113.76/113.97 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 113.76/113.97 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 113.76/113.97 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 113.76/113.97 Found x2:(X5 Xx0)
% 113.76/113.97 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 113.76/113.97 Found (fun (x2:(X5 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 113.76/113.97 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 113.76/113.97 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 113.76/113.97 Found x4:(X5 Xx0)
% 113.76/113.97 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 113.76/113.97 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 113.76/113.97 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 113.76/113.97 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 113.76/113.97 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 113.76/113.97 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 113.76/113.97 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 113.76/113.97 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 113.76/113.97 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 113.76/113.97 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 113.76/113.97 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 113.76/113.97 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 113.76/113.97 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 113.76/113.97 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 113.76/113.97 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 113.76/113.97 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 113.76/113.97 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 113.76/113.97 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 113.76/113.97 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 113.76/113.97 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 113.76/113.97 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 114.08/114.31 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 114.08/114.31 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 114.08/114.31 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 114.08/114.31 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 114.08/114.31 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 114.08/114.31 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 114.08/114.31 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 114.08/114.31 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 114.08/114.31 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 114.08/114.31 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 114.08/114.31 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 114.08/114.31 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 114.08/114.31 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 114.08/114.31 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 114.08/114.31 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 114.08/114.31 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 114.08/114.31 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 114.08/114.31 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 114.08/114.31 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 114.08/114.31 Found x4:(X5 Xx0)
% 114.08/114.31 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 114.08/114.31 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 114.08/114.31 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 114.08/114.31 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 114.08/114.31 Found x4:(X5 Xx0)
% 114.08/114.31 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 114.08/114.31 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 114.08/114.31 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 114.08/114.31 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 114.08/114.31 Found x4:(X5 Xx0)
% 114.08/114.31 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 114.08/114.31 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 114.65/114.90 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 114.65/114.90 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 114.65/114.90 Found x4:(X5 Xx0)
% 114.65/114.90 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 114.65/114.90 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 114.65/114.90 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 114.65/114.90 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 114.65/114.90 Found x4:(X5 Xx0)
% 114.65/114.90 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 114.65/114.90 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 114.65/114.90 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 114.65/114.90 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 114.65/114.90 Found x4:(X5 Xx0)
% 114.65/114.90 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 114.65/114.90 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 114.65/114.90 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 114.65/114.90 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 114.65/114.90 Found x4:(X5 Xx0)
% 114.65/114.90 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 114.65/114.90 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 114.65/114.90 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 114.65/114.90 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 114.65/114.90 Found x4:(X5 Xx0)
% 114.65/114.90 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 114.65/114.90 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 114.65/114.90 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 114.65/114.90 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 114.65/114.90 Found x2:(X5 Xx0)
% 114.65/114.90 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 114.65/114.90 Found (fun (x2:(X5 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 114.65/114.90 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 114.65/114.90 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 114.97/115.19 Found x2:(X5 Xx0)
% 114.97/115.19 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 114.97/115.19 Found (fun (x2:(X5 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 114.97/115.19 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 114.97/115.19 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 114.97/115.19 Found x2:(X5 Xx0)
% 114.97/115.19 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 114.97/115.19 Found (fun (x2:(X5 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 114.97/115.19 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 114.97/115.19 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 114.97/115.19 Found x2:(X5 Xx0)
% 114.97/115.19 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 114.97/115.19 Found (fun (x2:(X5 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 114.97/115.19 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 114.97/115.19 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 114.97/115.19 Found x2:(X5 Xx0)
% 114.97/115.19 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 114.97/115.19 Found (fun (x2:(X5 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 114.97/115.19 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 114.97/115.19 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 114.97/115.19 Found x2:(X5 Xx0)
% 114.97/115.19 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 114.97/115.19 Found (fun (x2:(X5 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 114.97/115.19 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 114.97/115.19 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 114.97/115.19 Found x4:(X5 Xx0)
% 114.97/115.19 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 114.97/115.19 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 114.97/115.19 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 114.97/115.19 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 114.97/115.19 Found x4:(X5 Xx0)
% 114.97/115.19 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 114.97/115.19 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 114.97/115.19 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 116.30/116.52 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 116.30/116.52 Found x4:(X5 Xx0)
% 116.30/116.52 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 116.30/116.52 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 116.30/116.52 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 116.30/116.52 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 116.30/116.52 Found x4:(X5 Xx0)
% 116.30/116.52 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 116.30/116.52 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 116.30/116.52 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 116.30/116.52 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 116.30/116.52 Found x4:(X5 Xx0)
% 116.30/116.52 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 116.30/116.52 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 116.30/116.52 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 116.30/116.52 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 116.30/116.52 Found x6:(X5 Xx0)
% 116.30/116.52 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 116.30/116.52 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 116.30/116.52 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 116.30/116.52 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 116.30/116.52 Found x400:=(x40 x5):((cK x2) Xx)
% 116.30/116.52 Found (x40 x5) as proof of ((cK X5) Xx)
% 116.30/116.52 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 116.30/116.52 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 116.30/116.52 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 116.30/116.52 Found x6:(X5 Xx0)
% 116.30/116.52 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 116.30/116.52 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 116.30/116.52 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 116.30/116.52 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 116.30/116.52 Found x400:=(x40 x5):((cK x2) Xx)
% 116.30/116.52 Found (x40 x5) as proof of ((cK X5) Xx)
% 116.30/116.52 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 116.30/116.52 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 116.30/116.52 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 116.30/116.52 Found x4:(X5 Xx0)
% 116.30/116.52 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 116.30/116.52 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 116.30/116.52 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 116.51/116.72 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 116.51/116.72 Found x6:(X5 Xx0)
% 116.51/116.72 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 116.51/116.72 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 116.51/116.72 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 116.51/116.72 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 116.51/116.72 Found x400:=(x40 x5):((cK x2) Xx)
% 116.51/116.72 Found (x40 x5) as proof of ((cK X5) Xx)
% 116.51/116.72 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 116.51/116.72 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 116.51/116.72 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 116.51/116.72 Found x6:(X5 Xx0)
% 116.51/116.72 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 116.51/116.72 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 116.51/116.72 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 116.51/116.72 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 116.51/116.72 Found x400:=(x40 x5):((cK x2) Xx)
% 116.51/116.72 Found (x40 x5) as proof of ((cK X5) Xx)
% 116.51/116.72 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 116.51/116.72 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 116.51/116.72 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 116.51/116.72 Found x6:(X5 Xx0)
% 116.51/116.72 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 116.51/116.72 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 116.51/116.72 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 116.51/116.72 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 116.51/116.72 Found x400:=(x40 x5):((cK x2) Xx)
% 116.51/116.72 Found (x40 x5) as proof of ((cK X5) Xx)
% 116.51/116.72 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 116.51/116.72 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 116.51/116.72 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 116.51/116.72 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 116.51/116.72 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 116.51/116.72 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 116.51/116.72 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 116.51/116.72 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 116.51/116.72 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 116.51/116.72 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 116.51/116.72 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 116.51/116.72 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 116.51/116.72 Found x6:(X5 Xx0)
% 116.51/116.72 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 116.78/117.01 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 116.78/117.01 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 116.78/117.01 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 116.78/117.01 Found x400:=(x40 x5):((cK x2) Xx)
% 116.78/117.01 Found (x40 x5) as proof of ((cK X5) Xx)
% 116.78/117.01 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 116.78/117.01 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 116.78/117.01 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 116.78/117.01 Found x6:(X5 Xx0)
% 116.78/117.01 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 116.78/117.01 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 116.78/117.01 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 116.78/117.01 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 116.78/117.01 Found x400:=(x40 x5):((cK x2) Xx)
% 116.78/117.01 Found (x40 x5) as proof of ((cK X5) Xx)
% 116.78/117.01 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 116.78/117.01 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 116.78/117.01 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 116.78/117.01 Found x4:(X5 Xx0)
% 116.78/117.01 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 116.78/117.01 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 116.78/117.01 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 116.78/117.01 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 116.78/117.01 Found x4:(X5 Xx0)
% 116.78/117.01 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 116.78/117.01 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 116.78/117.01 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 116.78/117.01 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 116.78/117.01 Found x6:(X5 Xx0)
% 116.78/117.01 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 116.78/117.01 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 116.78/117.01 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 116.78/117.01 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 116.78/117.01 Found x400:=(x40 x5):((cK x2) Xx)
% 116.78/117.01 Found (x40 x5) as proof of ((cK X5) Xx)
% 116.78/117.01 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 116.78/117.01 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 116.78/117.01 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 116.78/117.01 Found x6:(X5 Xx0)
% 116.78/117.01 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 116.78/117.01 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 116.78/117.01 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 116.78/117.01 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 117.54/117.79 Found x400:=(x40 x5):((cK x2) Xx)
% 117.54/117.79 Found (x40 x5) as proof of ((cK X5) Xx)
% 117.54/117.79 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 117.54/117.79 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 117.54/117.79 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 117.54/117.79 Found x4:(X5 Xx0)
% 117.54/117.79 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 117.54/117.79 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 117.54/117.79 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 117.54/117.79 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 117.54/117.79 Found x6:(X5 Xx0)
% 117.54/117.79 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 117.54/117.79 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 117.54/117.79 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 117.54/117.79 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 117.54/117.79 Found x400:=(x40 x5):((cK x2) Xx)
% 117.54/117.79 Found (x40 x5) as proof of ((cK X5) Xx)
% 117.54/117.79 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 117.54/117.79 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 117.54/117.79 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 117.54/117.79 Found x4:(X5 Xx0)
% 117.54/117.79 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 117.54/117.79 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 117.54/117.79 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 117.54/117.79 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 117.54/117.79 Found x4:(X5 Xx0)
% 117.54/117.79 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 117.54/117.79 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 117.54/117.79 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 117.54/117.79 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 117.54/117.79 Found x6:(X5 Xx0)
% 117.54/117.79 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 117.54/117.79 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 117.54/117.79 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 117.54/117.79 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 117.54/117.79 Found x400:=(x40 x5):((cK x2) Xx)
% 117.54/117.79 Found (x40 x5) as proof of ((cK X5) Xx)
% 117.54/117.79 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 117.54/117.79 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 117.54/117.79 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 117.54/117.79 Found x6:(X5 Xx0)
% 117.54/117.79 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 117.54/117.79 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 117.65/117.96 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 117.65/117.96 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 117.65/117.96 Found x400:=(x40 x5):((cK x2) Xx)
% 117.65/117.96 Found (x40 x5) as proof of ((cK X5) Xx)
% 117.65/117.96 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 117.65/117.96 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 117.65/117.96 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 117.65/117.96 Found x6:(X5 Xx0)
% 117.65/117.96 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 117.65/117.96 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 117.65/117.96 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 117.65/117.96 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 117.65/117.96 Found x400:=(x40 x5):((cK x2) Xx)
% 117.65/117.96 Found (x40 x5) as proof of ((cK X5) Xx)
% 117.65/117.96 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 117.65/117.96 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 117.65/117.96 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 117.65/117.96 Found x4:(X5 Xx0)
% 117.65/117.96 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 117.65/117.96 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 117.65/117.96 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 117.65/117.96 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 117.65/117.96 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 117.65/117.96 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 117.65/117.96 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 117.65/117.96 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 117.65/117.96 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 117.65/117.96 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 117.65/117.96 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 117.65/117.96 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 117.65/117.96 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 117.65/117.96 Found x6:(X5 Xx0)
% 117.65/117.96 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 117.65/117.96 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 117.65/117.96 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 117.65/117.96 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 117.65/117.96 Found x400:=(x40 x5):((cK x2) Xx)
% 117.65/117.96 Found (x40 x5) as proof of ((cK X5) Xx)
% 117.65/117.96 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 117.65/117.96 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 117.65/117.96 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 117.65/117.96 Found x2:(X5 Xx0)
% 117.65/117.96 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 117.85/118.10 Found (fun (x2:(X5 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 117.85/118.10 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 117.85/118.10 Found (fun (Xx0:a) (x2:(X5 Xx0))=> x2) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 117.85/118.10 Found x6:(X5 Xx0)
% 117.85/118.10 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 117.85/118.10 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 117.85/118.10 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 117.85/118.10 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 117.85/118.10 Found x400:=(x40 x5):((cK x2) Xx)
% 117.85/118.10 Found (x40 x5) as proof of ((cK X5) Xx)
% 117.85/118.10 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 117.85/118.10 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 117.85/118.10 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 117.85/118.10 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 117.85/118.10 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 117.85/118.10 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 117.85/118.10 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 117.85/118.10 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 117.85/118.10 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 117.85/118.10 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 117.85/118.10 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 117.85/118.10 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 117.85/118.10 Found x6:(X5 Xx0)
% 117.85/118.10 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 117.85/118.10 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 117.85/118.10 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 117.85/118.10 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 117.85/118.10 Found x400:=(x40 x5):((cK x2) Xx)
% 117.85/118.10 Found (x40 x5) as proof of ((cK X5) Xx)
% 117.85/118.10 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 117.85/118.10 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 117.85/118.10 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 117.85/118.10 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 117.85/118.10 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 117.85/118.10 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 117.85/118.10 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 117.85/118.10 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 117.85/118.10 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 117.85/118.10 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 117.85/118.10 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 118.05/118.27 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 118.05/118.27 Found x6:(X5 Xx0)
% 118.05/118.27 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 118.05/118.27 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 118.05/118.27 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 118.05/118.27 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 118.05/118.27 Found x400:=(x40 x5):((cK x2) Xx)
% 118.05/118.27 Found (x40 x5) as proof of ((cK X5) Xx)
% 118.05/118.27 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 118.05/118.27 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 118.05/118.27 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 118.05/118.27 Found x6:(X5 Xx0)
% 118.05/118.27 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 118.05/118.27 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 118.05/118.27 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 118.05/118.27 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 118.05/118.27 Found x400:=(x40 x5):((cK x2) Xx)
% 118.05/118.27 Found (x40 x5) as proof of ((cK X5) Xx)
% 118.05/118.27 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 118.05/118.27 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 118.05/118.27 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 118.05/118.27 Found x6:(X5 Xx0)
% 118.05/118.27 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 118.05/118.27 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 118.05/118.27 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 118.05/118.27 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 118.05/118.27 Found x400:=(x40 x5):((cK x2) Xx)
% 118.05/118.27 Found (x40 x5) as proof of ((cK X5) Xx)
% 118.05/118.27 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 118.05/118.27 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 118.05/118.27 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 118.05/118.27 Found x6:(X5 Xx0)
% 118.05/118.27 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 118.05/118.27 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 118.05/118.27 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 118.05/118.27 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 118.05/118.27 Found x400:=(x40 x5):((cK x2) Xx)
% 118.05/118.27 Found (x40 x5) as proof of ((cK X5) Xx)
% 118.05/118.27 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 118.05/118.27 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 118.05/118.27 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 118.05/118.27 Found x6:(X5 Xx0)
% 118.05/118.27 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 118.05/118.27 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 118.05/118.27 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 118.28/118.54 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 118.28/118.54 Found x400:=(x40 x5):((cK x2) Xx)
% 118.28/118.54 Found (x40 x5) as proof of ((cK X5) Xx)
% 118.28/118.54 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 118.28/118.54 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 118.28/118.54 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 118.28/118.54 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 118.28/118.54 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 118.28/118.54 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 118.28/118.54 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 118.28/118.54 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 118.28/118.54 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 118.28/118.54 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 118.28/118.54 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 118.28/118.54 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 118.28/118.54 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 118.28/118.54 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 118.28/118.54 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 118.28/118.54 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 118.28/118.54 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 118.28/118.54 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 118.28/118.54 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 118.28/118.54 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 118.28/118.54 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 118.28/118.54 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 118.28/118.54 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 118.28/118.54 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 118.28/118.54 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 118.28/118.54 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 118.28/118.54 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 118.28/118.54 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 118.28/118.54 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 118.28/118.54 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 118.28/118.54 Found x6:(X5 Xx0)
% 118.28/118.54 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 118.57/118.81 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 118.57/118.81 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 118.57/118.81 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 118.57/118.81 Found x400:=(x40 x5):((cK x2) Xx)
% 118.57/118.81 Found (x40 x5) as proof of ((cK X5) Xx)
% 118.57/118.81 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 118.57/118.81 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 118.57/118.81 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 118.57/118.81 Found x6:(X5 Xx0)
% 118.57/118.81 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 118.57/118.81 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 118.57/118.81 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 118.57/118.81 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 118.57/118.81 Found x400:=(x40 x5):((cK x2) Xx)
% 118.57/118.81 Found (x40 x5) as proof of ((cK X5) Xx)
% 118.57/118.81 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 118.57/118.81 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 118.57/118.81 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 118.57/118.81 Found x6:(X5 Xx0)
% 118.57/118.81 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 118.57/118.81 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 118.57/118.81 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 118.57/118.81 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 118.57/118.81 Found x400:=(x40 x5):((cK x2) Xx)
% 118.57/118.81 Found (x40 x5) as proof of ((cK X5) Xx)
% 118.57/118.81 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 118.57/118.81 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 118.57/118.81 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 118.57/118.81 Found x4:(X5 Xx0)
% 118.57/118.81 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 118.57/118.81 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 118.57/118.81 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 118.57/118.81 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 118.57/118.81 Found x4:(X5 Xx0)
% 118.57/118.81 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 118.57/118.81 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 118.57/118.81 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 118.57/118.81 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 118.57/118.81 Found x6:(X5 Xx0)
% 118.57/118.81 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 118.57/118.81 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 118.57/118.81 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 118.75/118.97 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 118.75/118.97 Found x400:=(x40 x5):((cK x2) Xx)
% 118.75/118.97 Found (x40 x5) as proof of ((cK X5) Xx)
% 118.75/118.97 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 118.75/118.97 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 118.75/118.97 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 118.75/118.97 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 118.75/118.97 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 118.75/118.97 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 118.75/118.97 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 118.75/118.97 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 118.75/118.97 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 118.75/118.97 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 118.75/118.97 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 118.75/118.97 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 118.75/118.97 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 118.75/118.97 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 118.75/118.97 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 118.75/118.97 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 118.75/118.97 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 118.75/118.97 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 118.75/118.97 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 118.75/118.97 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 118.75/118.97 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 118.75/118.97 Found x4:(X5 Xx0)
% 118.75/118.97 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 118.75/118.97 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 118.75/118.97 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 118.75/118.97 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 118.75/118.97 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 118.75/118.97 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 118.75/118.97 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 118.75/118.97 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 118.75/118.97 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 118.75/118.97 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 118.75/118.97 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 118.75/118.97 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 118.89/119.14 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 118.89/119.14 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 118.89/119.14 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 118.89/119.14 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 118.89/119.14 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 118.89/119.14 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 118.89/119.14 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 118.89/119.14 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 118.89/119.14 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 118.89/119.14 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 118.89/119.14 Found x4:(X5 Xx0)
% 118.89/119.14 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 118.89/119.14 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 118.89/119.14 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 118.89/119.14 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 118.89/119.14 Found x4:(X5 Xx0)
% 118.89/119.14 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 118.89/119.14 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 118.89/119.14 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 118.89/119.14 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 118.89/119.14 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 118.89/119.14 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 118.89/119.14 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 118.89/119.14 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 118.89/119.14 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 118.89/119.14 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 118.89/119.14 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 118.89/119.14 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 118.89/119.14 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 119.04/119.24 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 119.04/119.24 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 119.04/119.24 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 119.04/119.24 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 119.04/119.24 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 119.04/119.24 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 119.04/119.24 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 119.04/119.24 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 119.04/119.24 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 119.04/119.24 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 119.04/119.24 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 119.04/119.24 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 119.04/119.24 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 119.04/119.24 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 119.04/119.24 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 119.04/119.24 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 119.04/119.24 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 119.04/119.24 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 119.04/119.24 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 119.04/119.24 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 119.04/119.24 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 119.04/119.24 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 119.04/119.24 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 119.04/119.24 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 119.04/119.24 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 119.04/119.24 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 119.04/119.24 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 119.04/119.24 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 119.04/119.24 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 119.04/119.24 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 119.04/119.24 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 119.04/119.24 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 119.04/119.24 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 119.04/119.24 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 119.04/119.30 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 119.04/119.30 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 119.04/119.30 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 119.04/119.30 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 119.04/119.30 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 119.04/119.30 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 119.04/119.30 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 119.04/119.30 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 119.04/119.30 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 119.04/119.30 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 119.04/119.30 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 119.04/119.30 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 119.04/119.30 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 119.04/119.30 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 119.04/119.30 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 119.04/119.30 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 119.04/119.30 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 119.04/119.30 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 119.04/119.30 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 119.04/119.30 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 119.04/119.30 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 119.04/119.30 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 119.04/119.30 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 119.04/119.30 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 119.04/119.30 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 119.04/119.30 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 119.04/119.30 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 119.04/119.30 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 119.04/119.30 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 119.58/119.80 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 119.58/119.80 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 119.58/119.80 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 119.58/119.80 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 119.58/119.80 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 119.58/119.80 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 119.58/119.80 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 119.58/119.80 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 119.58/119.80 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 119.58/119.80 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 119.58/119.80 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 119.58/119.80 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 119.58/119.80 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 119.58/119.80 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 119.58/119.80 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 119.58/119.80 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 119.58/119.80 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 119.58/119.80 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 119.58/119.80 Found x4:(X5 Xx0)
% 119.58/119.80 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 119.58/119.80 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 119.58/119.80 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 119.58/119.80 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 119.58/119.80 Found x4:(X5 Xx0)
% 119.58/119.80 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 119.58/119.80 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 119.58/119.80 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 119.58/119.80 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 119.58/119.80 Found x4:(X5 Xx0)
% 119.58/119.80 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 119.58/119.80 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 119.58/119.80 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 120.47/120.68 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 120.47/120.68 Found x4:(X5 Xx0)
% 120.47/120.68 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 120.47/120.68 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 120.47/120.68 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 120.47/120.68 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 120.47/120.68 Found x4:(X5 Xx0)
% 120.47/120.68 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 120.47/120.68 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 120.47/120.68 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 120.47/120.68 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 120.47/120.68 Found x4:(X5 Xx0)
% 120.47/120.68 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 120.47/120.68 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 120.47/120.68 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 120.47/120.68 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 120.47/120.68 Found x4:(X5 Xx0)
% 120.47/120.68 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 120.47/120.68 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 120.47/120.68 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 120.47/120.68 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 120.47/120.68 Found x4:(X5 Xx0)
% 120.47/120.68 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 120.47/120.68 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 120.47/120.68 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 120.47/120.68 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 120.47/120.68 Found x4:(X5 Xx0)
% 120.47/120.68 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 120.47/120.68 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 120.47/120.68 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 120.47/120.68 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 120.47/120.68 Found x4:(X5 Xx0)
% 120.47/120.68 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 120.47/120.68 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 122.38/122.58 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 122.38/122.58 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 122.38/122.58 Found x4:(X5 Xx0)
% 122.38/122.58 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 122.38/122.58 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 122.38/122.58 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 122.38/122.58 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 122.38/122.58 Found x4:(X5 Xx0)
% 122.38/122.58 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 122.38/122.58 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 122.38/122.58 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 122.38/122.58 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 122.38/122.58 Found x4:(X5 Xx0)
% 122.38/122.58 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 122.38/122.58 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 122.38/122.58 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 122.38/122.58 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 122.38/122.58 Found x4:(X5 Xx0)
% 122.38/122.58 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 122.38/122.58 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 122.38/122.58 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 122.38/122.58 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 122.38/122.58 Found x4:(X5 Xx0)
% 122.38/122.58 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 122.38/122.58 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 122.38/122.58 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 122.38/122.58 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 122.38/122.58 Found x4:(X5 Xx0)
% 122.38/122.58 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 122.38/122.58 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 122.38/122.58 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 122.38/122.58 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 122.73/122.94 Found x4:(X5 Xx0)
% 122.73/122.94 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 122.73/122.94 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 122.73/122.94 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 122.73/122.94 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 122.73/122.94 Found x4:(X5 Xx0)
% 122.73/122.94 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 122.73/122.94 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 122.73/122.94 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 122.73/122.94 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 122.73/122.94 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 122.73/122.94 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 122.73/122.94 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 122.73/122.94 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 122.73/122.94 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 122.73/122.94 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 122.73/122.94 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 122.73/122.94 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 122.73/122.94 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 122.73/122.94 Found x4:(X5 Xx0)
% 122.73/122.94 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 122.73/122.94 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 122.73/122.94 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 122.73/122.94 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 122.73/122.94 Found x4:(X5 Xx0)
% 122.73/122.94 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 122.73/122.94 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 122.73/122.94 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 122.73/122.94 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 122.73/122.94 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 122.73/122.94 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 122.73/122.94 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 122.73/122.94 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 122.73/122.94 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 123.19/123.40 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 123.19/123.40 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 123.19/123.40 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 123.19/123.40 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 123.19/123.40 Found x4:(X5 Xx0)
% 123.19/123.40 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 123.19/123.40 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 123.19/123.40 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 123.19/123.40 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 123.19/123.40 Found x4:(X5 Xx0)
% 123.19/123.40 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 123.19/123.40 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 123.19/123.40 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 123.19/123.40 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 123.19/123.40 Found x4:(X5 Xx0)
% 123.19/123.40 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 123.19/123.40 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 123.19/123.40 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 123.19/123.40 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 123.19/123.40 Found x4:(X5 Xx0)
% 123.19/123.40 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 123.19/123.40 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 123.19/123.40 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 123.19/123.40 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 123.19/123.40 Found x4:(X5 Xx0)
% 123.19/123.40 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 123.19/123.40 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 123.19/123.40 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 123.19/123.40 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 123.19/123.40 Found x4:(X5 Xx0)
% 123.19/123.40 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 123.19/123.40 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 123.58/123.78 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 123.58/123.78 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 123.58/123.78 Found x4:(X5 Xx0)
% 123.58/123.78 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 123.58/123.78 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 123.58/123.78 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 123.58/123.78 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 123.58/123.78 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 123.58/123.78 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 123.58/123.78 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 123.58/123.78 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 123.58/123.78 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 123.58/123.78 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 123.58/123.78 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 123.58/123.78 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 123.58/123.78 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 123.58/123.78 Found x4:(X5 Xx0)
% 123.58/123.78 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 123.58/123.78 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 123.58/123.78 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 123.58/123.78 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 123.58/123.78 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 123.58/123.78 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 123.58/123.78 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 123.58/123.78 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 123.58/123.78 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 123.58/123.78 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 123.58/123.78 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 123.58/123.78 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 123.58/123.78 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 123.58/123.78 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 123.58/123.82 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 123.58/123.82 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 123.58/123.82 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 123.58/123.82 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 123.58/123.82 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 123.58/123.82 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 123.58/123.82 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 123.58/123.82 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 123.58/123.82 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 123.58/123.82 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 123.58/123.82 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 123.58/123.82 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 123.58/123.82 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 123.58/123.82 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 123.58/123.82 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 123.58/123.82 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 123.58/123.82 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 123.58/123.82 Found x6:(X5 Xx0)
% 123.58/123.82 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 123.58/123.82 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 123.58/123.82 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 123.58/123.82 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 123.58/123.82 Found x400:=(x40 x5):((cK x2) Xx)
% 123.58/123.82 Found (x40 x5) as proof of ((cK X5) Xx)
% 123.58/123.82 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 123.58/123.82 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 123.58/123.82 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 123.58/123.82 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 123.58/123.82 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 123.58/123.82 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 123.58/123.82 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 123.58/123.82 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 123.58/123.82 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 123.58/123.82 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 123.58/123.82 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 123.58/123.82 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 123.67/123.91 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 123.67/123.91 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 123.67/123.91 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 123.67/123.91 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 123.67/123.91 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 123.67/123.91 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 123.67/123.91 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 123.67/123.91 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 123.67/123.91 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 123.67/123.91 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 123.67/123.91 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 123.67/123.91 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 123.67/123.91 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 123.67/123.91 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 123.67/123.91 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 123.67/123.91 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 123.67/123.91 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 123.67/123.91 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 123.67/123.91 Found x6:(X5 Xx0)
% 123.67/123.91 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 123.67/123.91 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 123.67/123.91 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 123.67/123.91 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 123.67/123.91 Found x400:=(x40 x5):((cK x2) Xx)
% 123.67/123.91 Found (x40 x5) as proof of ((cK X5) Xx)
% 123.67/123.91 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 123.67/123.91 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 123.67/123.91 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 123.67/123.91 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 123.67/123.91 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 123.67/123.91 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 123.67/123.91 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 123.67/123.91 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 123.67/123.91 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 123.67/123.91 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 123.79/124.01 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 123.79/124.01 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 123.79/124.01 Found x6:(X5 Xx0)
% 123.79/124.01 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 123.79/124.01 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 123.79/124.01 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 123.79/124.01 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 123.79/124.01 Found x400:=(x40 x5):((cK x2) Xx)
% 123.79/124.01 Found (x40 x5) as proof of ((cK X5) Xx)
% 123.79/124.01 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 123.79/124.01 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 123.79/124.01 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 123.79/124.01 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 123.79/124.01 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 123.79/124.01 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 123.79/124.01 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 123.79/124.01 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 123.79/124.01 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 123.79/124.01 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 123.79/124.01 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 123.79/124.01 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 123.79/124.01 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 123.79/124.01 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 123.79/124.01 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 123.79/124.01 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 123.79/124.01 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 123.79/124.01 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 123.79/124.01 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 123.79/124.01 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 123.79/124.01 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 123.79/124.01 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 123.79/124.01 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 123.79/124.01 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 123.79/124.01 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 123.79/124.01 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 123.87/124.10 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 123.87/124.10 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 123.87/124.10 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 123.87/124.10 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 123.87/124.10 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 123.87/124.10 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 123.87/124.10 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 123.87/124.10 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 123.87/124.10 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 123.87/124.10 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 123.87/124.10 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 123.87/124.10 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 123.87/124.10 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 123.87/124.10 Found x6:(X5 Xx0)
% 123.87/124.10 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 123.87/124.10 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 123.87/124.10 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 123.87/124.10 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 123.87/124.10 Found x400:=(x40 x5):((cK x2) Xx)
% 123.87/124.10 Found (x40 x5) as proof of ((cK X5) Xx)
% 123.87/124.10 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 123.87/124.10 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 123.87/124.10 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 123.87/124.10 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 123.87/124.10 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 123.87/124.10 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 123.87/124.10 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 123.87/124.10 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 123.87/124.10 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 123.87/124.10 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 123.87/124.10 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 123.87/124.10 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 123.87/124.10 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 123.87/124.10 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 123.96/124.18 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 123.96/124.18 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 123.96/124.18 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 123.96/124.18 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 123.96/124.18 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 123.96/124.18 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 123.96/124.18 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 123.96/124.18 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 123.96/124.18 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 123.96/124.18 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 123.96/124.18 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 123.96/124.18 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 123.96/124.18 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 123.96/124.18 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 123.96/124.18 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 123.96/124.18 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 123.96/124.18 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 123.96/124.18 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 123.96/124.18 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 123.96/124.18 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 123.96/124.18 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 123.96/124.18 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 123.96/124.18 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 123.96/124.18 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 123.96/124.18 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 123.96/124.18 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 123.96/124.18 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 123.96/124.18 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 123.96/124.18 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 123.96/124.18 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 123.96/124.18 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 123.96/124.18 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 124.03/124.30 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 124.03/124.30 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 124.03/124.30 Found x6:(X5 Xx0)
% 124.03/124.30 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 124.03/124.30 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 124.03/124.30 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 124.03/124.30 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 124.03/124.30 Found x400:=(x40 x5):((cK x2) Xx)
% 124.03/124.30 Found (x40 x5) as proof of ((cK X5) Xx)
% 124.03/124.30 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 124.03/124.30 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 124.03/124.30 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 124.03/124.30 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 124.03/124.30 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 124.03/124.30 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 124.03/124.30 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 124.03/124.30 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 124.03/124.30 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 124.03/124.30 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 124.03/124.30 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 124.03/124.30 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 124.03/124.30 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 124.03/124.30 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 124.03/124.30 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 124.03/124.30 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 124.03/124.30 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 124.03/124.30 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 124.03/124.30 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 124.03/124.30 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 124.03/124.30 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 124.03/124.30 Found x6:(X5 Xx0)
% 124.03/124.30 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 124.03/124.30 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 124.03/124.30 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 124.24/124.49 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 124.24/124.49 Found x400:=(x40 x5):((cK x2) Xx)
% 124.24/124.49 Found (x40 x5) as proof of ((cK X5) Xx)
% 124.24/124.49 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 124.24/124.49 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 124.24/124.49 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 124.24/124.49 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 124.24/124.49 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 124.24/124.49 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 124.24/124.49 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 124.24/124.49 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 124.24/124.49 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 124.24/124.49 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 124.24/124.49 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 124.24/124.49 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 124.24/124.49 Found x6:(X5 Xx0)
% 124.24/124.49 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 124.24/124.49 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 124.24/124.49 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 124.24/124.49 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 124.24/124.49 Found x400:=(x40 x5):((cK x2) Xx)
% 124.24/124.49 Found (x40 x5) as proof of ((cK X5) Xx)
% 124.24/124.49 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 124.24/124.49 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 124.24/124.49 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 124.24/124.49 Found x6:(X5 Xx0)
% 124.24/124.49 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 124.24/124.49 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 124.24/124.49 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 124.24/124.49 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 124.24/124.49 Found x400:=(x40 x5):((cK x2) Xx)
% 124.24/124.49 Found (x40 x5) as proof of ((cK X5) Xx)
% 124.24/124.49 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 124.24/124.49 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 124.24/124.49 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 124.24/124.49 Found x6:(X5 Xx0)
% 124.24/124.49 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 124.24/124.49 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 124.24/124.49 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 124.24/124.49 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 124.24/124.49 Found x400:=(x40 x5):((cK x2) Xx)
% 124.24/124.49 Found (x40 x5) as proof of ((cK X5) Xx)
% 124.24/124.49 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 124.24/124.49 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 124.33/124.56 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 124.33/124.56 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 124.33/124.56 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 124.33/124.56 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 124.33/124.56 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 124.33/124.56 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 124.33/124.56 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 124.33/124.56 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 124.33/124.56 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 124.33/124.56 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 124.33/124.56 Found x6:(X5 Xx0)
% 124.33/124.56 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 124.33/124.56 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 124.33/124.56 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 124.33/124.56 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 124.33/124.56 Found x400:=(x40 x5):((cK x2) Xx)
% 124.33/124.56 Found (x40 x5) as proof of ((cK X5) Xx)
% 124.33/124.56 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 124.33/124.56 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 124.33/124.56 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 124.33/124.56 Found x6:(X5 Xx0)
% 124.33/124.56 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 124.33/124.56 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 124.33/124.56 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 124.33/124.56 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 124.33/124.56 Found x400:=(x40 x5):((cK x2) Xx)
% 124.33/124.56 Found (x40 x5) as proof of ((cK X5) Xx)
% 124.33/124.56 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 124.33/124.56 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 124.33/124.56 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 124.33/124.56 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 124.33/124.56 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 124.33/124.56 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 124.33/124.56 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 124.33/124.56 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 124.33/124.56 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 124.33/124.56 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 124.33/124.56 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 124.33/124.56 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 124.33/124.56 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 124.39/124.63 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 124.39/124.63 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 124.39/124.63 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 124.39/124.63 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 124.39/124.63 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 124.39/124.63 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 124.39/124.63 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 124.39/124.63 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 124.39/124.63 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 124.39/124.63 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 124.39/124.63 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 124.39/124.63 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 124.39/124.63 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 124.39/124.63 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 124.39/124.63 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 124.39/124.63 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 124.39/124.63 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 124.39/124.63 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 124.39/124.63 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 124.39/124.63 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 124.39/124.63 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 124.39/124.63 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 124.39/124.63 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 124.39/124.63 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 124.39/124.63 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 124.39/124.63 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 124.39/124.63 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 124.39/124.63 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 124.39/124.63 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 124.39/124.63 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 124.39/124.63 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 124.39/124.63 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 124.39/124.63 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 124.56/124.78 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 124.56/124.78 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 124.56/124.78 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 124.56/124.78 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 124.56/124.78 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 124.56/124.78 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 124.56/124.78 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 124.56/124.78 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 124.56/124.78 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 124.56/124.78 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 124.56/124.78 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 124.56/124.78 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 124.56/124.78 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 124.56/124.78 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 124.56/124.78 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 124.56/124.78 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 124.56/124.78 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 124.56/124.78 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 124.56/124.78 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 124.56/124.78 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 124.56/124.78 Found x6:(X5 Xx0)
% 124.56/124.78 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 124.56/124.78 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 124.56/124.78 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 124.56/124.78 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 124.56/124.78 Found x400:=(x40 x5):((cK x2) Xx)
% 124.56/124.78 Found (x40 x5) as proof of ((cK X5) Xx)
% 124.56/124.78 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 124.56/124.78 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 124.56/124.78 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 124.56/124.78 Found x6:(X5 Xx0)
% 124.56/124.78 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 124.56/124.78 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 124.73/124.95 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 124.73/124.95 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 124.73/124.95 Found x400:=(x40 x5):((cK x2) Xx)
% 124.73/124.95 Found (x40 x5) as proof of ((cK X5) Xx)
% 124.73/124.95 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 124.73/124.95 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 124.73/124.95 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 124.73/124.95 Found x6:(X5 Xx0)
% 124.73/124.95 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 124.73/124.95 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 124.73/124.95 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 124.73/124.95 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 124.73/124.95 Found x400:=(x40 x5):((cK x2) Xx)
% 124.73/124.95 Found (x40 x5) as proof of ((cK X5) Xx)
% 124.73/124.95 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 124.73/124.95 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 124.73/124.95 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 124.73/124.95 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 124.73/124.95 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 124.73/124.95 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 124.73/124.95 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 124.73/124.95 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 124.73/124.95 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 124.73/124.95 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 124.73/124.95 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 124.73/124.95 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 124.73/124.95 Found x6:(X5 Xx0)
% 124.73/124.95 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 124.73/124.95 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 124.73/124.95 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 124.73/124.95 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 124.73/124.95 Found x400:=(x40 x5):((cK x2) Xx)
% 124.73/124.95 Found (x40 x5) as proof of ((cK X5) Xx)
% 124.73/124.95 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 124.73/124.95 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 124.73/124.95 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 124.73/124.95 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 124.73/124.95 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 124.73/124.95 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 124.73/124.95 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 124.73/124.95 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 124.73/124.95 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 124.73/124.95 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 124.73/124.95 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 124.78/125.00 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 124.78/125.00 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 124.78/125.00 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 124.78/125.00 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 124.78/125.00 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 124.78/125.00 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 124.78/125.00 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 124.78/125.00 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 124.78/125.00 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 124.78/125.00 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 124.78/125.00 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 124.78/125.00 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 124.78/125.00 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 124.78/125.00 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 124.78/125.00 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 124.78/125.00 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 124.78/125.00 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 124.78/125.00 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 124.78/125.00 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 124.78/125.00 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 124.78/125.00 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 124.78/125.00 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 124.78/125.00 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 124.78/125.00 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 124.78/125.00 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 124.78/125.00 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 124.78/125.00 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 124.78/125.00 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 124.78/125.00 Found x6:(X5 Xx0)
% 124.78/125.00 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 125.36/125.62 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 125.36/125.62 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 125.36/125.62 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 125.36/125.62 Found x400:=(x40 x5):((cK x2) Xx)
% 125.36/125.62 Found (x40 x5) as proof of ((cK X5) Xx)
% 125.36/125.62 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 125.36/125.62 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 125.36/125.62 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 125.36/125.62 Found x4:(X5 Xx0)
% 125.36/125.62 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 125.36/125.62 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 125.36/125.62 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 125.36/125.62 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 125.36/125.62 Found x4:(X5 Xx0)
% 125.36/125.62 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 125.36/125.62 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 125.36/125.62 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 125.36/125.62 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 125.36/125.62 Found x4:(X5 Xx0)
% 125.36/125.62 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 125.36/125.62 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 125.36/125.62 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 125.36/125.62 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 125.36/125.62 Found x4:(X5 Xx0)
% 125.36/125.62 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 125.36/125.62 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 125.36/125.62 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 125.36/125.62 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 125.36/125.62 Found x4:(X5 Xx0)
% 125.36/125.62 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 125.36/125.62 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 125.36/125.62 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 125.36/125.62 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 125.36/125.62 Found x4:(X5 Xx0)
% 125.36/125.62 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 125.36/125.62 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 127.73/127.96 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 127.73/127.96 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 127.73/127.96 Found x4:(X5 Xx0)
% 127.73/127.96 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 127.73/127.96 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 127.73/127.96 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 127.73/127.96 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 127.73/127.96 Found x4:(X5 Xx0)
% 127.73/127.96 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 127.73/127.96 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 127.73/127.96 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 127.73/127.96 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 127.73/127.96 Found x4:(X5 Xx0)
% 127.73/127.96 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 127.73/127.96 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 127.73/127.96 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 127.73/127.96 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 127.73/127.96 Found x4:(X5 Xx0)
% 127.73/127.96 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 127.73/127.96 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 127.73/127.96 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 127.73/127.96 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 127.73/127.96 Found x4:(X5 Xx0)
% 127.73/127.96 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 127.73/127.96 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 127.73/127.96 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 127.73/127.96 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 127.73/127.96 Found x4:(X5 Xx0)
% 127.73/127.96 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 127.73/127.96 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 127.73/127.96 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 127.73/127.96 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 128.29/128.53 Found x4:(X5 Xx0)
% 128.29/128.53 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 128.29/128.53 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 128.29/128.53 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 128.29/128.53 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 128.29/128.53 Found x4:(X5 Xx0)
% 128.29/128.53 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 128.29/128.53 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 128.29/128.53 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 128.29/128.53 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 128.29/128.53 Found x4:(X5 Xx0)
% 128.29/128.53 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 128.29/128.53 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 128.29/128.53 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 128.29/128.53 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 128.29/128.53 Found x4:(X5 Xx0)
% 128.29/128.53 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 128.29/128.53 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 128.29/128.53 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 128.29/128.53 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 128.29/128.53 Found x4:(X5 Xx0)
% 128.29/128.53 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 128.29/128.53 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 128.29/128.53 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 128.29/128.53 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 128.29/128.53 Found x4:(X5 Xx0)
% 128.29/128.53 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 128.29/128.53 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 128.29/128.53 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 128.29/128.53 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 128.29/128.53 Found x4:(X5 Xx0)
% 128.29/128.53 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 128.29/128.53 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 128.29/128.53 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 128.76/129.02 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 128.76/129.02 Found x4:(X5 Xx0)
% 128.76/129.02 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 128.76/129.02 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 128.76/129.02 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 128.76/129.02 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 128.76/129.02 Found x4:(X5 Xx0)
% 128.76/129.02 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 128.76/129.02 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 128.76/129.02 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 128.76/129.02 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 128.76/129.02 Found x4:(X5 Xx0)
% 128.76/129.02 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 128.76/129.02 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 128.76/129.02 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 128.76/129.02 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 128.76/129.02 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 128.76/129.02 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 128.76/129.02 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 128.76/129.02 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 128.76/129.02 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 128.76/129.02 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 128.76/129.02 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 128.76/129.02 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 128.76/129.02 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 128.76/129.02 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 128.76/129.02 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 128.76/129.02 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 128.76/129.02 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 128.76/129.02 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 128.76/129.02 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 128.76/129.02 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 128.76/129.02 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 128.85/129.09 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 128.85/129.09 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 128.85/129.09 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 128.85/129.09 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 128.85/129.09 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 128.85/129.09 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 128.85/129.09 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 128.85/129.09 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 128.85/129.09 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 128.85/129.09 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 128.85/129.09 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 128.85/129.09 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 128.85/129.09 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 128.85/129.09 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 128.85/129.09 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 128.85/129.09 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 128.85/129.09 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 128.85/129.09 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 128.85/129.09 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 128.85/129.09 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 128.85/129.09 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 128.85/129.09 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 128.85/129.09 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 128.85/129.09 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 128.85/129.09 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 128.85/129.09 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 128.85/129.09 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 128.85/129.09 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 128.85/129.09 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 128.85/129.09 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 128.85/129.09 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 128.85/129.09 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 128.94/129.20 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 128.94/129.20 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 128.94/129.20 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 128.94/129.20 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 128.94/129.20 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 128.94/129.20 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 128.94/129.20 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 128.94/129.20 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 128.94/129.20 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 128.94/129.20 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 128.94/129.20 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 128.94/129.20 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 128.94/129.20 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 128.94/129.20 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 128.94/129.20 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 128.94/129.20 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 128.94/129.20 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 128.94/129.20 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 128.94/129.20 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 128.94/129.20 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 128.94/129.20 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 128.94/129.20 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 128.94/129.20 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 128.94/129.20 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 128.94/129.20 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 128.94/129.20 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 128.94/129.20 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 128.94/129.20 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 128.94/129.20 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 128.94/129.20 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 128.94/129.20 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.22/129.51 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.22/129.51 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 129.22/129.51 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 129.22/129.51 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 129.22/129.51 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 129.22/129.51 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 129.22/129.51 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.22/129.51 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.22/129.51 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.22/129.51 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.22/129.51 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 129.22/129.51 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 129.22/129.51 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 129.22/129.51 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 129.22/129.51 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 129.22/129.51 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.22/129.51 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.22/129.51 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.22/129.51 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.22/129.51 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 129.22/129.51 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 129.22/129.51 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 129.22/129.51 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 129.22/129.51 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 129.22/129.51 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.22/129.51 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.22/129.51 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.22/129.51 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.22/129.51 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 129.22/129.51 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 129.29/129.54 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 129.29/129.54 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 129.29/129.54 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 129.29/129.54 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.29/129.54 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.29/129.54 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.29/129.54 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.29/129.54 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 129.29/129.54 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 129.29/129.54 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 129.29/129.54 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 129.29/129.54 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 129.29/129.54 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.29/129.54 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.29/129.54 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.29/129.54 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.29/129.54 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 129.29/129.54 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 129.29/129.54 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 129.29/129.54 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 129.29/129.54 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 129.29/129.54 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.29/129.54 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.29/129.54 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.29/129.54 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.29/129.54 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 129.29/129.54 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 129.29/129.54 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 129.29/129.54 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 129.29/129.54 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 129.29/129.54 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.29/129.54 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.29/129.56 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.29/129.56 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.29/129.56 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 129.29/129.56 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 129.29/129.56 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 129.29/129.56 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 129.29/129.56 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 129.29/129.56 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.29/129.56 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.29/129.56 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.29/129.56 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.29/129.56 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 129.29/129.56 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 129.29/129.56 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 129.29/129.56 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 129.29/129.56 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 129.29/129.56 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.29/129.56 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.29/129.56 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.29/129.56 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.29/129.56 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 129.29/129.56 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 129.29/129.56 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 129.29/129.56 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 129.29/129.56 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 129.29/129.56 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.29/129.56 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.29/129.56 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.29/129.56 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.36/129.60 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 129.36/129.60 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 129.36/129.60 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 129.36/129.60 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 129.36/129.60 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 129.36/129.60 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.36/129.60 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.36/129.60 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.36/129.60 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.36/129.60 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 129.36/129.60 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 129.36/129.60 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 129.36/129.60 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 129.36/129.60 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 129.36/129.60 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.36/129.60 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.36/129.60 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.36/129.60 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.36/129.60 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 129.36/129.60 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 129.36/129.60 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 129.36/129.60 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 129.36/129.60 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 129.36/129.60 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.36/129.60 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.36/129.60 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.36/129.60 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.36/129.60 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 129.36/129.60 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 129.36/129.60 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 129.36/129.60 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 129.36/129.60 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 129.36/129.60 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.36/129.60 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.36/129.65 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.36/129.65 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.36/129.65 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 129.36/129.65 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 129.36/129.65 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 129.36/129.65 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 129.36/129.65 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 129.36/129.65 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.36/129.65 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.36/129.65 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.36/129.65 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.36/129.65 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 129.36/129.65 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 129.36/129.65 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 129.36/129.65 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 129.36/129.65 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 129.36/129.65 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.36/129.65 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.36/129.65 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.36/129.65 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.36/129.65 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 129.36/129.65 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 129.36/129.65 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 129.36/129.65 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 129.36/129.65 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 129.36/129.65 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.36/129.65 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.36/129.65 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.36/129.65 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.52/129.77 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 129.52/129.77 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 129.52/129.77 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 129.52/129.77 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 129.52/129.77 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 129.52/129.77 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.52/129.77 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.52/129.77 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.52/129.77 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.52/129.77 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 129.52/129.77 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 129.52/129.77 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 129.52/129.77 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 129.52/129.77 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 129.52/129.77 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.52/129.77 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.52/129.77 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.52/129.77 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.52/129.77 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 129.52/129.77 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 129.52/129.77 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 129.52/129.77 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 129.52/129.77 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 129.52/129.77 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.52/129.77 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.52/129.77 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.52/129.77 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.52/129.77 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 129.52/129.77 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 129.52/129.77 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 129.52/129.77 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 129.52/129.77 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 129.52/129.77 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.61/129.84 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.61/129.84 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.61/129.84 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.61/129.84 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 129.61/129.84 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 129.61/129.84 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 129.61/129.84 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 129.61/129.84 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 129.61/129.84 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.61/129.84 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.61/129.84 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.61/129.84 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.61/129.84 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 129.61/129.84 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 129.61/129.84 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 129.61/129.84 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 129.61/129.84 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 129.61/129.84 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.61/129.84 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.61/129.84 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.61/129.84 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.61/129.84 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 129.61/129.84 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 129.61/129.84 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 129.61/129.84 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 129.61/129.84 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 129.61/129.84 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.61/129.84 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.61/129.84 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.61/129.84 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.81/130.07 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 129.81/130.07 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 129.81/130.07 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 129.81/130.07 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 129.81/130.07 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 129.81/130.07 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.81/130.07 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.81/130.07 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.81/130.07 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.81/130.07 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 129.81/130.07 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 129.81/130.07 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 129.81/130.07 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 129.81/130.07 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 129.81/130.07 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.81/130.07 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.81/130.07 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.81/130.07 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 129.81/130.07 Found x6:(X5 Xx0)
% 129.81/130.07 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 129.81/130.07 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 129.81/130.07 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 129.81/130.07 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 129.81/130.07 Found x400:=(x40 x5):((cK x2) Xx)
% 129.81/130.07 Found (x40 x5) as proof of ((cK X5) Xx)
% 129.81/130.07 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 129.81/130.07 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 129.81/130.07 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 129.81/130.07 Found x6:(X5 Xx0)
% 129.81/130.07 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 129.81/130.07 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 129.81/130.07 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 129.81/130.07 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 129.81/130.07 Found x400:=(x40 x5):((cK x2) Xx)
% 129.81/130.07 Found (x40 x5) as proof of ((cK X5) Xx)
% 130.21/130.48 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 130.21/130.48 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 130.21/130.48 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 130.21/130.48 Found x6:(X5 Xx0)
% 130.21/130.48 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 130.21/130.48 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 130.21/130.48 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 130.21/130.48 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 130.21/130.48 Found x400:=(x40 x5):((cK x2) Xx)
% 130.21/130.48 Found (x40 x5) as proof of ((cK X5) Xx)
% 130.21/130.48 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 130.21/130.48 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 130.21/130.48 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 130.21/130.48 Found x6:(X5 Xx0)
% 130.21/130.48 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 130.21/130.48 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 130.21/130.48 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 130.21/130.48 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 130.21/130.48 Found x400:=(x40 x5):((cK x2) Xx)
% 130.21/130.48 Found (x40 x5) as proof of ((cK X5) Xx)
% 130.21/130.48 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 130.21/130.48 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 130.21/130.48 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 130.21/130.48 Found x6:(X5 Xx0)
% 130.21/130.48 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 130.21/130.48 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 130.21/130.48 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 130.21/130.48 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 130.21/130.48 Found x400:=(x40 x5):((cK x2) Xx)
% 130.21/130.48 Found (x40 x5) as proof of ((cK X5) Xx)
% 130.21/130.48 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 130.21/130.48 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 130.21/130.48 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 130.21/130.48 Found x6:(X5 Xx0)
% 130.21/130.48 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 130.21/130.48 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 130.21/130.48 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 130.21/130.48 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 130.21/130.48 Found x400:=(x40 x5):((cK x2) Xx)
% 130.21/130.48 Found (x40 x5) as proof of ((cK X5) Xx)
% 130.21/130.48 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 130.21/130.48 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 130.21/130.48 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 130.21/130.48 Found x4:(X5 Xx0)
% 130.21/130.48 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 130.21/130.48 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 130.21/130.48 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 130.21/130.48 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 130.21/130.48 Found x4:(X5 Xx0)
% 130.21/130.48 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 132.48/132.72 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 132.48/132.72 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 132.48/132.72 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 132.48/132.72 Found x4:(X5 Xx0)
% 132.48/132.72 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 132.48/132.72 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 132.48/132.72 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 132.48/132.72 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 132.48/132.72 Found x4:(X5 Xx0)
% 132.48/132.72 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 132.48/132.72 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 132.48/132.72 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 132.48/132.72 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 132.48/132.72 Found x4:(X5 Xx0)
% 132.48/132.72 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 132.48/132.72 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 132.48/132.72 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 132.48/132.72 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 132.48/132.72 Found x4:(X5 Xx0)
% 132.48/132.72 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 132.48/132.72 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 132.48/132.72 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 132.48/132.72 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 132.48/132.72 Found x4:(X5 Xx0)
% 132.48/132.72 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 132.48/132.72 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 132.48/132.72 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 132.48/132.72 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 132.48/132.72 Found x4:(X5 Xx0)
% 132.48/132.72 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 132.48/132.72 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 132.48/132.72 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 133.21/133.47 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 133.21/133.47 Found x4:(X5 Xx0)
% 133.21/133.47 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 133.21/133.47 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 133.21/133.47 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 133.21/133.47 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 133.21/133.47 Found x4:(X5 Xx0)
% 133.21/133.47 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 133.21/133.47 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 133.21/133.47 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 133.21/133.47 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 133.21/133.47 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 133.21/133.47 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 133.21/133.47 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 133.21/133.47 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 133.21/133.47 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 133.21/133.47 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 133.21/133.47 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 133.21/133.47 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 133.21/133.47 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 133.21/133.47 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 133.21/133.47 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 133.21/133.47 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 133.21/133.47 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 133.21/133.47 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 133.21/133.47 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 133.21/133.47 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 133.21/133.47 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 133.21/133.47 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 133.21/133.47 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 133.21/133.47 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 133.21/133.47 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 133.21/133.47 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 133.21/133.47 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 133.37/133.59 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 133.37/133.59 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 133.37/133.59 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 133.37/133.59 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 133.37/133.59 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 133.37/133.59 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 133.37/133.59 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 133.37/133.59 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 133.37/133.59 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 133.37/133.59 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 133.37/133.59 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 133.37/133.59 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 133.37/133.59 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 133.37/133.59 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 133.37/133.59 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 133.37/133.59 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 133.37/133.59 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 133.37/133.59 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 133.37/133.59 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 133.37/133.59 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 133.37/133.59 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 133.37/133.59 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 133.37/133.59 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 133.37/133.59 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 133.37/133.59 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 133.37/133.59 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 133.37/133.59 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 133.37/133.59 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 133.37/133.59 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 133.37/133.59 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 133.52/133.77 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 133.52/133.77 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 133.52/133.77 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 133.52/133.77 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 133.52/133.77 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 133.52/133.77 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 133.52/133.77 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 133.52/133.77 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 133.52/133.77 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 133.52/133.77 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 133.52/133.77 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 133.52/133.77 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 133.52/133.77 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 133.52/133.77 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 133.52/133.77 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 133.52/133.77 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 133.52/133.77 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 133.52/133.77 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 133.52/133.77 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 133.52/133.77 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 133.52/133.77 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 133.52/133.77 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 133.52/133.77 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 133.52/133.77 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 133.52/133.77 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 133.52/133.77 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 133.52/133.77 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 133.52/133.77 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 133.52/133.77 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 133.52/133.77 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 133.52/133.77 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 133.52/133.77 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 133.52/133.78 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 133.52/133.78 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 133.52/133.78 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 133.52/133.78 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 133.52/133.78 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 133.52/133.78 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 133.52/133.78 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 133.52/133.78 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 133.52/133.78 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 133.52/133.78 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 133.52/133.78 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 133.52/133.78 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 133.52/133.78 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 133.52/133.78 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 133.52/133.78 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 133.52/133.78 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 133.52/133.78 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 133.52/133.78 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 133.52/133.78 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 133.52/133.78 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 133.52/133.78 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 133.52/133.78 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 133.52/133.78 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 133.52/133.78 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 133.52/133.78 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 133.52/133.78 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 133.52/133.78 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 133.52/133.78 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 133.52/133.78 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 133.52/133.78 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 133.52/133.78 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 133.52/133.80 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 133.52/133.80 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 133.52/133.80 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 133.52/133.80 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 133.52/133.80 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 133.52/133.80 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 133.52/133.80 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 133.52/133.80 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 133.52/133.80 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 133.52/133.80 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 133.52/133.80 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 133.52/133.80 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 133.52/133.80 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 133.52/133.80 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 133.52/133.80 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 133.52/133.80 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 133.52/133.80 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 133.52/133.80 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 133.52/133.80 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 133.52/133.80 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 133.52/133.80 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 133.52/133.80 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 133.52/133.80 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 133.52/133.80 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 133.52/133.80 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 133.52/133.80 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 133.52/133.80 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 133.52/133.80 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 133.52/133.80 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 133.52/133.80 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 133.84/134.09 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 133.84/134.09 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 133.84/134.09 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 133.84/134.09 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 133.84/134.09 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 133.84/134.09 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 133.84/134.09 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 133.84/134.09 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 133.84/134.09 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 133.84/134.09 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 133.84/134.09 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 133.84/134.09 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 133.84/134.09 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 133.84/134.09 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 133.84/134.09 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 133.84/134.09 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 133.84/134.09 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 133.84/134.09 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 133.84/134.09 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 133.84/134.09 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 133.84/134.09 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 133.84/134.09 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 133.84/134.09 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 133.84/134.09 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 133.84/134.09 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 133.84/134.09 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 133.84/134.09 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 133.84/134.09 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 133.84/134.09 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 133.84/134.09 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 133.84/134.09 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 133.84/134.09 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 136.40/136.69 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 136.40/136.69 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 136.40/136.69 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 136.40/136.69 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 136.40/136.69 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 136.40/136.69 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 136.40/136.69 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 136.40/136.69 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 136.40/136.69 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 136.40/136.69 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 136.40/136.69 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 136.40/136.69 Found x4:(X5 Xx0)
% 136.40/136.69 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 136.40/136.69 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 136.40/136.69 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 136.40/136.69 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 136.40/136.69 Found x6:(X5 Xx0)
% 136.40/136.69 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 136.40/136.69 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 136.40/136.69 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 136.40/136.69 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 136.40/136.69 Found x400:=(x40 x5):((cK x2) Xx)
% 136.40/136.69 Found (x40 x5) as proof of ((cK X5) Xx)
% 136.40/136.69 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 136.40/136.69 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 136.40/136.69 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 136.40/136.69 Found x4:(X5 Xx0)
% 136.40/136.69 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 136.40/136.69 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 136.40/136.69 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 136.40/136.69 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 136.40/136.69 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 136.40/136.69 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 136.40/136.69 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 136.40/136.69 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 136.40/136.69 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 136.59/136.91 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 136.59/136.91 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 136.59/136.91 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 136.59/136.91 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 136.59/136.91 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 136.59/136.91 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 136.59/136.91 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 136.59/136.91 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 136.59/136.91 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 136.59/136.91 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 136.59/136.91 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 136.59/136.91 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 136.59/136.91 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 136.59/136.91 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 136.59/136.91 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 136.59/136.91 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 136.59/136.91 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 136.59/136.91 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 136.59/136.91 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 136.59/136.91 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 136.59/136.91 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 136.59/136.91 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 136.59/136.91 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 136.59/136.91 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 136.59/136.91 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 136.59/136.91 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 136.59/136.91 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 136.59/136.91 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 136.59/136.91 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 136.59/136.91 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 137.68/137.93 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 137.68/137.93 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 137.68/137.93 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 137.68/137.93 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 137.68/137.93 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 137.68/137.93 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 137.68/137.93 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 137.68/137.93 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 137.68/137.93 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 137.68/137.93 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 137.68/137.93 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 137.68/137.93 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 137.68/137.93 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 137.68/137.93 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 137.68/137.93 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 137.68/137.93 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 137.68/137.93 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 137.68/137.93 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 137.68/137.93 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 137.68/137.93 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 137.68/137.93 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 137.68/137.93 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 137.68/137.93 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 137.68/137.93 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 137.68/137.93 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 137.68/137.93 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 137.68/137.93 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 137.68/137.93 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 137.68/137.93 Found x4:(X5 Xx0)
% 137.68/137.93 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 137.68/137.93 Found (fun (x4:(X5 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 142.35/142.60 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 142.35/142.60 Found (fun (Xx0:a) (x4:(X5 Xx0))=> x4) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 142.35/142.60 Found x6:(X5 Xx0)
% 142.35/142.60 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 142.35/142.60 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 142.35/142.60 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 142.35/142.60 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 142.35/142.60 Found x400:=(x40 x5):((cK x1) Xx)
% 142.35/142.60 Found (x40 x5) as proof of ((cK X5) Xx)
% 142.35/142.60 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 142.35/142.60 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 142.35/142.60 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 142.35/142.60 Found x6:(X5 Xx0)
% 142.35/142.60 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 142.35/142.60 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 142.35/142.60 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 142.35/142.60 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 142.35/142.60 Found x400:=(x40 x5):((cK x2) Xx)
% 142.35/142.60 Found (x40 x5) as proof of ((cK X5) Xx)
% 142.35/142.60 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 142.35/142.60 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 142.35/142.60 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 142.35/142.60 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 142.35/142.60 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 142.35/142.60 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 142.35/142.60 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 142.35/142.60 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 142.35/142.60 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 142.35/142.60 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 142.35/142.60 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 142.35/142.60 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 142.35/142.60 Found x6:(X5 Xx0)
% 142.35/142.60 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 142.35/142.60 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 142.35/142.60 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 142.35/142.60 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 142.35/142.60 Found x400:=(x40 x5):((cK x1) Xx)
% 142.35/142.60 Found (x40 x5) as proof of ((cK X5) Xx)
% 142.35/142.60 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 142.35/142.60 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 142.35/142.60 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 142.35/142.60 Found x6:(X5 Xx0)
% 148.18/148.43 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 148.18/148.43 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 148.18/148.43 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 148.18/148.43 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 148.18/148.43 Found x400:=(x40 x5):((cK x2) Xx)
% 148.18/148.43 Found (x40 x5) as proof of ((cK X5) Xx)
% 148.18/148.43 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 148.18/148.43 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 148.18/148.43 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 148.18/148.43 Found x6:(X5 Xx0)
% 148.18/148.43 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 148.18/148.43 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 148.18/148.43 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 148.18/148.43 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 148.18/148.43 Found x400:=(x40 x5):((cK x1) Xx)
% 148.18/148.43 Found (x40 x5) as proof of ((cK X5) Xx)
% 148.18/148.43 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 148.18/148.43 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 148.18/148.43 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 148.18/148.43 Found x6:(X5 Xx0)
% 148.18/148.43 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 148.18/148.43 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 148.18/148.43 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 148.18/148.43 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 148.18/148.43 Found x400:=(x40 x5):((cK x2) Xx)
% 148.18/148.43 Found (x40 x5) as proof of ((cK X5) Xx)
% 148.18/148.43 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 148.18/148.43 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 148.18/148.43 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 148.18/148.43 Found x6:(X5 Xx0)
% 148.18/148.43 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 148.18/148.43 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 148.18/148.43 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 148.18/148.43 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 148.18/148.43 Found x400:=(x40 x5):((cK x2) Xx)
% 148.18/148.43 Found (x40 x5) as proof of ((cK X5) Xx)
% 148.18/148.43 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 148.18/148.43 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 148.18/148.43 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 148.18/148.43 Found x6:(X5 Xx0)
% 148.18/148.43 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 148.18/148.43 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 148.18/148.43 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 148.18/148.43 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 148.18/148.43 Found x400:=(x40 x5):((cK x1) Xx)
% 148.18/148.43 Found (x40 x5) as proof of ((cK X5) Xx)
% 148.18/148.43 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 148.18/148.43 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 148.18/148.43 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 150.68/150.97 Found x6:(X5 Xx0)
% 150.68/150.97 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 150.68/150.97 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 150.68/150.97 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 150.68/150.97 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 150.68/150.97 Found x400:=(x40 x5):((cK x2) Xx)
% 150.68/150.97 Found (x40 x5) as proof of ((cK X5) Xx)
% 150.68/150.97 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 150.68/150.97 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 150.68/150.97 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 150.68/150.97 Found x6:(X5 Xx0)
% 150.68/150.97 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 150.68/150.97 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 150.68/150.97 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 150.68/150.97 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 150.68/150.97 Found x400:=(x40 x5):((cK x2) Xx)
% 150.68/150.97 Found (x40 x5) as proof of ((cK X5) Xx)
% 150.68/150.97 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 150.68/150.97 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 150.68/150.97 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 150.68/150.97 Found x6:(X5 Xx0)
% 150.68/150.97 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 150.68/150.97 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 150.68/150.97 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 150.68/150.97 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 150.68/150.97 Found x400:=(x40 x5):((cK x2) Xx)
% 150.68/150.97 Found (x40 x5) as proof of ((cK X5) Xx)
% 150.68/150.97 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 150.68/150.97 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 150.68/150.97 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 150.68/150.97 Found x6:(X5 Xx0)
% 150.68/150.97 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 150.68/150.97 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 150.68/150.97 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 150.68/150.97 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 150.68/150.97 Found x400:=(x40 x5):((cK x1) Xx)
% 150.68/150.97 Found (x40 x5) as proof of ((cK X5) Xx)
% 150.68/150.97 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 150.68/150.97 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 150.68/150.97 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 150.68/150.97 Found x6:(X5 Xx0)
% 150.68/150.97 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 150.68/150.97 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 150.68/150.97 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 150.68/150.97 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 150.68/150.97 Found x400:=(x40 x5):((cK x2) Xx)
% 150.68/150.97 Found (x40 x5) as proof of ((cK X5) Xx)
% 150.68/150.97 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 150.68/150.97 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 151.78/152.02 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 151.78/152.02 Found x6:(X5 Xx0)
% 151.78/152.02 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 151.78/152.02 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 151.78/152.02 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 151.78/152.02 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 151.78/152.02 Found x400:=(x40 x5):((cK x2) Xx)
% 151.78/152.02 Found (x40 x5) as proof of ((cK X5) Xx)
% 151.78/152.02 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 151.78/152.02 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 151.78/152.02 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 151.78/152.02 Found x6:(X5 Xx0)
% 151.78/152.02 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 151.78/152.02 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 151.78/152.02 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 151.78/152.02 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 151.78/152.02 Found x400:=(x40 x5):((cK x2) Xx)
% 151.78/152.02 Found (x40 x5) as proof of ((cK X5) Xx)
% 151.78/152.02 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 151.78/152.02 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 151.78/152.02 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 151.78/152.02 Found x6:(X5 Xx0)
% 151.78/152.02 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 151.78/152.02 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 151.78/152.02 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 151.78/152.02 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 151.78/152.02 Found x400:=(x40 x5):((cK x2) Xx)
% 151.78/152.02 Found (x40 x5) as proof of ((cK X5) Xx)
% 151.78/152.02 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 151.78/152.02 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 151.78/152.02 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 151.78/152.02 Found x6:(X5 Xx0)
% 151.78/152.02 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 151.78/152.02 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 151.78/152.02 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 151.78/152.02 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 151.78/152.02 Found x400:=(x40 x5):((cK x2) Xx)
% 151.78/152.02 Found (x40 x5) as proof of ((cK X5) Xx)
% 151.78/152.02 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 151.78/152.02 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 151.78/152.02 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 151.78/152.02 Found x6:(X5 Xx0)
% 151.78/152.02 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 151.78/152.02 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 151.78/152.02 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 151.78/152.02 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 151.78/152.02 Found x400:=(x40 x5):((cK x1) Xx)
% 151.78/152.02 Found (x40 x5) as proof of ((cK X5) Xx)
% 151.78/152.02 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 152.22/152.47 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 152.22/152.47 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 152.22/152.47 Found x6:(X5 Xx0)
% 152.22/152.47 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 152.22/152.47 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 152.22/152.47 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 152.22/152.47 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 152.22/152.47 Found x400:=(x40 x5):((cK x2) Xx)
% 152.22/152.47 Found (x40 x5) as proof of ((cK X5) Xx)
% 152.22/152.47 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 152.22/152.47 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 152.22/152.47 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 152.22/152.47 Found x6:(X5 Xx0)
% 152.22/152.47 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 152.22/152.47 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 152.22/152.47 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 152.22/152.47 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 152.22/152.47 Found x400:=(x40 x5):((cK x2) Xx)
% 152.22/152.47 Found (x40 x5) as proof of ((cK X5) Xx)
% 152.22/152.47 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 152.22/152.47 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 152.22/152.47 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 152.22/152.47 Found x6:(X5 Xx0)
% 152.22/152.47 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 152.22/152.47 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 152.22/152.47 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 152.22/152.47 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 152.22/152.47 Found x400:=(x40 x5):((cK x2) Xx)
% 152.22/152.47 Found (x40 x5) as proof of ((cK X5) Xx)
% 152.22/152.47 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 152.22/152.47 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 152.22/152.47 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 152.22/152.47 Found x6:(X5 Xx0)
% 152.22/152.47 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 152.22/152.47 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 152.22/152.47 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 152.22/152.47 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 152.22/152.47 Found x400:=(x40 x5):((cK x2) Xx)
% 152.22/152.47 Found (x40 x5) as proof of ((cK X5) Xx)
% 152.22/152.47 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 152.22/152.47 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 152.22/152.47 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 152.22/152.47 Found x6:(X5 Xx0)
% 152.22/152.47 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 152.22/152.47 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 152.22/152.47 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 152.22/152.47 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 152.22/152.47 Found x400:=(x40 x5):((cK x2) Xx)
% 152.22/152.47 Found (x40 x5) as proof of ((cK X5) Xx)
% 152.22/152.47 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 153.31/153.59 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 153.31/153.59 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 153.31/153.59 Found x6:(X5 Xx0)
% 153.31/153.59 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 153.31/153.59 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 153.31/153.59 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 153.31/153.59 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 153.31/153.59 Found x400:=(x40 x5):((cK x2) Xx)
% 153.31/153.59 Found (x40 x5) as proof of ((cK X5) Xx)
% 153.31/153.59 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 153.31/153.59 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 153.31/153.59 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 153.31/153.59 Found x6:(X5 Xx0)
% 153.31/153.59 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 153.31/153.59 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 153.31/153.59 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 153.31/153.59 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 153.31/153.59 Found x400:=(x40 x5):((cK x2) Xx)
% 153.31/153.59 Found (x40 x5) as proof of ((cK X5) Xx)
% 153.31/153.59 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 153.31/153.59 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 153.31/153.59 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 153.31/153.59 Found x6:(X5 Xx0)
% 153.31/153.59 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 153.31/153.59 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 153.31/153.59 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 153.31/153.59 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 153.31/153.59 Found x400:=(x40 x5):((cK x2) Xx)
% 153.31/153.59 Found (x40 x5) as proof of ((cK X5) Xx)
% 153.31/153.59 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 153.31/153.59 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 153.31/153.59 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 153.31/153.59 Found x6:(X5 Xx0)
% 153.31/153.59 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 153.31/153.59 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 153.31/153.59 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 153.31/153.59 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 153.31/153.59 Found x400:=(x40 x5):((cK x2) Xx)
% 153.31/153.59 Found (x40 x5) as proof of ((cK X5) Xx)
% 153.31/153.59 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 153.31/153.59 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 153.31/153.59 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 153.31/153.59 Found x6:(X5 Xx0)
% 153.31/153.59 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 153.31/153.59 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 153.31/153.59 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 153.31/153.59 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 153.31/153.59 Found x400:=(x40 x5):((cK x2) Xx)
% 153.31/153.59 Found (x40 x5) as proof of ((cK X5) Xx)
% 153.46/153.77 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 153.46/153.77 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 153.46/153.77 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 153.46/153.77 Found x6:(X5 Xx0)
% 153.46/153.77 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 153.46/153.77 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 153.46/153.77 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 153.46/153.77 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 153.46/153.77 Found x400:=(x40 x5):((cK x2) Xx)
% 153.46/153.77 Found (x40 x5) as proof of ((cK X5) Xx)
% 153.46/153.77 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 153.46/153.77 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 153.46/153.77 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 153.46/153.77 Found x6:(X5 Xx0)
% 153.46/153.77 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 153.46/153.77 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 153.46/153.77 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 153.46/153.77 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 153.46/153.77 Found x400:=(x40 x5):((cK x2) Xx)
% 153.46/153.77 Found (x40 x5) as proof of ((cK X5) Xx)
% 153.46/153.77 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 153.46/153.77 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 153.46/153.77 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 153.46/153.77 Found x6:(X5 Xx0)
% 153.46/153.77 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 153.46/153.77 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 153.46/153.77 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 153.46/153.77 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 153.46/153.77 Found x400:=(x40 x5):((cK x2) Xx)
% 153.46/153.77 Found (x40 x5) as proof of ((cK X5) Xx)
% 153.46/153.77 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 153.46/153.77 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 153.46/153.77 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 153.46/153.77 Found x6:(X5 Xx0)
% 153.46/153.77 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 153.46/153.77 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 153.46/153.77 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 153.46/153.77 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 153.46/153.77 Found x400:=(x40 x5):((cK x2) Xx)
% 153.46/153.77 Found (x40 x5) as proof of ((cK X5) Xx)
% 153.46/153.77 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 153.46/153.77 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 153.46/153.77 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 153.46/153.77 Found x6:(X5 Xx0)
% 153.46/153.77 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 153.46/153.77 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 153.46/153.77 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 153.46/153.77 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 153.46/153.77 Found x400:=(x40 x5):((cK x2) Xx)
% 153.68/153.95 Found (x40 x5) as proof of ((cK X5) Xx)
% 153.68/153.95 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 153.68/153.95 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 153.68/153.95 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 153.68/153.95 Found x6:(X5 Xx0)
% 153.68/153.95 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 153.68/153.95 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 153.68/153.95 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 153.68/153.95 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 153.68/153.95 Found x400:=(x40 x5):((cK x2) Xx)
% 153.68/153.95 Found (x40 x5) as proof of ((cK X5) Xx)
% 153.68/153.95 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 153.68/153.95 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 153.68/153.95 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 153.68/153.95 Found x6:(X5 Xx0)
% 153.68/153.95 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 153.68/153.95 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 153.68/153.95 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 153.68/153.95 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 153.68/153.95 Found x400:=(x40 x5):((cK x2) Xx)
% 153.68/153.95 Found (x40 x5) as proof of ((cK X5) Xx)
% 153.68/153.95 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 153.68/153.95 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 153.68/153.95 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 153.68/153.95 Found x6:(X5 Xx0)
% 153.68/153.95 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 153.68/153.95 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 153.68/153.95 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 153.68/153.95 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 153.68/153.95 Found x400:=(x40 x5):((cK x2) Xx)
% 153.68/153.95 Found (x40 x5) as proof of ((cK X5) Xx)
% 153.68/153.95 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 153.68/153.95 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 153.68/153.95 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 153.68/153.95 Found x6:(X5 Xx0)
% 153.68/153.95 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 153.68/153.95 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 153.68/153.95 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 153.68/153.95 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 153.68/153.95 Found x400:=(x40 x5):((cK x2) Xx)
% 153.68/153.95 Found (x40 x5) as proof of ((cK X5) Xx)
% 153.68/153.95 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 153.68/153.95 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 153.68/153.95 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 153.68/153.95 Found x40:=(x4 Xx):((x1 Xx)->((cK x1) Xx))
% 153.68/153.95 Found (x4 Xx) as proof of ((x1 Xx)->((cK X5) Xx))
% 153.68/153.95 Found (x4 Xx) as proof of ((x1 Xx)->((cK X5) Xx))
% 153.68/153.95 Found (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx)) as proof of ((x1 Xx)->((cK X5) Xx))
% 153.68/153.95 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 X5) Xx)))
% 153.68/153.95 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 153.68/153.95 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 154.90/155.17 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 X5) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 154.90/155.17 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 X5) Xx)) (fun (x4:(forall (Xx0:a), ((x1 Xx0)->((cK x1) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 154.90/155.17 Found x6:(X5 Xx0)
% 154.90/155.17 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 154.90/155.17 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 154.90/155.17 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 154.90/155.17 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 154.90/155.17 Found x400:=(x40 x5):((cK x2) Xx)
% 154.90/155.17 Found (x40 x5) as proof of ((cK X5) Xx)
% 154.90/155.17 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 154.90/155.17 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 154.90/155.17 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 154.90/155.17 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 154.90/155.17 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 154.90/155.17 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 154.90/155.17 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 154.90/155.17 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 154.90/155.17 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 154.90/155.17 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 154.90/155.17 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 154.90/155.17 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 X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% 154.90/155.17 Found x6:(X5 Xx0)
% 154.90/155.17 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 154.90/155.17 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 154.90/155.17 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 154.90/155.17 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 154.90/155.17 Found x400:=(x40 x5):((cK x2) Xx)
% 154.90/155.17 Found (x40 x5) as proof of ((cK X5) Xx)
% 154.90/155.17 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 154.90/155.17 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 154.90/155.17 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 154.90/155.17 Found x6:(X5 Xx0)
% 154.90/155.17 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 154.90/155.17 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 154.90/155.17 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 154.90/155.17 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 155.02/155.35 Found x400:=(x40 x5):((cK x2) Xx)
% 155.02/155.35 Found (x40 x5) as proof of ((cK X5) Xx)
% 155.02/155.35 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 155.02/155.35 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 155.02/155.35 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 155.02/155.35 Found x6:(X5 Xx0)
% 155.02/155.35 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 155.02/155.35 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 155.02/155.35 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 155.02/155.35 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 155.02/155.35 Found x400:=(x40 x5):((cK x2) Xx)
% 155.02/155.35 Found (x40 x5) as proof of ((cK X5) Xx)
% 155.02/155.35 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 155.02/155.35 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 155.02/155.35 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 155.02/155.35 Found x6:(X5 Xx0)
% 155.02/155.35 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 155.02/155.35 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 155.02/155.35 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 155.02/155.35 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 155.02/155.35 Found x400:=(x40 x5):((cK x2) Xx)
% 155.02/155.35 Found (x40 x5) as proof of ((cK X5) Xx)
% 155.02/155.35 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 155.02/155.35 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 155.02/155.35 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 155.02/155.35 Found x6:(X5 Xx0)
% 155.02/155.35 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 155.02/155.35 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 155.02/155.35 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 155.02/155.35 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 155.02/155.35 Found x400:=(x40 x5):((cK x2) Xx)
% 155.02/155.35 Found (x40 x5) as proof of ((cK X5) Xx)
% 155.02/155.35 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 155.02/155.35 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 155.02/155.35 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 155.02/155.35 Found x6:(X5 Xx0)
% 155.02/155.35 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 155.02/155.35 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 155.02/155.35 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 155.02/155.35 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 155.02/155.35 Found x400:=(x40 x5):((cK x2) Xx)
% 155.02/155.35 Found (x40 x5) as proof of ((cK X5) Xx)
% 155.02/155.35 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 155.02/155.35 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 155.02/155.35 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 155.02/155.35 Found x6:(X5 Xx0)
% 155.02/155.35 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 155.02/155.35 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 155.02/155.35 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 155.02/155.35 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 155.30/155.56 Found x400:=(x40 x5):((cK x2) Xx)
% 155.30/155.56 Found (x40 x5) as proof of ((cK X5) Xx)
% 155.30/155.56 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 155.30/155.56 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 155.30/155.56 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 155.30/155.56 Found x6:(X5 Xx0)
% 155.30/155.56 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 155.30/155.56 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 155.30/155.56 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 155.30/155.56 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 155.30/155.56 Found x400:=(x40 x5):((cK x2) Xx)
% 155.30/155.56 Found (x40 x5) as proof of ((cK X5) Xx)
% 155.30/155.56 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 155.30/155.56 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 155.30/155.56 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 155.30/155.56 Found x6:(X5 Xx0)
% 155.30/155.56 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 155.30/155.56 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 155.30/155.56 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 155.30/155.56 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 155.30/155.56 Found x400:=(x40 x5):((cK x2) Xx)
% 155.30/155.56 Found (x40 x5) as proof of ((cK X5) Xx)
% 155.30/155.56 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 155.30/155.56 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 155.30/155.56 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 155.30/155.56 Found x6:(X5 Xx0)
% 155.30/155.56 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 155.30/155.56 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 155.30/155.56 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 155.30/155.56 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 155.30/155.56 Found x400:=(x40 x5):((cK x2) Xx)
% 155.30/155.56 Found (x40 x5) as proof of ((cK X5) Xx)
% 155.30/155.56 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 155.30/155.56 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 155.30/155.56 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 155.30/155.56 Found x6:(X5 Xx0)
% 155.30/155.56 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 155.30/155.56 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 155.30/155.56 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 155.30/155.56 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 155.30/155.56 Found x400:=(x40 x5):((cK x2) Xx)
% 155.30/155.56 Found (x40 x5) as proof of ((cK X5) Xx)
% 155.30/155.56 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 155.30/155.56 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 155.30/155.56 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 155.30/155.56 Found x6:(X5 Xx0)
% 155.30/155.56 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 155.30/155.56 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 155.30/155.56 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 155.30/155.56 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 155.73/155.98 Found x400:=(x40 x5):((cK x2) Xx)
% 155.73/155.98 Found (x40 x5) as proof of ((cK X5) Xx)
% 155.73/155.98 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 155.73/155.98 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 155.73/155.98 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 155.73/155.98 Found x6:(X5 Xx0)
% 155.73/155.98 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 155.73/155.98 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 155.73/155.98 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 155.73/155.98 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 155.73/155.98 Found x400:=(x40 x5):((cK x2) Xx)
% 155.73/155.98 Found (x40 x5) as proof of ((cK X5) Xx)
% 155.73/155.98 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 155.73/155.98 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 155.73/155.98 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 155.73/155.98 Found x6:(X5 Xx0)
% 155.73/155.98 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 155.73/155.98 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 155.73/155.98 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 155.73/155.98 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 155.73/155.98 Found x400:=(x40 x5):((cK x2) Xx)
% 155.73/155.98 Found (x40 x5) as proof of ((cK X5) Xx)
% 155.73/155.98 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 155.73/155.98 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 155.73/155.98 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 155.73/155.98 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 155.73/155.98 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 155.73/155.98 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 155.73/155.98 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 155.73/155.98 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 155.73/155.98 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 155.73/155.98 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 155.73/155.98 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 155.73/155.98 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 X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% 155.73/155.98 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 155.73/155.98 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 155.73/155.98 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 155.73/155.98 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 155.73/155.98 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 155.73/155.98 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 155.73/155.98 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 155.73/155.98 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 155.79/156.04 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 X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% 155.79/156.04 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 155.79/156.04 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 155.79/156.04 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 155.79/156.04 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 155.79/156.04 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 155.79/156.04 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 155.79/156.04 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 155.79/156.04 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 155.79/156.04 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 X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% 155.79/156.04 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 155.79/156.04 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 155.79/156.04 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 155.79/156.04 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 155.79/156.04 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 155.79/156.04 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 155.79/156.04 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 155.79/156.04 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 155.79/156.04 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 X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% 155.79/156.04 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 155.79/156.04 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 155.79/156.04 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 155.79/156.04 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 155.79/156.04 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 155.79/156.04 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 155.79/156.04 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 155.79/156.04 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 155.79/156.04 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 X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% 157.08/157.38 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 157.08/157.38 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 157.08/157.38 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 157.08/157.38 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 157.08/157.38 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 157.08/157.38 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 157.08/157.38 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 157.08/157.38 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 157.08/157.38 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 X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% 157.08/157.38 Found x6:(X5 Xx0)
% 157.08/157.38 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 157.08/157.38 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 157.08/157.38 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 157.08/157.38 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 157.08/157.38 Found x300:=(x30 x4):((cK x1) Xx)
% 157.08/157.38 Found (x30 x4) as proof of ((cK X5) Xx)
% 157.08/157.38 Found ((x3 Xx) x4) as proof of ((cK X5) Xx)
% 157.08/157.38 Found ((x3 Xx) x4) as proof of ((cK X5) Xx)
% 157.08/157.38 Found ((x3 Xx) x4) as proof of ((cK X5) Xx)
% 157.08/157.38 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 157.08/157.38 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 157.08/157.38 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 157.08/157.38 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 157.08/157.38 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 157.08/157.38 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 157.08/157.38 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 157.08/157.38 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 157.08/157.38 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 X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% 157.08/157.38 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 157.08/157.38 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 157.08/157.38 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 157.08/157.38 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 157.08/157.38 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 157.08/157.38 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 157.08/157.38 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 157.08/157.38 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 157.24/157.50 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 X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% 157.24/157.50 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 157.24/157.50 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 157.24/157.50 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 157.24/157.50 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 157.24/157.50 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 157.24/157.50 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 157.24/157.50 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 157.24/157.50 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 157.24/157.50 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 X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% 157.24/157.50 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 157.24/157.50 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 157.24/157.50 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 157.24/157.50 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 157.24/157.50 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 157.24/157.50 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 157.24/157.50 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 157.24/157.50 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 157.24/157.50 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 X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% 157.24/157.50 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 157.24/157.50 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 157.24/157.50 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 157.24/157.50 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 157.24/157.50 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 157.24/157.50 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 157.24/157.50 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 157.24/157.50 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 157.24/157.50 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 X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% 157.29/157.54 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 157.29/157.54 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 157.29/157.54 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 157.29/157.54 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 157.29/157.54 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 157.29/157.54 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 157.29/157.54 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 157.29/157.54 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 157.29/157.54 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 X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% 157.29/157.54 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 157.29/157.54 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 157.29/157.54 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 157.29/157.54 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 157.29/157.54 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 157.29/157.54 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 157.29/157.54 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 157.29/157.54 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 157.29/157.54 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 X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% 157.29/157.54 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 157.29/157.54 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 157.29/157.54 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 157.29/157.54 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 157.29/157.54 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 157.29/157.54 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 157.29/157.54 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 157.29/157.54 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 157.29/157.54 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 X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% 157.29/157.54 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 157.29/157.54 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 157.29/157.54 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 157.29/157.60 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 157.29/157.60 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 157.29/157.60 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 157.29/157.60 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 157.29/157.60 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 157.29/157.60 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 X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% 157.29/157.60 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 157.29/157.60 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 157.29/157.60 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 157.29/157.60 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 157.29/157.60 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 157.29/157.60 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 157.29/157.60 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 157.29/157.60 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 157.29/157.60 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 X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% 157.29/157.60 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 157.29/157.60 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 157.29/157.60 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 157.29/157.60 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 157.29/157.60 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 157.29/157.60 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 157.29/157.60 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 157.29/157.60 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 157.29/157.60 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 X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% 157.29/157.60 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 157.29/157.60 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 157.29/157.60 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 157.29/157.60 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 157.29/157.60 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 157.29/157.60 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 157.29/157.62 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 157.29/157.62 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 157.29/157.62 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 X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% 157.29/157.62 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 157.29/157.62 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 157.29/157.62 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 157.29/157.62 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 157.29/157.62 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 157.29/157.62 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 157.29/157.62 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 157.29/157.62 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 157.29/157.62 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 X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% 157.29/157.62 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 157.29/157.62 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 157.29/157.62 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 157.29/157.62 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 157.29/157.62 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 157.29/157.62 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 157.29/157.62 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 157.29/157.62 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 157.29/157.62 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 X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% 157.29/157.62 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 157.29/157.62 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 157.29/157.62 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 157.29/157.62 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 157.29/157.62 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 157.29/157.62 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 157.29/157.62 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 157.29/157.62 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 157.47/157.76 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 X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% 157.47/157.76 Found x6:(X5 Xx0)
% 157.47/157.76 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 157.47/157.76 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 157.47/157.76 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 157.47/157.76 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 157.47/157.76 Found x400:=(x40 x5):((cK x2) Xx)
% 157.47/157.76 Found (x40 x5) as proof of ((cK X5) Xx)
% 157.47/157.76 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 157.47/157.76 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 157.47/157.76 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 157.47/157.76 Found x6:(X5 Xx0)
% 157.47/157.76 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 157.47/157.76 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 157.47/157.76 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 157.47/157.76 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 157.47/157.76 Found x400:=(x40 x5):((cK x2) Xx)
% 157.47/157.76 Found (x40 x5) as proof of ((cK X5) Xx)
% 157.47/157.76 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 157.47/157.76 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 157.47/157.76 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 157.47/157.76 Found x6:(X5 Xx0)
% 157.47/157.76 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 157.47/157.76 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 157.47/157.76 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 157.47/157.76 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 157.47/157.76 Found x400:=(x40 x5):((cK x2) Xx)
% 157.47/157.76 Found (x40 x5) as proof of ((cK X5) Xx)
% 157.47/157.76 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 157.47/157.76 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 157.47/157.76 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 157.47/157.76 Found x6:(X5 Xx0)
% 157.47/157.76 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 157.47/157.76 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 157.47/157.76 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 157.47/157.76 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 157.47/157.76 Found x400:=(x40 x5):((cK x2) Xx)
% 157.47/157.76 Found (x40 x5) as proof of ((cK X5) Xx)
% 157.47/157.76 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 157.47/157.76 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 157.47/157.76 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 157.47/157.76 Found x6:(X5 Xx0)
% 157.47/157.76 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 157.47/157.76 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 157.47/157.76 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 157.70/157.94 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 157.70/157.94 Found x400:=(x40 x5):((cK x2) Xx)
% 157.70/157.94 Found (x40 x5) as proof of ((cK X5) Xx)
% 157.70/157.94 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 157.70/157.94 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 157.70/157.94 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 157.70/157.94 Found x6:(X5 Xx0)
% 157.70/157.94 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 157.70/157.94 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 157.70/157.94 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 157.70/157.94 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 157.70/157.94 Found x400:=(x40 x5):((cK x2) Xx)
% 157.70/157.94 Found (x40 x5) as proof of ((cK X5) Xx)
% 157.70/157.94 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 157.70/157.94 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 157.70/157.94 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 157.70/157.94 Found x6:(X5 Xx0)
% 157.70/157.94 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 157.70/157.94 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 157.70/157.94 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 157.70/157.94 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 157.70/157.94 Found x400:=(x40 x5):((cK x2) Xx)
% 157.70/157.94 Found (x40 x5) as proof of ((cK X5) Xx)
% 157.70/157.94 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 157.70/157.94 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 157.70/157.94 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 157.70/157.94 Found x6:(X5 Xx0)
% 157.70/157.94 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 157.70/157.94 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 157.70/157.94 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 157.70/157.94 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 157.70/157.94 Found x400:=(x40 x5):((cK x2) Xx)
% 157.70/157.94 Found (x40 x5) as proof of ((cK X5) Xx)
% 157.70/157.94 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 157.70/157.94 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 157.70/157.94 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 157.70/157.94 Found x6:(X5 Xx0)
% 157.70/157.94 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 157.70/157.94 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 157.70/157.94 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 157.70/157.94 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 157.70/157.94 Found x400:=(x40 x5):((cK x2) Xx)
% 157.70/157.94 Found (x40 x5) as proof of ((cK X5) Xx)
% 157.70/157.94 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 157.70/157.94 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 157.70/157.94 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 157.70/157.94 Found x6:(X5 Xx0)
% 157.70/157.94 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 157.70/157.94 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 158.92/159.17 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 158.92/159.17 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 158.92/159.17 Found x400:=(x40 x5):((cK x2) Xx)
% 158.92/159.17 Found (x40 x5) as proof of ((cK X5) Xx)
% 158.92/159.17 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 158.92/159.17 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 158.92/159.17 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 158.92/159.17 Found x6:(X5 Xx0)
% 158.92/159.17 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 158.92/159.17 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 158.92/159.17 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 158.92/159.17 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 158.92/159.17 Found x400:=(x40 x5):((cK x2) Xx)
% 158.92/159.17 Found (x40 x5) as proof of ((cK X5) Xx)
% 158.92/159.17 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 158.92/159.17 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 158.92/159.17 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 158.92/159.17 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 158.92/159.17 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 158.92/159.17 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 158.92/159.17 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 158.92/159.17 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 158.92/159.17 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 158.92/159.17 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 158.92/159.17 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 158.92/159.17 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 X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% 158.92/159.17 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 158.92/159.17 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 158.92/159.17 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 158.92/159.17 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 158.92/159.17 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 158.92/159.17 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 158.92/159.17 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 158.92/159.17 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 158.92/159.17 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 X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% 158.92/159.17 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 158.92/159.17 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 158.92/159.17 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 158.92/159.17 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 158.92/159.18 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 158.92/159.18 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 158.92/159.18 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 158.92/159.18 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 158.92/159.18 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 X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% 158.92/159.18 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 158.92/159.18 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 158.92/159.18 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 158.92/159.18 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 158.92/159.18 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 158.92/159.18 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 158.92/159.18 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 158.92/159.18 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 158.92/159.18 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 X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% 158.92/159.18 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 158.92/159.18 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 158.92/159.18 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 158.92/159.18 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 158.92/159.18 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 158.92/159.18 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 158.92/159.18 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 158.92/159.18 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 158.92/159.18 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 X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% 158.92/159.18 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 158.92/159.18 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 158.92/159.18 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 158.92/159.18 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 158.92/159.18 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 158.92/159.18 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 158.92/159.18 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 158.92/159.22 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 158.92/159.22 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 X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% 158.92/159.22 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 158.92/159.22 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 158.92/159.22 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 158.92/159.22 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 158.92/159.22 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 158.92/159.22 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 158.92/159.22 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 158.92/159.22 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 158.92/159.22 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 X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% 158.92/159.22 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 158.92/159.22 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 158.92/159.22 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 158.92/159.22 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 158.92/159.22 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 158.92/159.22 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 158.92/159.22 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 158.92/159.22 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 158.92/159.22 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 X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% 158.92/159.22 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 158.92/159.22 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 158.92/159.22 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 158.92/159.22 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 158.92/159.22 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 158.92/159.22 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 158.92/159.22 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 158.92/159.22 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 158.92/159.23 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 X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% 158.92/159.23 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 158.92/159.23 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 158.92/159.23 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 158.92/159.23 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 158.92/159.23 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 158.92/159.23 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 158.92/159.23 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 158.92/159.23 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 158.92/159.23 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 X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% 158.92/159.23 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 158.92/159.23 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 158.92/159.23 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 158.92/159.23 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 158.92/159.23 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 158.92/159.23 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 158.92/159.23 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 158.92/159.23 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 158.92/159.23 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 X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% 158.92/159.23 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 158.92/159.23 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 158.92/159.23 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 158.92/159.23 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 158.92/159.23 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 158.92/159.23 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 158.92/159.23 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 158.92/159.23 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 158.92/159.23 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 X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% 158.92/159.24 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 158.92/159.24 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 158.92/159.24 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 158.92/159.24 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 158.92/159.24 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 158.92/159.24 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 158.92/159.24 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 158.92/159.24 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 158.92/159.24 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 X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% 158.92/159.24 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 158.92/159.24 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 158.92/159.24 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 158.92/159.24 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 158.92/159.24 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 158.92/159.24 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 158.92/159.24 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 158.92/159.24 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 158.92/159.24 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 X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% 158.92/159.24 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 158.92/159.24 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 158.92/159.24 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 158.92/159.24 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 158.92/159.24 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 158.92/159.24 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 158.92/159.24 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 158.92/159.24 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 158.92/159.24 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 X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% 158.92/159.24 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 158.92/159.24 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 158.92/159.24 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 158.92/159.24 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 159.01/159.28 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 159.01/159.28 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 159.01/159.28 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 159.01/159.28 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 159.01/159.28 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 X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% 159.01/159.28 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 159.01/159.28 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 159.01/159.28 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 159.01/159.28 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 159.01/159.28 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 159.01/159.28 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 159.01/159.28 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 159.01/159.28 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 159.01/159.28 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 X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% 159.01/159.28 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 159.01/159.28 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 159.01/159.28 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 159.01/159.28 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 159.01/159.28 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 159.01/159.28 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 159.01/159.28 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 159.01/159.28 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 159.01/159.28 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 X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% 159.01/159.28 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 159.01/159.28 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 159.01/159.28 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 159.01/159.28 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 159.01/159.28 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 159.01/159.28 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 159.01/159.28 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 159.12/159.36 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 159.12/159.36 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 X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% 159.12/159.36 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 159.12/159.36 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 159.12/159.36 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 159.12/159.36 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 159.12/159.36 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 159.12/159.36 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 159.12/159.36 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 159.12/159.36 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 159.12/159.36 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 X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% 159.12/159.36 Found x6:(X5 Xx0)
% 159.12/159.36 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 159.12/159.36 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 159.12/159.36 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 159.12/159.36 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 159.12/159.36 Found x400:=(x40 x5):((cK x2) Xx)
% 159.12/159.36 Found (x40 x5) as proof of ((cK X5) Xx)
% 159.12/159.36 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 159.12/159.36 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 159.12/159.36 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 159.12/159.36 Found x6:(X5 Xx0)
% 159.12/159.36 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 159.12/159.36 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 159.12/159.36 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 159.12/159.36 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 159.12/159.36 Found x400:=(x40 x5):((cK x2) Xx)
% 159.12/159.36 Found (x40 x5) as proof of ((cK X5) Xx)
% 159.12/159.36 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 159.12/159.36 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 159.12/159.36 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 159.12/159.36 Found x6:(X5 Xx0)
% 159.12/159.36 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 159.12/159.36 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 159.12/159.36 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 159.12/159.36 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 160.10/160.39 Found x400:=(x40 x5):((cK x2) Xx)
% 160.10/160.39 Found (x40 x5) as proof of ((cK X5) Xx)
% 160.10/160.39 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 160.10/160.39 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 160.10/160.39 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 160.10/160.39 Found x6:(X5 Xx0)
% 160.10/160.39 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 160.10/160.39 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 160.10/160.39 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 160.10/160.39 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 160.10/160.39 Found x400:=(x40 x5):((cK x2) Xx)
% 160.10/160.39 Found (x40 x5) as proof of ((cK X5) Xx)
% 160.10/160.39 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 160.10/160.39 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 160.10/160.39 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 160.10/160.39 Found x6:(X5 Xx0)
% 160.10/160.39 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 160.10/160.39 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 160.10/160.39 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 160.10/160.39 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 160.10/160.39 Found x400:=(x40 x5):((cK x2) Xx)
% 160.10/160.39 Found (x40 x5) as proof of ((cK X5) Xx)
% 160.10/160.39 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 160.10/160.39 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 160.10/160.39 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 160.10/160.39 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 160.10/160.39 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 160.10/160.39 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 160.10/160.39 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 160.10/160.39 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 160.10/160.39 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 160.10/160.39 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 160.10/160.39 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 160.10/160.39 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 X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% 160.10/160.39 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 160.10/160.39 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 160.10/160.39 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 160.10/160.39 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 160.10/160.39 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 160.10/160.39 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 160.10/160.39 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 160.10/160.39 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 160.19/160.46 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 X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% 160.19/160.46 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 160.19/160.46 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 160.19/160.46 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 160.19/160.46 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 160.19/160.46 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 160.19/160.46 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 160.19/160.46 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 160.19/160.46 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 160.19/160.46 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 X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% 160.19/160.46 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 160.19/160.46 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 160.19/160.46 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 160.19/160.46 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 160.19/160.46 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 160.19/160.46 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 160.19/160.46 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 160.19/160.46 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 160.19/160.46 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 X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% 160.19/160.46 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 160.19/160.46 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 160.19/160.46 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 160.19/160.46 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 160.19/160.46 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 160.19/160.46 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 160.19/160.46 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 160.19/160.46 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 160.19/160.46 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 X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% 160.25/160.55 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 160.25/160.55 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 160.25/160.55 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 160.25/160.55 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 160.25/160.55 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 160.25/160.55 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 160.25/160.55 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 160.25/160.55 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 160.25/160.55 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 X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% 160.25/160.55 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 160.25/160.55 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 160.25/160.55 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 160.25/160.55 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 160.25/160.55 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 160.25/160.55 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 160.25/160.55 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 160.25/160.55 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 160.25/160.55 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 X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% 160.25/160.55 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 160.25/160.55 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 160.25/160.55 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 160.25/160.55 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 160.25/160.55 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 160.25/160.55 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 160.25/160.55 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 160.25/160.55 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 160.25/160.55 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 X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% 160.25/160.55 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 160.25/160.55 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 160.25/160.55 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 160.25/160.55 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 160.25/160.56 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 160.25/160.56 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 160.25/160.56 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 160.25/160.56 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 160.25/160.56 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 X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% 160.25/160.56 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 160.25/160.56 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 160.25/160.56 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 160.25/160.56 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 160.25/160.56 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 160.25/160.56 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 160.25/160.56 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 160.25/160.56 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 160.25/160.56 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 X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% 160.25/160.56 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 160.25/160.56 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 160.25/160.56 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 160.25/160.56 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 160.25/160.56 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 160.25/160.56 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 160.25/160.56 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 160.25/160.56 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 160.25/160.56 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 X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% 160.25/160.56 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 160.25/160.56 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 160.25/160.56 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 160.25/160.56 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 160.25/160.56 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 160.25/160.56 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 160.25/160.56 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 160.33/160.57 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 160.33/160.57 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 X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% 160.33/160.57 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 160.33/160.57 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 160.33/160.57 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 160.33/160.57 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 160.33/160.57 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 160.33/160.57 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 160.33/160.57 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 160.33/160.57 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 160.33/160.57 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 X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% 160.33/160.57 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 160.33/160.57 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 160.33/160.57 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 160.33/160.57 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 160.33/160.57 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 160.33/160.57 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 160.33/160.57 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 160.33/160.57 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 160.33/160.57 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 X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% 160.33/160.57 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 160.33/160.57 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 160.33/160.57 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 160.33/160.57 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 160.33/160.57 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 160.33/160.57 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 160.33/160.57 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 160.33/160.57 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 160.93/161.20 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 X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% 160.93/161.20 Found x6:(X5 Xx0)
% 160.93/161.20 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 160.93/161.20 Found (fun (x6:(X5 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 160.93/161.20 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of ((X5 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 160.93/161.20 Found (fun (Xx0:a) (x6:(X5 Xx0))=> x6) as proof of (forall (Xx:a), ((X5 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 160.93/161.20 Found x400:=(x40 x5):((cK x2) Xx)
% 160.93/161.20 Found (x40 x5) as proof of ((cK X5) Xx)
% 160.93/161.20 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 160.93/161.20 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 160.93/161.20 Found ((x4 Xx) x5) as proof of ((cK X5) Xx)
% 160.93/161.20 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 160.93/161.20 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 160.93/161.20 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 160.93/161.20 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 160.93/161.20 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 160.93/161.20 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 160.93/161.20 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 160.93/161.20 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 160.93/161.20 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 X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% 160.93/161.20 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 160.93/161.20 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 160.93/161.20 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 160.93/161.20 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 160.93/161.20 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 160.93/161.20 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 160.93/161.20 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 160.93/161.20 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 160.93/161.20 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 X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% 160.93/161.20 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 160.93/161.20 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 160.93/161.20 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 160.93/161.20 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 160.93/161.20 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 160.93/161.24 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 160.93/161.24 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 160.93/161.24 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 160.93/161.24 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 X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% 160.93/161.24 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 160.93/161.24 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 160.93/161.24 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 160.93/161.24 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 160.93/161.24 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 160.93/161.24 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 160.93/161.24 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 160.93/161.24 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 160.93/161.24 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 X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% 160.93/161.24 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 160.93/161.24 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 160.93/161.24 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 160.93/161.24 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 160.93/161.24 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 160.93/161.24 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 160.93/161.24 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 160.93/161.24 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 160.93/161.24 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 X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% 160.93/161.24 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 160.93/161.24 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 160.93/161.24 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 160.93/161.24 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 160.93/161.24 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 160.93/161.24 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 160.93/161.24 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 160.93/161.24 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 192.28/192.58 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 X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% 192.28/192.58 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 192.28/192.58 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 192.28/192.58 Found (x4 Xx) as proof of ((x2 Xx)->((cK X5) Xx))
% 192.28/192.58 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X5) Xx))
% 192.28/192.58 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X5) Xx)))
% 192.28/192.58 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 192.28/192.58 Found ((and_rect0 ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 192.28/192.58 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X5) Xx)
% 192.28/192.58 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 X5) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)))) as proof of ((cK X5) Xx)
% 192.28/192.58 Found x4:(X6 Xx0)
% 192.28/192.58 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 192.28/192.58 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 192.28/192.58 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 192.28/192.58 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 192.28/192.58 Found x4:(X6 Xx0)
% 192.28/192.58 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 192.28/192.58 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 192.28/192.58 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 192.28/192.58 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 192.28/192.58 Found x6:(X6 Xx0)
% 192.28/192.58 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 192.28/192.58 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 192.28/192.58 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 192.28/192.58 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 192.28/192.58 Found x400:=(x40 x5):((cK x2) Xx)
% 192.28/192.58 Found (x40 x5) as proof of ((cK X6) Xx)
% 192.28/192.58 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 192.28/192.58 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 192.28/192.58 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 192.28/192.58 Found x4:(X6 Xx0)
% 192.28/192.58 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 192.28/192.58 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 201.71/202.01 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 201.71/202.01 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 201.71/202.01 Found x4:(X6 Xx0)
% 201.71/202.01 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 201.71/202.01 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 201.71/202.01 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 201.71/202.01 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 201.71/202.01 Found x6:(X6 Xx0)
% 201.71/202.01 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 201.71/202.01 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 201.71/202.01 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 201.71/202.01 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 201.71/202.01 Found x400:=(x40 x5):((cK x2) Xx)
% 201.71/202.01 Found (x40 x5) as proof of ((cK X6) Xx)
% 201.71/202.01 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 201.71/202.01 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 201.71/202.01 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 201.71/202.01 Found x6:(X6 Xx0)
% 201.71/202.01 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 201.71/202.01 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 201.71/202.01 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 201.71/202.01 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 201.71/202.01 Found x400:=(x40 x5):((cK x2) Xx)
% 201.71/202.01 Found (x40 x5) as proof of ((cK X6) Xx)
% 201.71/202.01 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 201.71/202.01 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 201.71/202.01 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 201.71/202.01 Found x6:(X6 Xx0)
% 201.71/202.01 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 201.71/202.01 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 201.71/202.01 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 201.71/202.01 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 201.71/202.01 Found x400:=(x40 x5):((cK x2) Xx)
% 201.71/202.01 Found (x40 x5) as proof of ((cK X6) Xx)
% 201.71/202.01 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 201.71/202.01 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 201.71/202.01 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 201.71/202.01 Found x4:(X6 Xx0)
% 201.71/202.01 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 201.71/202.01 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 201.71/202.01 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 201.71/202.01 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 210.11/210.42 Found x4:(X6 Xx0)
% 210.11/210.42 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 210.11/210.42 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 210.11/210.42 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 210.11/210.42 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 210.11/210.42 Found x4:(X6 Xx0)
% 210.11/210.42 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 210.11/210.42 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 210.11/210.42 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 210.11/210.42 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 210.11/210.42 Found x4:(X6 Xx0)
% 210.11/210.42 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 210.11/210.42 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 210.11/210.42 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 210.11/210.42 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 210.11/210.42 Found x6:(X6 Xx0)
% 210.11/210.42 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 210.11/210.42 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 210.11/210.42 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 210.11/210.42 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 210.11/210.42 Found x400:=(x40 x5):((cK x2) Xx)
% 210.11/210.42 Found (x40 x5) as proof of ((cK X6) Xx)
% 210.11/210.42 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 210.11/210.42 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 210.11/210.42 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 210.11/210.42 Found x6:(X6 Xx0)
% 210.11/210.42 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 210.11/210.42 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 210.11/210.42 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 210.11/210.42 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 210.11/210.42 Found x400:=(x40 x5):((cK x2) Xx)
% 210.11/210.42 Found (x40 x5) as proof of ((cK X6) Xx)
% 210.11/210.42 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 210.11/210.42 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 210.11/210.42 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 210.11/210.42 Found x6:(X6 Xx0)
% 210.11/210.42 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 210.11/210.42 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 210.11/210.42 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 210.11/210.42 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 213.38/213.64 Found x400:=(x40 x5):((cK x2) Xx)
% 213.38/213.64 Found (x40 x5) as proof of ((cK X6) Xx)
% 213.38/213.64 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 213.38/213.64 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 213.38/213.64 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 213.38/213.64 Found x6:(X6 Xx0)
% 213.38/213.64 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 213.38/213.64 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 213.38/213.64 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 213.38/213.64 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 213.38/213.64 Found x400:=(x40 x5):((cK x2) Xx)
% 213.38/213.64 Found (x40 x5) as proof of ((cK X6) Xx)
% 213.38/213.64 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 213.38/213.64 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 213.38/213.64 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 213.38/213.64 Found x6:(X6 Xx0)
% 213.38/213.64 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 213.38/213.64 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 213.38/213.64 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 213.38/213.64 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 213.38/213.64 Found x400:=(x40 x5):((cK x2) Xx)
% 213.38/213.64 Found (x40 x5) as proof of ((cK X6) Xx)
% 213.38/213.64 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 213.38/213.64 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 213.38/213.64 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 213.38/213.64 Found x6:(X6 Xx0)
% 213.38/213.64 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 213.38/213.64 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 213.38/213.64 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 213.38/213.64 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 213.38/213.64 Found x400:=(x40 x5):((cK x2) Xx)
% 213.38/213.64 Found (x40 x5) as proof of ((cK X6) Xx)
% 213.38/213.64 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 213.38/213.64 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 213.38/213.64 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 213.38/213.64 Found x4:(X6 Xx0)
% 213.38/213.64 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 213.38/213.64 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 213.38/213.64 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 213.38/213.64 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 213.38/213.64 Found x4:(X6 Xx0)
% 213.38/213.64 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 213.38/213.64 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 213.38/213.64 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 213.38/213.64 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 213.38/213.64 Found x4:(X6 Xx0)
% 213.38/213.64 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 221.73/222.09 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 221.73/222.09 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 221.73/222.09 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 221.73/222.09 Found x2:(X6 Xx0)
% 221.73/222.09 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 221.73/222.09 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 221.73/222.09 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 221.73/222.09 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 221.73/222.09 Found x4:(X6 Xx0)
% 221.73/222.09 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 221.73/222.09 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 221.73/222.09 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 221.73/222.09 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 221.73/222.09 Found x4:(X6 Xx0)
% 221.73/222.09 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 221.73/222.09 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 221.73/222.09 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 221.73/222.09 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 221.73/222.09 Found x4:(X6 Xx0)
% 221.73/222.09 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 221.73/222.09 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 221.73/222.09 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 221.73/222.09 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 221.73/222.09 Found x6:(X6 Xx0)
% 221.73/222.09 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 221.73/222.09 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 221.73/222.09 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 221.73/222.09 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 221.73/222.09 Found x400:=(x40 x5):((cK x2) Xx)
% 221.73/222.09 Found (x40 x5) as proof of ((cK X6) Xx)
% 221.73/222.09 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 221.73/222.09 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 221.73/222.09 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 221.73/222.09 Found x6:(X6 Xx0)
% 221.73/222.09 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 221.73/222.09 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 221.73/222.09 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 222.57/222.85 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 222.57/222.85 Found x400:=(x40 x5):((cK x2) Xx)
% 222.57/222.85 Found (x40 x5) as proof of ((cK X6) Xx)
% 222.57/222.85 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 222.57/222.85 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 222.57/222.85 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 222.57/222.85 Found x6:(X6 Xx0)
% 222.57/222.85 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 222.57/222.85 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 222.57/222.85 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 222.57/222.85 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 222.57/222.85 Found x400:=(x40 x5):((cK x2) Xx)
% 222.57/222.85 Found (x40 x5) as proof of ((cK X6) Xx)
% 222.57/222.85 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 222.57/222.85 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 222.57/222.85 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 222.57/222.85 Found x6:(X6 Xx0)
% 222.57/222.85 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 222.57/222.85 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 222.57/222.85 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 222.57/222.85 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 222.57/222.85 Found x400:=(x40 x5):((cK x2) Xx)
% 222.57/222.85 Found (x40 x5) as proof of ((cK X6) Xx)
% 222.57/222.85 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 222.57/222.85 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 222.57/222.85 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 222.57/222.85 Found x6:(X6 Xx0)
% 222.57/222.85 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 222.57/222.85 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 222.57/222.85 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 222.57/222.85 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 222.57/222.85 Found x400:=(x40 x5):((cK x2) Xx)
% 222.57/222.85 Found (x40 x5) as proof of ((cK X6) Xx)
% 222.57/222.85 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 222.57/222.85 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 222.57/222.85 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 222.57/222.85 Found x2:(X6 Xx0)
% 222.57/222.85 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 222.57/222.85 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 222.57/222.85 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 222.57/222.85 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 222.57/222.85 Found x2:(X6 Xx0)
% 222.57/222.85 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 222.57/222.85 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 222.57/222.85 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 222.57/222.85 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 222.87/223.13 Found x2:(X6 Xx0)
% 222.87/223.13 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 222.87/223.13 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 222.87/223.13 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 222.87/223.13 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 222.87/223.13 Found x2:(X6 Xx0)
% 222.87/223.13 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 222.87/223.13 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 222.87/223.13 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 222.87/223.13 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 222.87/223.13 Found x6:(X6 Xx0)
% 222.87/223.13 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 222.87/223.13 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 222.87/223.13 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 222.87/223.13 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 222.87/223.13 Found x400:=(x40 x5):((cK x2) Xx)
% 222.87/223.13 Found (x40 x5) as proof of ((cK X6) Xx)
% 222.87/223.13 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 222.87/223.13 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 222.87/223.13 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 222.87/223.13 Found x2:(X6 Xx0)
% 222.87/223.13 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 222.87/223.13 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 222.87/223.13 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 222.87/223.13 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 222.87/223.13 Found x2:(X6 Xx0)
% 222.87/223.13 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 222.87/223.13 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 222.87/223.13 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 222.87/223.13 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 222.87/223.13 Found x2:(X6 Xx0)
% 222.87/223.13 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 222.87/223.13 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 222.87/223.13 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 222.87/223.13 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 222.87/223.13 Found x6:(X6 Xx0)
% 223.14/223.42 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 223.14/223.42 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 223.14/223.42 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 223.14/223.42 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 223.14/223.42 Found x400:=(x40 x5):((cK x2) Xx)
% 223.14/223.42 Found (x40 x5) as proof of ((cK X6) Xx)
% 223.14/223.42 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 223.14/223.42 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 223.14/223.42 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 223.14/223.42 Found x6:(X6 Xx0)
% 223.14/223.42 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 223.14/223.42 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 223.14/223.42 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 223.14/223.42 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 223.14/223.42 Found x400:=(x40 x5):((cK x2) Xx)
% 223.14/223.42 Found (x40 x5) as proof of ((cK X6) Xx)
% 223.14/223.42 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 223.14/223.42 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 223.14/223.42 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 223.14/223.42 Found x6:(X6 Xx0)
% 223.14/223.42 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 223.14/223.42 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 223.14/223.42 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 223.14/223.42 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 223.14/223.42 Found x400:=(x40 x5):((cK x2) Xx)
% 223.14/223.42 Found (x40 x5) as proof of ((cK X6) Xx)
% 223.14/223.42 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 223.14/223.42 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 223.14/223.42 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 223.14/223.42 Found x6:(X6 Xx0)
% 223.14/223.42 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 223.14/223.42 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 223.14/223.42 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 223.14/223.42 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 223.14/223.42 Found x400:=(x40 x5):((cK x2) Xx)
% 223.14/223.42 Found (x40 x5) as proof of ((cK X6) Xx)
% 223.14/223.42 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 223.14/223.42 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 223.14/223.42 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 223.14/223.42 Found x6:(X6 Xx0)
% 223.14/223.42 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 223.14/223.42 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 223.14/223.42 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 223.14/223.42 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 223.14/223.42 Found x400:=(x40 x5):((cK x2) Xx)
% 223.14/223.42 Found (x40 x5) as proof of ((cK X6) Xx)
% 223.14/223.42 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 223.14/223.42 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 223.14/223.42 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 224.75/225.07 Found x4:(X6 Xx0)
% 224.75/225.07 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 224.75/225.07 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 224.75/225.07 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 224.75/225.07 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 224.75/225.07 Found x4:(X6 Xx0)
% 224.75/225.07 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 224.75/225.07 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 224.75/225.07 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 224.75/225.07 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 224.75/225.07 Found x4:(X6 Xx0)
% 224.75/225.07 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 224.75/225.07 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 224.75/225.07 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 224.75/225.07 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 224.75/225.07 Found x4:(X6 Xx0)
% 224.75/225.07 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 224.75/225.07 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 224.75/225.07 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 224.75/225.07 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 224.75/225.07 Found x4:(X6 Xx0)
% 224.75/225.07 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 224.75/225.07 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 224.75/225.07 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 224.75/225.07 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 224.75/225.07 Found x2:(X6 Xx0)
% 224.75/225.07 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 224.75/225.07 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 224.75/225.07 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 224.75/225.07 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 224.75/225.07 Found x2:(X6 Xx0)
% 224.75/225.07 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 224.75/225.07 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 224.75/225.07 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 225.03/225.37 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 225.03/225.37 Found x2:(X6 Xx0)
% 225.03/225.37 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 225.03/225.37 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 225.03/225.37 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 225.03/225.37 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 225.03/225.37 Found x2:(X6 Xx0)
% 225.03/225.37 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 225.03/225.37 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 225.03/225.37 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 225.03/225.37 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 225.03/225.37 Found x2:(X6 Xx0)
% 225.03/225.37 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 225.03/225.37 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 225.03/225.37 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 225.03/225.37 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 225.03/225.37 Found x2:(X6 Xx0)
% 225.03/225.37 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 225.03/225.37 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 225.03/225.37 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 225.03/225.37 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 225.03/225.37 Found x2:(X6 Xx0)
% 225.03/225.37 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 225.03/225.37 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 225.03/225.37 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 225.03/225.37 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 225.03/225.37 Found x2:(X6 Xx0)
% 225.03/225.37 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 225.03/225.37 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 225.03/225.37 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 225.03/225.37 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 225.03/225.37 Found x2:(X6 Xx0)
% 225.03/225.37 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 225.24/225.59 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 225.24/225.59 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 225.24/225.59 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 225.24/225.59 Found x2:(X6 Xx0)
% 225.24/225.59 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 225.24/225.59 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 225.24/225.59 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 225.24/225.59 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 225.24/225.59 Found x2:(X6 Xx0)
% 225.24/225.59 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 225.24/225.59 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 225.24/225.59 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 225.24/225.59 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 225.24/225.59 Found x2:(X6 Xx0)
% 225.24/225.59 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 225.24/225.59 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 225.24/225.59 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 225.24/225.59 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 225.24/225.59 Found x2:(X6 Xx0)
% 225.24/225.59 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 225.24/225.59 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 225.24/225.59 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 225.24/225.59 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 225.24/225.59 Found x2:(X6 Xx0)
% 225.24/225.59 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 225.24/225.59 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 225.24/225.59 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 225.24/225.59 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 225.24/225.59 Found x2:(X6 Xx0)
% 225.24/225.59 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 225.24/225.59 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 225.24/225.59 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 225.24/225.59 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 228.54/228.84 Found x2:(X6 Xx0)
% 228.54/228.84 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 228.54/228.84 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 228.54/228.84 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 228.54/228.84 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 228.54/228.84 Found x2:(X6 Xx0)
% 228.54/228.84 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 228.54/228.84 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 228.54/228.84 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 228.54/228.84 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 228.54/228.84 Found x2:(X6 Xx0)
% 228.54/228.84 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 228.54/228.84 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 228.54/228.84 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 228.54/228.84 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 228.54/228.84 Found x2:(X6 Xx0)
% 228.54/228.84 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 228.54/228.84 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 228.54/228.84 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 228.54/228.84 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 228.54/228.84 Found x2:(X6 Xx0)
% 228.54/228.84 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 228.54/228.84 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 228.54/228.84 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 228.54/228.84 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 228.54/228.84 Found x2:(X6 Xx0)
% 228.54/228.84 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 228.54/228.84 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 228.54/228.84 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 228.54/228.84 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 228.54/228.84 Found x4:(X6 Xx0)
% 228.54/228.84 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 228.54/228.84 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 231.35/231.70 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 231.35/231.70 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 231.35/231.70 Found x4:(X6 Xx0)
% 231.35/231.70 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 231.35/231.70 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 231.35/231.70 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 231.35/231.70 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 231.35/231.70 Found x4:(X6 Xx0)
% 231.35/231.70 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 231.35/231.70 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 231.35/231.70 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 231.35/231.70 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 231.35/231.70 Found x4:(X6 Xx0)
% 231.35/231.70 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 231.35/231.70 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 231.35/231.70 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 231.35/231.70 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 231.35/231.70 Found x4:(X6 Xx0)
% 231.35/231.70 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 231.35/231.70 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 231.35/231.70 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 231.35/231.70 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 231.35/231.70 Found x6:(X6 Xx0)
% 231.35/231.70 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 231.35/231.70 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 231.35/231.70 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 231.35/231.70 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 231.35/231.70 Found x400:=(x40 x5):((cK x2) Xx)
% 231.35/231.70 Found (x40 x5) as proof of ((cK X6) Xx)
% 231.35/231.70 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 231.35/231.70 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 231.35/231.70 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 231.35/231.70 Found x6:(X6 Xx0)
% 231.35/231.70 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 231.35/231.70 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 231.35/231.70 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 232.13/232.39 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 232.13/232.39 Found x400:=(x40 x5):((cK x2) Xx)
% 232.13/232.39 Found (x40 x5) as proof of ((cK X6) Xx)
% 232.13/232.39 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 232.13/232.39 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 232.13/232.39 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 232.13/232.39 Found x2:(X6 Xx0)
% 232.13/232.39 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 232.13/232.39 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 232.13/232.39 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 232.13/232.39 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 232.13/232.39 Found x6:(X6 Xx0)
% 232.13/232.39 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 232.13/232.39 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 232.13/232.39 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 232.13/232.39 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 232.13/232.39 Found x400:=(x40 x5):((cK x2) Xx)
% 232.13/232.39 Found (x40 x5) as proof of ((cK X6) Xx)
% 232.13/232.39 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 232.13/232.39 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 232.13/232.39 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 232.13/232.39 Found x2:(X6 Xx0)
% 232.13/232.39 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 232.13/232.39 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 232.13/232.39 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 232.13/232.39 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 232.13/232.39 Found x2:(X6 Xx0)
% 232.13/232.39 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 232.13/232.39 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 232.13/232.39 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 232.13/232.39 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 232.13/232.39 Found x2:(X6 Xx0)
% 232.13/232.39 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 232.13/232.39 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 232.13/232.39 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 232.13/232.39 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 232.13/232.39 Found x2:(X6 Xx0)
% 232.13/232.39 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 232.13/232.39 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 232.13/232.39 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 232.36/232.62 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 232.36/232.62 Found x2:(X6 Xx0)
% 232.36/232.62 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 232.36/232.62 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 232.36/232.62 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 232.36/232.62 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 232.36/232.62 Found x2:(X6 Xx0)
% 232.36/232.62 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 232.36/232.62 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 232.36/232.62 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 232.36/232.62 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 232.36/232.62 Found x2:(X6 Xx0)
% 232.36/232.62 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 232.36/232.62 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 232.36/232.62 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 232.36/232.62 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 232.36/232.62 Found x2:(X6 Xx0)
% 232.36/232.62 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 232.36/232.62 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 232.36/232.62 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 232.36/232.62 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 232.36/232.62 Found x2:(X6 Xx0)
% 232.36/232.62 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 232.36/232.62 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 232.36/232.62 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 232.36/232.62 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 232.36/232.62 Found x2:(X6 Xx0)
% 232.36/232.62 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 232.36/232.62 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 232.36/232.62 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 232.36/232.62 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 232.36/232.62 Found x2:(X6 Xx0)
% 232.36/232.62 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 232.45/232.79 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 232.45/232.79 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 232.45/232.79 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 232.45/232.79 Found x2:(X6 Xx0)
% 232.45/232.79 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 232.45/232.79 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 232.45/232.79 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 232.45/232.79 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 232.45/232.79 Found x2:(X6 Xx0)
% 232.45/232.79 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 232.45/232.79 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 232.45/232.79 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 232.45/232.79 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 232.45/232.79 Found x2:(X6 Xx0)
% 232.45/232.79 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 232.45/232.79 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 232.45/232.79 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 232.45/232.79 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 232.45/232.79 Found x2:(X6 Xx0)
% 232.45/232.79 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 232.45/232.79 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 232.45/232.79 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 232.45/232.79 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 232.45/232.79 Found x2:(X6 Xx0)
% 232.45/232.79 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 232.45/232.79 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 232.45/232.79 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 232.45/232.79 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 232.45/232.79 Found x2:(X6 Xx0)
% 232.45/232.79 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 232.45/232.79 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 232.45/232.79 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 232.45/232.79 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 232.73/232.99 Found x2:(X6 Xx0)
% 232.73/232.99 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 232.73/232.99 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 232.73/232.99 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 232.73/232.99 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 232.73/232.99 Found x2:(X6 Xx0)
% 232.73/232.99 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 232.73/232.99 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 232.73/232.99 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 232.73/232.99 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 232.73/232.99 Found x2:(X6 Xx0)
% 232.73/232.99 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 232.73/232.99 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 232.73/232.99 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 232.73/232.99 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 232.73/232.99 Found x2:(X6 Xx0)
% 232.73/232.99 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 232.73/232.99 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 232.73/232.99 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 232.73/232.99 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 232.73/232.99 Found x2:(X6 Xx0)
% 232.73/232.99 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 232.73/232.99 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 232.73/232.99 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 232.73/232.99 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 232.73/232.99 Found x2:(X6 Xx0)
% 232.73/232.99 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 232.73/232.99 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 232.73/232.99 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 232.73/232.99 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 232.73/232.99 Found x2:(X6 Xx0)
% 232.73/232.99 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 232.73/232.99 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 232.93/233.21 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 232.93/233.21 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 232.93/233.21 Found x2:(X6 Xx0)
% 232.93/233.21 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 232.93/233.21 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 232.93/233.21 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 232.93/233.21 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 232.93/233.21 Found x2:(X6 Xx0)
% 232.93/233.21 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 232.93/233.21 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 232.93/233.21 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 232.93/233.21 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 232.93/233.21 Found x2:(X6 Xx0)
% 232.93/233.21 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 232.93/233.21 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 232.93/233.21 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 232.93/233.21 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 232.93/233.21 Found x2:(X6 Xx0)
% 232.93/233.21 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 232.93/233.21 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 232.93/233.21 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 232.93/233.21 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 232.93/233.21 Found x2:(X6 Xx0)
% 232.93/233.21 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 232.93/233.21 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 232.93/233.21 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 232.93/233.21 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 232.93/233.21 Found x2:(X6 Xx0)
% 232.93/233.21 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 232.93/233.21 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 232.93/233.21 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 232.93/233.21 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 232.93/233.21 Found x2:(X6 Xx0)
% 232.93/233.21 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 233.06/233.40 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 233.06/233.40 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 233.06/233.40 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 233.06/233.40 Found x2:(X6 Xx0)
% 233.06/233.40 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 233.06/233.40 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 233.06/233.40 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 233.06/233.40 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 233.06/233.40 Found x2:(X6 Xx0)
% 233.06/233.40 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 233.06/233.40 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 233.06/233.40 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 233.06/233.40 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 233.06/233.40 Found x2:(X6 Xx0)
% 233.06/233.40 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 233.06/233.40 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 233.06/233.40 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 233.06/233.40 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 233.06/233.40 Found x6:(X6 Xx0)
% 233.06/233.40 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 233.06/233.40 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 233.06/233.40 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 233.06/233.40 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 233.06/233.40 Found x400:=(x40 x5):((cK x2) Xx)
% 233.06/233.40 Found (x40 x5) as proof of ((cK X6) Xx)
% 233.06/233.40 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 233.06/233.40 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 233.06/233.40 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 233.06/233.40 Found x6:(X6 Xx0)
% 233.06/233.40 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 233.06/233.40 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 233.06/233.40 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 233.06/233.40 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 233.06/233.40 Found x400:=(x40 x5):((cK x2) Xx)
% 233.06/233.40 Found (x40 x5) as proof of ((cK X6) Xx)
% 233.06/233.40 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 233.06/233.40 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 233.06/233.40 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 233.52/233.85 Found x6:(X6 Xx0)
% 233.52/233.85 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 233.52/233.85 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 233.52/233.85 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 233.52/233.85 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 233.52/233.85 Found x400:=(x40 x5):((cK x2) Xx)
% 233.52/233.85 Found (x40 x5) as proof of ((cK X6) Xx)
% 233.52/233.85 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 233.52/233.85 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 233.52/233.85 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 233.52/233.85 Found x6:(X6 Xx0)
% 233.52/233.85 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 233.52/233.85 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 233.52/233.85 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 233.52/233.85 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 233.52/233.85 Found x400:=(x40 x5):((cK x2) Xx)
% 233.52/233.85 Found (x40 x5) as proof of ((cK X6) Xx)
% 233.52/233.85 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 233.52/233.85 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 233.52/233.85 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 233.52/233.85 Found x6:(X6 Xx0)
% 233.52/233.85 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 233.52/233.85 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 233.52/233.85 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 233.52/233.85 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 233.52/233.85 Found x400:=(x40 x5):((cK x2) Xx)
% 233.52/233.85 Found (x40 x5) as proof of ((cK X6) Xx)
% 233.52/233.85 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 233.52/233.85 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 233.52/233.85 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 233.52/233.85 Found x6:(X6 Xx0)
% 233.52/233.85 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 233.52/233.85 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 233.52/233.85 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 233.52/233.85 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 233.52/233.85 Found x400:=(x40 x5):((cK x2) Xx)
% 233.52/233.85 Found (x40 x5) as proof of ((cK X6) Xx)
% 233.52/233.85 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 233.52/233.85 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 233.52/233.85 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 233.52/233.85 Found x6:(X6 Xx0)
% 233.52/233.85 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 233.52/233.85 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 233.52/233.85 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 233.52/233.85 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 233.52/233.85 Found x400:=(x40 x5):((cK x2) Xx)
% 233.52/233.85 Found (x40 x5) as proof of ((cK X6) Xx)
% 233.52/233.85 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 233.52/233.85 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 233.76/234.07 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 233.76/234.07 Found x6:(X6 Xx0)
% 233.76/234.07 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 233.76/234.07 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 233.76/234.07 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 233.76/234.07 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 233.76/234.07 Found x400:=(x40 x5):((cK x2) Xx)
% 233.76/234.07 Found (x40 x5) as proof of ((cK X6) Xx)
% 233.76/234.07 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 233.76/234.07 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 233.76/234.07 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 233.76/234.07 Found x6:(X6 Xx0)
% 233.76/234.07 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 233.76/234.07 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 233.76/234.07 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 233.76/234.07 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 233.76/234.07 Found x400:=(x40 x5):((cK x2) Xx)
% 233.76/234.07 Found (x40 x5) as proof of ((cK X6) Xx)
% 233.76/234.07 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 233.76/234.07 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 233.76/234.07 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 233.76/234.07 Found x6:(X6 Xx0)
% 233.76/234.07 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 233.76/234.07 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 233.76/234.07 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 233.76/234.07 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 233.76/234.07 Found x400:=(x40 x5):((cK x2) Xx)
% 233.76/234.07 Found (x40 x5) as proof of ((cK X6) Xx)
% 233.76/234.07 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 233.76/234.07 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 233.76/234.07 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 233.76/234.07 Found x6:(X6 Xx0)
% 233.76/234.07 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 233.76/234.07 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 233.76/234.07 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 233.76/234.07 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 233.76/234.07 Found x400:=(x40 x5):((cK x2) Xx)
% 233.76/234.07 Found (x40 x5) as proof of ((cK X6) Xx)
% 233.76/234.07 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 233.76/234.07 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 233.76/234.07 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 233.76/234.07 Found x6:(X6 Xx0)
% 233.76/234.07 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 233.76/234.07 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 233.76/234.07 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 233.76/234.07 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 233.76/234.07 Found x400:=(x40 x5):((cK x2) Xx)
% 233.76/234.07 Found (x40 x5) as proof of ((cK X6) Xx)
% 233.76/234.07 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 233.76/234.07 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 234.57/234.86 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 234.57/234.86 Found x6:(X6 Xx0)
% 234.57/234.86 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 234.57/234.86 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 234.57/234.86 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 234.57/234.86 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 234.57/234.86 Found x400:=(x40 x5):((cK x2) Xx)
% 234.57/234.86 Found (x40 x5) as proof of ((cK X6) Xx)
% 234.57/234.86 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 234.57/234.86 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 234.57/234.86 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 234.57/234.86 Found x4:(X6 Xx0)
% 234.57/234.86 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 234.57/234.86 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 234.57/234.86 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 234.57/234.86 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 234.57/234.86 Found x4:(X6 Xx0)
% 234.57/234.86 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 234.57/234.86 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 234.57/234.86 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 234.57/234.86 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 234.57/234.86 Found x4:(X6 Xx0)
% 234.57/234.86 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 234.57/234.86 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 234.57/234.86 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 234.57/234.86 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 234.57/234.86 Found x6:(X6 Xx0)
% 234.57/234.86 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 234.57/234.86 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 234.57/234.86 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 234.57/234.86 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 234.57/234.86 Found x400:=(x40 x5):((cK x2) Xx)
% 234.57/234.86 Found (x40 x5) as proof of ((cK X6) Xx)
% 234.57/234.86 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 234.57/234.86 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 234.57/234.86 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 234.57/234.86 Found x6:(X6 Xx0)
% 234.57/234.86 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 234.57/234.86 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 234.57/234.86 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 234.57/234.86 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 235.02/235.30 Found x400:=(x40 x5):((cK x2) Xx)
% 235.02/235.30 Found (x40 x5) as proof of ((cK X6) Xx)
% 235.02/235.30 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 235.02/235.30 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 235.02/235.30 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 235.02/235.30 Found x4:(X6 Xx0)
% 235.02/235.30 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 235.02/235.30 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 235.02/235.30 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 235.02/235.30 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 235.02/235.30 Found x4:(X6 Xx0)
% 235.02/235.30 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 235.02/235.30 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 235.02/235.30 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 235.02/235.30 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 235.02/235.30 Found x4:(X6 Xx0)
% 235.02/235.30 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 235.02/235.30 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 235.02/235.30 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 235.02/235.30 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 235.02/235.30 Found x4:(X6 Xx0)
% 235.02/235.30 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 235.02/235.30 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 235.02/235.30 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 235.02/235.30 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 235.02/235.30 Found x6:(X6 Xx0)
% 235.02/235.30 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 235.02/235.30 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 235.02/235.30 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 235.02/235.30 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 235.02/235.30 Found x400:=(x40 x5):((cK x2) Xx)
% 235.02/235.30 Found (x40 x5) as proof of ((cK X6) Xx)
% 235.02/235.30 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 235.02/235.30 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 235.02/235.30 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 235.02/235.30 Found x4:(X6 Xx0)
% 235.02/235.30 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 235.02/235.30 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 235.02/235.30 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 235.02/235.30 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 235.54/235.81 Found x2:(X6 Xx0)
% 235.54/235.81 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 235.54/235.81 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 235.54/235.81 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 235.54/235.81 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 235.54/235.81 Found x2:(X6 Xx0)
% 235.54/235.81 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 235.54/235.81 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 235.54/235.81 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 235.54/235.81 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 235.54/235.81 Found x2:(X6 Xx0)
% 235.54/235.81 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 235.54/235.81 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 235.54/235.81 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 235.54/235.81 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 235.54/235.81 Found x2:(X6 Xx0)
% 235.54/235.81 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 235.54/235.81 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 235.54/235.81 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 235.54/235.81 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 235.54/235.81 Found x2:(X6 Xx0)
% 235.54/235.81 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 235.54/235.81 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 235.54/235.81 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 235.54/235.81 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 235.54/235.81 Found x2:(X6 Xx0)
% 235.54/235.81 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 235.54/235.81 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 235.54/235.81 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 235.54/235.81 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 235.54/235.81 Found x2:(X6 Xx0)
% 235.54/235.81 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 235.54/235.81 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 235.73/236.00 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 235.73/236.00 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 235.73/236.00 Found x2:(X6 Xx0)
% 235.73/236.00 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 235.73/236.00 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 235.73/236.00 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 235.73/236.00 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 235.73/236.00 Found x2:(X6 Xx0)
% 235.73/236.00 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 235.73/236.00 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 235.73/236.00 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 235.73/236.00 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 235.73/236.00 Found x2:(X6 Xx0)
% 235.73/236.00 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 235.73/236.00 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 235.73/236.00 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 235.73/236.00 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 235.73/236.00 Found x2:(X6 Xx0)
% 235.73/236.00 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 235.73/236.00 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 235.73/236.00 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 235.73/236.00 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 235.73/236.00 Found x2:(X6 Xx0)
% 235.73/236.00 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 235.73/236.00 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 235.73/236.00 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 235.73/236.00 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 235.73/236.00 Found x2:(X6 Xx0)
% 235.73/236.00 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 235.73/236.00 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 235.73/236.00 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 235.73/236.00 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 235.85/236.19 Found x2:(X6 Xx0)
% 235.85/236.19 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 235.85/236.19 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 235.85/236.19 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 235.85/236.19 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 235.85/236.19 Found x2:(X6 Xx0)
% 235.85/236.19 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 235.85/236.19 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 235.85/236.19 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 235.85/236.19 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 235.85/236.19 Found x2:(X6 Xx0)
% 235.85/236.19 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 235.85/236.19 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 235.85/236.19 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 235.85/236.19 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 235.85/236.19 Found x2:(X6 Xx0)
% 235.85/236.19 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 235.85/236.19 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 235.85/236.19 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 235.85/236.19 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 235.85/236.19 Found x2:(X6 Xx0)
% 235.85/236.19 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 235.85/236.19 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 235.85/236.19 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 235.85/236.19 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 235.85/236.19 Found x2:(X6 Xx0)
% 235.85/236.19 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 235.85/236.19 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 235.85/236.19 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 235.85/236.19 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 235.85/236.19 Found x2:(X6 Xx0)
% 235.85/236.19 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 235.85/236.19 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 235.85/236.19 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 236.04/236.39 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 236.04/236.39 Found x2:(X6 Xx0)
% 236.04/236.39 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 236.04/236.39 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 236.04/236.39 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 236.04/236.39 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 236.04/236.39 Found x2:(X6 Xx0)
% 236.04/236.39 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 236.04/236.39 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 236.04/236.39 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 236.04/236.39 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 236.04/236.39 Found x2:(X6 Xx0)
% 236.04/236.39 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 236.04/236.39 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 236.04/236.39 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 236.04/236.39 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 236.04/236.39 Found x2:(X6 Xx0)
% 236.04/236.39 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 236.04/236.39 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 236.04/236.39 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 236.04/236.39 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 236.04/236.39 Found x2:(X6 Xx0)
% 236.04/236.39 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 236.04/236.39 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 236.04/236.39 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 236.04/236.39 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 236.04/236.39 Found x2:(X6 Xx0)
% 236.04/236.39 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 236.04/236.39 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 236.04/236.39 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 236.04/236.39 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 236.04/236.39 Found x2:(X6 Xx0)
% 236.04/236.39 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 236.34/236.64 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 236.34/236.64 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 236.34/236.64 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 236.34/236.64 Found x2:(X6 Xx0)
% 236.34/236.64 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 236.34/236.64 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 236.34/236.64 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 236.34/236.64 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 236.34/236.64 Found x2:(X6 Xx0)
% 236.34/236.64 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 236.34/236.64 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 236.34/236.64 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 236.34/236.64 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 236.34/236.64 Found x2:(X6 Xx0)
% 236.34/236.64 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 236.34/236.64 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 236.34/236.64 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 236.34/236.64 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 236.34/236.64 Found x2:(X6 Xx0)
% 236.34/236.64 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 236.34/236.64 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 236.34/236.64 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 236.34/236.64 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 236.34/236.64 Found x2:(X6 Xx0)
% 236.34/236.64 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 236.34/236.64 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 236.34/236.64 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 236.34/236.64 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 236.34/236.64 Found x2:(X6 Xx0)
% 236.34/236.64 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 236.34/236.64 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 236.34/236.64 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 236.34/236.64 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 239.03/239.37 Found x2:(X6 Xx0)
% 239.03/239.37 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 239.03/239.37 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 239.03/239.37 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 239.03/239.37 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 239.03/239.37 Found x2:(X6 Xx0)
% 239.03/239.37 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 239.03/239.37 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 239.03/239.37 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 239.03/239.37 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 239.03/239.37 Found x4:(X6 Xx0)
% 239.03/239.37 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 239.03/239.37 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 239.03/239.37 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 239.03/239.37 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 239.03/239.37 Found x4:(X6 Xx0)
% 239.03/239.37 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 239.03/239.37 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 239.03/239.37 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 239.03/239.37 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 239.03/239.37 Found x4:(X6 Xx0)
% 239.03/239.37 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 239.03/239.37 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 239.03/239.37 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 239.03/239.37 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 239.03/239.37 Found x4:(X6 Xx0)
% 239.03/239.37 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 239.03/239.37 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 239.03/239.37 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 239.03/239.37 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 239.03/239.37 Found x4:(X6 Xx0)
% 239.03/239.37 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 239.03/239.37 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 241.12/241.46 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 241.12/241.46 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 241.12/241.46 Found x4:(X6 Xx0)
% 241.12/241.46 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 241.12/241.46 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 241.12/241.46 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 241.12/241.46 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 241.12/241.46 Found x4:(X6 Xx0)
% 241.12/241.46 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 241.12/241.46 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 241.12/241.46 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 241.12/241.46 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 241.12/241.46 Found x4:(X6 Xx0)
% 241.12/241.46 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 241.12/241.46 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 241.12/241.46 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 241.12/241.46 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 241.12/241.46 Found x6:(X6 Xx0)
% 241.12/241.46 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 241.12/241.46 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 241.12/241.46 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 241.12/241.46 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 241.12/241.46 Found x400:=(x40 x5):((cK x2) Xx)
% 241.12/241.46 Found (x40 x5) as proof of ((cK X6) Xx)
% 241.12/241.46 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 241.12/241.46 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 241.12/241.46 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 241.12/241.46 Found x6:(X6 Xx0)
% 241.12/241.46 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 241.12/241.46 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 241.12/241.46 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 241.12/241.46 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 241.12/241.46 Found x400:=(x40 x5):((cK x2) Xx)
% 241.12/241.46 Found (x40 x5) as proof of ((cK X6) Xx)
% 241.12/241.46 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 241.12/241.46 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 241.12/241.46 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 241.12/241.46 Found x6:(X6 Xx0)
% 241.12/241.46 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 241.12/241.46 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 241.57/241.86 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 241.57/241.86 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 241.57/241.86 Found x400:=(x40 x5):((cK x2) Xx)
% 241.57/241.86 Found (x40 x5) as proof of ((cK X6) Xx)
% 241.57/241.86 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 241.57/241.86 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 241.57/241.86 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 241.57/241.86 Found x6:(X6 Xx0)
% 241.57/241.86 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 241.57/241.86 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 241.57/241.86 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 241.57/241.86 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 241.57/241.86 Found x400:=(x40 x5):((cK x2) Xx)
% 241.57/241.86 Found (x40 x5) as proof of ((cK X6) Xx)
% 241.57/241.86 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 241.57/241.86 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 241.57/241.86 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 241.57/241.86 Found x6:(X6 Xx0)
% 241.57/241.86 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 241.57/241.86 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 241.57/241.86 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 241.57/241.86 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 241.57/241.86 Found x400:=(x40 x5):((cK x2) Xx)
% 241.57/241.86 Found (x40 x5) as proof of ((cK X6) Xx)
% 241.57/241.86 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 241.57/241.86 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 241.57/241.86 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 241.57/241.86 Found x6:(X6 Xx0)
% 241.57/241.86 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 241.57/241.86 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 241.57/241.86 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 241.57/241.86 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 241.57/241.86 Found x400:=(x40 x5):((cK x2) Xx)
% 241.57/241.86 Found (x40 x5) as proof of ((cK X6) Xx)
% 241.57/241.86 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 241.57/241.86 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 241.57/241.86 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 241.57/241.87 Found x2:(X6 Xx0)
% 241.57/241.87 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 241.57/241.87 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 241.57/241.87 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 241.57/241.87 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 241.57/241.87 Found x2:(X6 Xx0)
% 241.57/241.87 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 241.57/241.87 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 241.57/241.87 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 241.71/242.07 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 241.71/242.07 Found x2:(X6 Xx0)
% 241.71/242.07 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 241.71/242.07 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 241.71/242.07 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 241.71/242.07 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 241.71/242.07 Found x2:(X6 Xx0)
% 241.71/242.07 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 241.71/242.07 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 241.71/242.07 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 241.71/242.07 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 241.71/242.07 Found x2:(X6 Xx0)
% 241.71/242.07 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 241.71/242.07 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 241.71/242.07 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 241.71/242.07 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 241.71/242.07 Found x2:(X6 Xx0)
% 241.71/242.07 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 241.71/242.07 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 241.71/242.07 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 241.71/242.07 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 241.71/242.07 Found x2:(X6 Xx0)
% 241.71/242.07 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 241.71/242.07 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 241.71/242.07 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 241.71/242.07 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 241.71/242.07 Found x2:(X6 Xx0)
% 241.71/242.07 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 241.71/242.07 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 241.71/242.07 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 241.71/242.07 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 241.71/242.07 Found x2:(X6 Xx0)
% 241.71/242.07 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 241.95/242.25 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 241.95/242.25 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 241.95/242.25 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 241.95/242.25 Found x2:(X6 Xx0)
% 241.95/242.25 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 241.95/242.25 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 241.95/242.25 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 241.95/242.25 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 241.95/242.25 Found x2:(X6 Xx0)
% 241.95/242.25 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 241.95/242.25 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 241.95/242.25 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 241.95/242.25 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 241.95/242.25 Found x6:(X6 Xx0)
% 241.95/242.25 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 241.95/242.25 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 241.95/242.25 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 241.95/242.25 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 241.95/242.25 Found x400:=(x40 x5):((cK x2) Xx)
% 241.95/242.25 Found (x40 x5) as proof of ((cK X6) Xx)
% 241.95/242.25 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 241.95/242.25 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 241.95/242.25 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 241.95/242.25 Found x2:(X6 Xx0)
% 241.95/242.25 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 241.95/242.25 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 241.95/242.25 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 241.95/242.25 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 241.95/242.25 Found x2:(X6 Xx0)
% 241.95/242.25 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 241.95/242.25 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 241.95/242.25 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 241.95/242.25 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 241.95/242.25 Found x2:(X6 Xx0)
% 241.95/242.25 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 241.95/242.25 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 241.95/242.25 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 242.16/242.46 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 242.16/242.46 Found x2:(X6 Xx0)
% 242.16/242.46 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 242.16/242.46 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 242.16/242.46 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 242.16/242.46 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 242.16/242.46 Found x2:(X6 Xx0)
% 242.16/242.46 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 242.16/242.46 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 242.16/242.46 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 242.16/242.46 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 242.16/242.46 Found x2:(X6 Xx0)
% 242.16/242.46 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 242.16/242.46 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 242.16/242.46 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 242.16/242.46 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 242.16/242.46 Found x2:(X6 Xx0)
% 242.16/242.46 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 242.16/242.46 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 242.16/242.46 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 242.16/242.46 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 242.16/242.46 Found x2:(X6 Xx0)
% 242.16/242.46 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 242.16/242.46 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 242.16/242.46 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 242.16/242.46 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 242.16/242.46 Found x2:(X6 Xx0)
% 242.16/242.46 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 242.16/242.46 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 242.16/242.46 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 242.16/242.46 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 242.16/242.46 Found x2:(X6 Xx0)
% 242.16/242.46 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 242.94/243.24 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 242.94/243.24 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 242.94/243.24 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 242.94/243.24 Found x6:(X6 Xx0)
% 242.94/243.24 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 242.94/243.24 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 242.94/243.24 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 242.94/243.24 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 242.94/243.24 Found x400:=(x40 x5):((cK x2) Xx)
% 242.94/243.24 Found (x40 x5) as proof of ((cK X6) Xx)
% 242.94/243.24 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 242.94/243.24 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 242.94/243.24 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 242.94/243.24 Found x6:(X6 Xx0)
% 242.94/243.24 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 242.94/243.24 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 242.94/243.24 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 242.94/243.24 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 242.94/243.24 Found x400:=(x40 x5):((cK x2) Xx)
% 242.94/243.24 Found (x40 x5) as proof of ((cK X6) Xx)
% 242.94/243.24 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 242.94/243.24 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 242.94/243.24 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 242.94/243.24 Found x6:(X6 Xx0)
% 242.94/243.24 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 242.94/243.24 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 242.94/243.24 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 242.94/243.24 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 242.94/243.24 Found x400:=(x40 x5):((cK x2) Xx)
% 242.94/243.24 Found (x40 x5) as proof of ((cK X6) Xx)
% 242.94/243.24 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 242.94/243.24 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 242.94/243.24 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 242.94/243.24 Found x6:(X6 Xx0)
% 242.94/243.24 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 242.94/243.24 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 242.94/243.24 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 242.94/243.24 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 242.94/243.24 Found x400:=(x40 x5):((cK x2) Xx)
% 242.94/243.24 Found (x40 x5) as proof of ((cK X6) Xx)
% 242.94/243.24 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 242.94/243.24 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 242.94/243.24 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 242.94/243.24 Found x6:(X6 Xx0)
% 242.94/243.24 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 242.94/243.24 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 243.34/243.65 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 243.34/243.65 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 243.34/243.65 Found x400:=(x40 x5):((cK x2) Xx)
% 243.34/243.65 Found (x40 x5) as proof of ((cK X6) Xx)
% 243.34/243.65 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 243.34/243.65 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 243.34/243.65 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 243.34/243.65 Found x6:(X6 Xx0)
% 243.34/243.65 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 243.34/243.65 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 243.34/243.65 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 243.34/243.65 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 243.34/243.65 Found x400:=(x40 x5):((cK x2) Xx)
% 243.34/243.65 Found (x40 x5) as proof of ((cK X6) Xx)
% 243.34/243.65 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 243.34/243.65 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 243.34/243.65 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 243.34/243.65 Found x6:(X6 Xx0)
% 243.34/243.65 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 243.34/243.65 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 243.34/243.65 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 243.34/243.65 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 243.34/243.65 Found x400:=(x40 x5):((cK x2) Xx)
% 243.34/243.65 Found (x40 x5) as proof of ((cK X6) Xx)
% 243.34/243.65 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 243.34/243.65 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 243.34/243.65 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 243.34/243.65 Found x6:(X6 Xx0)
% 243.34/243.65 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 243.34/243.65 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 243.34/243.65 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 243.34/243.65 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 243.34/243.65 Found x400:=(x40 x5):((cK x2) Xx)
% 243.34/243.65 Found (x40 x5) as proof of ((cK X6) Xx)
% 243.34/243.65 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 243.34/243.65 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 243.34/243.65 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 243.34/243.65 Found x6:(X6 Xx0)
% 243.34/243.65 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 243.34/243.65 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 243.34/243.65 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 243.34/243.65 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 243.34/243.65 Found x400:=(x40 x5):((cK x2) Xx)
% 243.34/243.65 Found (x40 x5) as proof of ((cK X6) Xx)
% 243.34/243.65 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 243.34/243.65 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 243.34/243.65 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 243.34/243.65 Found x6:(X6 Xx0)
% 243.34/243.65 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 243.34/243.65 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 243.56/243.87 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 243.56/243.87 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 243.56/243.87 Found x400:=(x40 x5):((cK x2) Xx)
% 243.56/243.87 Found (x40 x5) as proof of ((cK X6) Xx)
% 243.56/243.87 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 243.56/243.87 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 243.56/243.87 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 243.56/243.87 Found x6:(X6 Xx0)
% 243.56/243.87 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 243.56/243.87 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 243.56/243.87 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 243.56/243.87 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 243.56/243.87 Found x400:=(x40 x5):((cK x2) Xx)
% 243.56/243.87 Found (x40 x5) as proof of ((cK X6) Xx)
% 243.56/243.87 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 243.56/243.87 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 243.56/243.87 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 243.56/243.87 Found x6:(X6 Xx0)
% 243.56/243.87 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 243.56/243.87 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 243.56/243.87 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 243.56/243.87 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 243.56/243.87 Found x400:=(x40 x5):((cK x2) Xx)
% 243.56/243.87 Found (x40 x5) as proof of ((cK X6) Xx)
% 243.56/243.87 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 243.56/243.87 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 243.56/243.87 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 243.56/243.87 Found x6:(X6 Xx0)
% 243.56/243.87 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 243.56/243.87 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 243.56/243.87 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 243.56/243.87 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 243.56/243.87 Found x400:=(x40 x5):((cK x2) Xx)
% 243.56/243.87 Found (x40 x5) as proof of ((cK X6) Xx)
% 243.56/243.87 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 243.56/243.87 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 243.56/243.87 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 243.56/243.87 Found x6:(X6 Xx0)
% 243.56/243.87 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 243.56/243.87 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 243.56/243.87 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 243.56/243.87 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 243.56/243.87 Found x400:=(x40 x5):((cK x2) Xx)
% 243.56/243.87 Found (x40 x5) as proof of ((cK X6) Xx)
% 243.56/243.87 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 243.56/243.87 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 243.56/243.87 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 243.56/243.87 Found x4:(X6 Xx0)
% 243.56/243.87 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 243.56/243.87 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 244.00/244.31 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 244.00/244.31 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 244.00/244.31 Found x4:(X6 Xx0)
% 244.00/244.31 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 244.00/244.31 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 244.00/244.31 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 244.00/244.31 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 244.00/244.31 Found x6:(X6 Xx0)
% 244.00/244.31 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 244.00/244.31 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 244.00/244.31 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 244.00/244.31 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 244.00/244.31 Found x400:=(x40 x5):((cK x2) Xx)
% 244.00/244.31 Found (x40 x5) as proof of ((cK X6) Xx)
% 244.00/244.31 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 244.00/244.31 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 244.00/244.31 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 244.00/244.31 Found x4:(X6 Xx0)
% 244.00/244.31 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 244.00/244.31 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 244.00/244.31 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 244.00/244.31 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 244.00/244.31 Found x4:(X6 Xx0)
% 244.00/244.31 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 244.00/244.31 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 244.00/244.31 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 244.00/244.31 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 244.00/244.31 Found x4:(X6 Xx0)
% 244.00/244.31 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 244.00/244.31 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 244.00/244.31 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 244.00/244.31 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 244.00/244.31 Found x4:(X6 Xx0)
% 244.00/244.31 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 244.00/244.31 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 244.00/244.31 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 244.62/244.92 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 244.62/244.92 Found x4:(X6 Xx0)
% 244.62/244.92 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 244.62/244.92 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 244.62/244.92 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 244.62/244.92 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 244.62/244.92 Found x6:(X6 Xx0)
% 244.62/244.92 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 244.62/244.92 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 244.62/244.92 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 244.62/244.92 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 244.62/244.92 Found x400:=(x40 x5):((cK x2) Xx)
% 244.62/244.92 Found (x40 x5) as proof of ((cK X6) Xx)
% 244.62/244.92 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 244.62/244.92 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 244.62/244.92 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 244.62/244.92 Found x4:(X6 Xx0)
% 244.62/244.92 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 244.62/244.92 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 244.62/244.92 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 244.62/244.92 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 244.62/244.92 Found x4:(X6 Xx0)
% 244.62/244.92 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 244.62/244.92 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 244.62/244.92 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 244.62/244.92 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 244.62/244.92 Found x4:(X6 Xx0)
% 244.62/244.92 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 244.62/244.92 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 244.62/244.92 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 244.62/244.92 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 244.62/244.92 Found x4:(X6 Xx0)
% 244.62/244.92 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 244.62/244.92 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 244.62/244.92 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 244.62/244.92 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 245.06/245.40 Found x4:(X6 Xx0)
% 245.06/245.40 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 245.06/245.40 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 245.06/245.40 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 245.06/245.40 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 245.06/245.40 Found x6:(X6 Xx0)
% 245.06/245.40 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 245.06/245.40 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 245.06/245.40 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 245.06/245.40 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 245.06/245.40 Found x400:=(x40 x5):((cK x2) Xx)
% 245.06/245.40 Found (x40 x5) as proof of ((cK X6) Xx)
% 245.06/245.40 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 245.06/245.40 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 245.06/245.40 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 245.06/245.40 Found x6:(X6 Xx0)
% 245.06/245.40 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 245.06/245.40 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 245.06/245.40 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 245.06/245.40 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 245.06/245.40 Found x400:=(x40 x5):((cK x2) Xx)
% 245.06/245.40 Found (x40 x5) as proof of ((cK X6) Xx)
% 245.06/245.40 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 245.06/245.40 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 245.06/245.40 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 245.06/245.40 Found x6:(X6 Xx0)
% 245.06/245.40 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 245.06/245.40 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 245.06/245.40 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 245.06/245.40 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 245.06/245.40 Found x400:=(x40 x5):((cK x2) Xx)
% 245.06/245.40 Found (x40 x5) as proof of ((cK X6) Xx)
% 245.06/245.40 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 245.06/245.40 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 245.06/245.40 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 245.06/245.40 Found x6:(X6 Xx0)
% 245.06/245.40 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 245.06/245.40 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 245.06/245.40 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 245.06/245.40 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 245.06/245.40 Found x400:=(x40 x5):((cK x2) Xx)
% 245.06/245.40 Found (x40 x5) as proof of ((cK X6) Xx)
% 245.06/245.40 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 245.06/245.40 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 245.06/245.40 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 245.06/245.40 Found x6:(X6 Xx0)
% 245.06/245.40 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 245.75/246.09 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 245.75/246.09 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 245.75/246.09 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 245.75/246.09 Found x400:=(x40 x5):((cK x2) Xx)
% 245.75/246.09 Found (x40 x5) as proof of ((cK X6) Xx)
% 245.75/246.09 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 245.75/246.09 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 245.75/246.09 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 245.75/246.09 Found x6:(X6 Xx0)
% 245.75/246.09 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 245.75/246.09 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 245.75/246.09 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 245.75/246.09 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 245.75/246.09 Found x400:=(x40 x5):((cK x2) Xx)
% 245.75/246.09 Found (x40 x5) as proof of ((cK X6) Xx)
% 245.75/246.09 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 245.75/246.09 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 245.75/246.09 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 245.75/246.09 Found x6:(X6 Xx0)
% 245.75/246.09 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 245.75/246.09 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 245.75/246.09 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 245.75/246.09 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 245.75/246.09 Found x400:=(x40 x5):((cK x2) Xx)
% 245.75/246.09 Found (x40 x5) as proof of ((cK X6) Xx)
% 245.75/246.09 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 245.75/246.09 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 245.75/246.09 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 245.75/246.09 Found x6:(X6 Xx0)
% 245.75/246.09 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 245.75/246.09 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 245.75/246.09 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 245.75/246.09 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 245.75/246.09 Found x400:=(x40 x5):((cK x2) Xx)
% 245.75/246.09 Found (x40 x5) as proof of ((cK X6) Xx)
% 245.75/246.09 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 245.75/246.09 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 245.75/246.09 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 245.75/246.09 Found x4:(X6 Xx0)
% 245.75/246.09 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 245.75/246.09 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 245.75/246.09 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 245.75/246.09 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 245.75/246.09 Found x6:(X6 Xx0)
% 245.75/246.09 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 245.75/246.09 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 247.44/247.71 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 247.44/247.71 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 247.44/247.71 Found x400:=(x40 x5):((cK x2) Xx)
% 247.44/247.71 Found (x40 x5) as proof of ((cK X6) Xx)
% 247.44/247.71 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 247.44/247.71 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 247.44/247.71 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 247.44/247.71 Found x2:(X6 Xx0)
% 247.44/247.71 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 247.44/247.71 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 247.44/247.71 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 247.44/247.71 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 247.44/247.71 Found x2:(X6 Xx0)
% 247.44/247.71 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 247.44/247.71 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 247.44/247.71 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 247.44/247.71 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 247.44/247.71 Found x2:(X6 Xx0)
% 247.44/247.71 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 247.44/247.71 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 247.44/247.71 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 247.44/247.71 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 247.44/247.71 Found x2:(X6 Xx0)
% 247.44/247.71 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 247.44/247.71 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 247.44/247.71 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 247.44/247.71 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 247.44/247.71 Found x2:(X6 Xx0)
% 247.44/247.71 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 247.44/247.71 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 247.44/247.71 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 247.44/247.71 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 247.44/247.71 Found x2:(X6 Xx0)
% 247.44/247.71 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 247.44/247.71 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 247.44/247.71 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 248.12/248.47 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 248.12/248.47 Found x2:(X6 Xx0)
% 248.12/248.47 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 248.12/248.47 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 248.12/248.47 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 248.12/248.47 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 248.12/248.47 Found x4:(X6 Xx0)
% 248.12/248.47 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 248.12/248.47 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 248.12/248.47 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 248.12/248.47 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 248.12/248.47 Found x4:(X6 Xx0)
% 248.12/248.47 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 248.12/248.47 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 248.12/248.47 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 248.12/248.47 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 248.12/248.47 Found x4:(X6 Xx0)
% 248.12/248.47 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 248.12/248.47 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 248.12/248.47 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 248.12/248.47 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 248.12/248.47 Found x4:(X6 Xx0)
% 248.12/248.47 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 248.12/248.47 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 248.12/248.47 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 248.12/248.47 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 248.12/248.47 Found x4:(X6 Xx0)
% 248.12/248.47 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 248.12/248.47 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 248.12/248.47 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 248.12/248.47 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 248.12/248.47 Found x4:(X6 Xx0)
% 248.12/248.47 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 248.12/248.47 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 249.02/249.30 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 249.02/249.30 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 249.02/249.30 Found x4:(X6 Xx0)
% 249.02/249.30 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 249.02/249.30 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 249.02/249.30 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 249.02/249.30 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 249.02/249.30 Found x4:(X6 Xx0)
% 249.02/249.30 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 249.02/249.30 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 249.02/249.30 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 249.02/249.30 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 249.02/249.30 Found x4:(X6 Xx0)
% 249.02/249.30 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 249.02/249.30 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 249.02/249.30 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 249.02/249.30 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 249.02/249.30 Found x4:(X6 Xx0)
% 249.02/249.30 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 249.02/249.30 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 249.02/249.30 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 249.02/249.30 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 249.02/249.30 Found x4:(X6 Xx0)
% 249.02/249.30 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 249.02/249.30 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 249.02/249.30 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 249.02/249.30 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 249.02/249.30 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 249.02/249.30 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 249.02/249.30 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 249.02/249.30 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 249.02/249.30 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 249.02/249.30 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 249.02/249.30 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 249.74/250.11 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 249.74/250.11 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 249.74/250.11 Found x4:(X6 Xx0)
% 249.74/250.11 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 249.74/250.11 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 249.74/250.11 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 249.74/250.11 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 249.74/250.11 Found x4:(X6 Xx0)
% 249.74/250.11 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 249.74/250.11 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 249.74/250.11 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 249.74/250.11 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 249.74/250.11 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 249.74/250.11 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 249.74/250.11 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 249.74/250.11 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 249.74/250.11 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 249.74/250.11 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 249.74/250.11 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 249.74/250.11 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 249.74/250.11 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 249.74/250.11 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 249.74/250.11 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 249.74/250.11 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 249.74/250.11 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 249.74/250.11 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 249.74/250.11 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 249.74/250.11 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 249.74/250.11 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 249.74/250.11 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 250.63/250.94 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 250.63/250.94 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 250.63/250.94 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 250.63/250.94 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 250.63/250.94 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 250.63/250.94 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 250.63/250.94 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 250.63/250.94 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 250.63/250.94 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 250.63/250.94 Found x6:(X6 Xx0)
% 250.63/250.94 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 250.63/250.94 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 250.63/250.94 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 250.63/250.94 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 250.63/250.94 Found x400:=(x40 x5):((cK x2) Xx)
% 250.63/250.94 Found (x40 x5) as proof of ((cK X6) Xx)
% 250.63/250.94 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 250.63/250.94 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 250.63/250.94 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 250.63/250.94 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 250.63/250.94 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 250.63/250.94 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 250.63/250.94 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 250.63/250.94 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 250.63/250.94 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 250.63/250.94 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 250.63/250.94 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 250.63/250.94 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 250.63/250.94 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 250.63/250.94 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 250.63/250.94 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 250.63/250.94 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 250.63/250.94 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 250.63/250.94 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 250.63/250.94 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 250.63/250.94 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 250.93/251.26 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 250.93/251.26 Found x6:(X6 Xx0)
% 250.93/251.26 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 250.93/251.26 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 250.93/251.26 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 250.93/251.26 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 250.93/251.26 Found x400:=(x40 x5):((cK x2) Xx)
% 250.93/251.26 Found (x40 x5) as proof of ((cK X6) Xx)
% 250.93/251.26 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 250.93/251.26 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 250.93/251.26 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 250.93/251.26 Found x6:(X6 Xx0)
% 250.93/251.26 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 250.93/251.26 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 250.93/251.26 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 250.93/251.26 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 250.93/251.26 Found x400:=(x40 x5):((cK x2) Xx)
% 250.93/251.26 Found (x40 x5) as proof of ((cK X6) Xx)
% 250.93/251.26 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 250.93/251.26 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 250.93/251.26 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 250.93/251.26 Found x6:(X6 Xx0)
% 250.93/251.26 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 250.93/251.26 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 250.93/251.26 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 250.93/251.26 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 250.93/251.26 Found x400:=(x40 x5):((cK x2) Xx)
% 250.93/251.26 Found (x40 x5) as proof of ((cK X6) Xx)
% 250.93/251.26 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 250.93/251.26 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 250.93/251.26 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 250.93/251.26 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 250.93/251.26 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 250.93/251.26 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 250.93/251.26 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 250.93/251.26 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 250.93/251.26 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 250.93/251.26 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 250.93/251.26 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 250.93/251.26 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 251.17/251.48 Found x6:(X6 Xx0)
% 251.17/251.48 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 251.17/251.48 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 251.17/251.48 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 251.17/251.48 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 251.17/251.48 Found x400:=(x40 x5):((cK x2) Xx)
% 251.17/251.48 Found (x40 x5) as proof of ((cK X6) Xx)
% 251.17/251.48 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 251.17/251.48 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 251.17/251.48 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 251.17/251.48 Found x6:(X6 Xx0)
% 251.17/251.48 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 251.17/251.48 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 251.17/251.48 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 251.17/251.48 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 251.17/251.48 Found x400:=(x40 x5):((cK x2) Xx)
% 251.17/251.48 Found (x40 x5) as proof of ((cK X6) Xx)
% 251.17/251.48 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 251.17/251.48 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 251.17/251.48 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 251.17/251.48 Found x6:(X6 Xx0)
% 251.17/251.48 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 251.17/251.48 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 251.17/251.48 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 251.17/251.48 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 251.17/251.48 Found x400:=(x40 x5):((cK x2) Xx)
% 251.17/251.48 Found (x40 x5) as proof of ((cK X6) Xx)
% 251.17/251.48 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 251.17/251.48 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 251.17/251.48 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 251.17/251.48 Found x6:(X6 Xx0)
% 251.17/251.48 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 251.17/251.48 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 251.17/251.48 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 251.17/251.48 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 251.17/251.48 Found x400:=(x40 x5):((cK x2) Xx)
% 251.17/251.48 Found (x40 x5) as proof of ((cK X6) Xx)
% 251.17/251.48 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 251.17/251.48 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 251.17/251.48 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 251.17/251.48 Found x6:(X6 Xx0)
% 251.17/251.48 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 251.17/251.48 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 251.17/251.48 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 251.17/251.48 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 251.17/251.48 Found x400:=(x40 x5):((cK x2) Xx)
% 251.17/251.48 Found (x40 x5) as proof of ((cK X6) Xx)
% 251.17/251.48 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 251.17/251.48 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 251.47/251.76 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 251.47/251.76 Found x6:(X6 Xx0)
% 251.47/251.76 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 251.47/251.76 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 251.47/251.76 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 251.47/251.76 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 251.47/251.76 Found x400:=(x40 x5):((cK x2) Xx)
% 251.47/251.76 Found (x40 x5) as proof of ((cK X6) Xx)
% 251.47/251.76 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 251.47/251.76 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 251.47/251.76 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 251.47/251.76 Found x6:(X6 Xx0)
% 251.47/251.76 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 251.47/251.76 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 251.47/251.76 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 251.47/251.76 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 251.47/251.76 Found x400:=(x40 x5):((cK x2) Xx)
% 251.47/251.76 Found (x40 x5) as proof of ((cK X6) Xx)
% 251.47/251.76 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 251.47/251.76 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 251.47/251.76 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 251.47/251.76 Found x6:(X6 Xx0)
% 251.47/251.76 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 251.47/251.76 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 251.47/251.76 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 251.47/251.76 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 251.47/251.76 Found x400:=(x40 x5):((cK x2) Xx)
% 251.47/251.76 Found (x40 x5) as proof of ((cK X6) Xx)
% 251.47/251.76 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 251.47/251.76 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 251.47/251.76 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 251.47/251.76 Found x6:(X6 Xx0)
% 251.47/251.76 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 251.47/251.76 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 251.47/251.76 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 251.47/251.76 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 251.47/251.76 Found x400:=(x40 x5):((cK x2) Xx)
% 251.47/251.76 Found (x40 x5) as proof of ((cK X6) Xx)
% 251.47/251.76 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 251.47/251.76 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 251.47/251.76 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 251.47/251.76 Found x6:(X6 Xx0)
% 251.47/251.76 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 251.47/251.76 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 251.47/251.76 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 251.47/251.76 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 251.47/251.76 Found x400:=(x40 x5):((cK x2) Xx)
% 251.47/251.76 Found (x40 x5) as proof of ((cK X6) Xx)
% 251.47/251.76 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 251.47/251.76 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 251.84/252.12 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 251.84/252.12 Found x6:(X6 Xx0)
% 251.84/252.12 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 251.84/252.12 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 251.84/252.12 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 251.84/252.12 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 251.84/252.12 Found x400:=(x40 x5):((cK x2) Xx)
% 251.84/252.12 Found (x40 x5) as proof of ((cK X6) Xx)
% 251.84/252.12 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 251.84/252.12 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 251.84/252.12 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 251.84/252.12 Found x6:(X6 Xx0)
% 251.84/252.12 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 251.84/252.12 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 251.84/252.12 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 251.84/252.12 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 251.84/252.12 Found x400:=(x40 x5):((cK x2) Xx)
% 251.84/252.12 Found (x40 x5) as proof of ((cK X6) Xx)
% 251.84/252.12 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 251.84/252.12 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 251.84/252.12 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 251.84/252.12 Found x4:(X6 Xx0)
% 251.84/252.12 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 251.84/252.12 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 251.84/252.12 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 251.84/252.12 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 251.84/252.12 Found x4:(X6 Xx0)
% 251.84/252.12 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 251.84/252.12 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 251.84/252.12 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 251.84/252.12 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 251.84/252.12 Found x6:(X6 Xx0)
% 251.84/252.12 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 251.84/252.12 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 251.84/252.12 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 251.84/252.12 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 251.84/252.12 Found x400:=(x40 x5):((cK x2) Xx)
% 251.84/252.12 Found (x40 x5) as proof of ((cK X6) Xx)
% 251.84/252.12 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 251.84/252.12 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 251.84/252.12 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 251.84/252.12 Found x4:(X6 Xx0)
% 251.84/252.12 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 251.84/252.12 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 251.84/252.12 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 252.14/252.47 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 252.14/252.47 Found x6:(X6 Xx0)
% 252.14/252.47 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 252.14/252.47 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 252.14/252.47 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 252.14/252.47 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 252.14/252.47 Found x400:=(x40 x5):((cK x2) Xx)
% 252.14/252.47 Found (x40 x5) as proof of ((cK X6) Xx)
% 252.14/252.47 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 252.14/252.47 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 252.14/252.47 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 252.14/252.47 Found x4:(X6 Xx0)
% 252.14/252.47 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 252.14/252.47 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 252.14/252.47 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 252.14/252.47 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 252.14/252.47 Found x4:(X6 Xx0)
% 252.14/252.47 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 252.14/252.47 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 252.14/252.47 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 252.14/252.47 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 252.14/252.47 Found x4:(X6 Xx0)
% 252.14/252.47 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 252.14/252.47 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 252.14/252.47 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 252.14/252.47 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 252.14/252.47 Found x6:(X6 Xx0)
% 252.14/252.47 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 252.14/252.47 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 252.14/252.47 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 252.14/252.47 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 252.14/252.47 Found x400:=(x40 x5):((cK x2) Xx)
% 252.14/252.47 Found (x40 x5) as proof of ((cK X6) Xx)
% 252.14/252.47 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 252.14/252.47 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 252.14/252.47 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 252.14/252.47 Found x4:(X6 Xx0)
% 252.14/252.47 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 252.14/252.47 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 252.66/252.94 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 252.66/252.94 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 252.66/252.94 Found x4:(X6 Xx0)
% 252.66/252.94 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 252.66/252.94 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 252.66/252.94 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 252.66/252.94 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 252.66/252.94 Found x4:(X6 Xx0)
% 252.66/252.94 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 252.66/252.94 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 252.66/252.94 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 252.66/252.94 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 252.66/252.94 Found x4:(X6 Xx0)
% 252.66/252.94 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 252.66/252.94 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 252.66/252.94 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 252.66/252.94 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 252.66/252.94 Found x4:(X6 Xx0)
% 252.66/252.94 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 252.66/252.94 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 252.66/252.94 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 252.66/252.94 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 252.66/252.94 Found x4:(X6 Xx0)
% 252.66/252.94 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 252.66/252.94 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 252.66/252.94 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 252.66/252.94 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 252.66/252.94 Found x6:(X6 Xx0)
% 252.66/252.94 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 252.66/252.94 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 252.66/252.94 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 252.66/252.94 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 252.66/252.94 Found x400:=(x40 x5):((cK x2) Xx)
% 253.03/253.36 Found (x40 x5) as proof of ((cK X6) Xx)
% 253.03/253.36 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 253.03/253.36 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 253.03/253.36 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 253.03/253.36 Found x4:(X6 Xx0)
% 253.03/253.36 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 253.03/253.36 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 253.03/253.36 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 253.03/253.36 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 253.03/253.36 Found x6:(X6 Xx0)
% 253.03/253.36 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 253.03/253.36 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 253.03/253.37 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 253.03/253.37 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 253.03/253.37 Found x400:=(x40 x5):((cK x2) Xx)
% 253.03/253.37 Found (x40 x5) as proof of ((cK X6) Xx)
% 253.03/253.37 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 253.03/253.37 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 253.03/253.37 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 253.03/253.37 Found x6:(X6 Xx0)
% 253.03/253.37 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 253.03/253.37 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 253.03/253.37 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 253.03/253.37 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 253.03/253.37 Found x400:=(x40 x5):((cK x2) Xx)
% 253.03/253.37 Found (x40 x5) as proof of ((cK X6) Xx)
% 253.03/253.37 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 253.03/253.37 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 253.03/253.37 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 253.03/253.37 Found x4:(X6 Xx0)
% 253.03/253.37 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 253.03/253.37 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 253.03/253.37 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 253.03/253.37 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 253.03/253.37 Found x4:(X6 Xx0)
% 253.03/253.37 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 253.03/253.37 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 253.03/253.37 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 253.03/253.37 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 253.03/253.37 Found x4:(X6 Xx0)
% 253.03/253.37 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 253.03/253.37 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 253.03/253.37 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 253.63/253.96 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 253.63/253.96 Found x4:(X6 Xx0)
% 253.63/253.96 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 253.63/253.96 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 253.63/253.96 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 253.63/253.96 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 253.63/253.96 Found x2:(X6 Xx0)
% 253.63/253.96 Found x2 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 253.63/253.96 Found (fun (x2:(X6 Xx0))=> x2) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 253.63/253.96 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 253.63/253.96 Found (fun (Xx0:a) (x2:(X6 Xx0))=> x2) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 253.63/253.96 Found x6:(X6 Xx0)
% 253.63/253.96 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 253.63/253.96 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 253.63/253.96 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 253.63/253.96 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 253.63/253.96 Found x400:=(x40 x5):((cK x2) Xx)
% 253.63/253.96 Found (x40 x5) as proof of ((cK X6) Xx)
% 253.63/253.96 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 253.63/253.96 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 253.63/253.96 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 253.63/253.96 Found x4:(X6 Xx0)
% 253.63/253.96 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 253.63/253.96 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 253.63/253.96 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 253.63/253.96 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 253.63/253.96 Found x4:(X6 Xx0)
% 253.63/253.96 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 253.63/253.96 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 253.63/253.96 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 253.63/253.96 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 253.63/253.96 Found x4:(X6 Xx0)
% 253.63/253.96 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 253.63/253.96 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 253.63/253.96 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 253.63/253.96 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 254.05/254.40 Found x6:(X6 Xx0)
% 254.05/254.40 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 254.05/254.40 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 254.05/254.40 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 254.05/254.40 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 254.05/254.40 Found x400:=(x40 x5):((cK x2) Xx)
% 254.05/254.40 Found (x40 x5) as proof of ((cK X6) Xx)
% 254.05/254.40 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 254.05/254.40 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 254.05/254.40 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 254.05/254.40 Found x6:(X6 Xx0)
% 254.05/254.40 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 254.05/254.40 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 254.05/254.40 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 254.05/254.40 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 254.05/254.40 Found x400:=(x40 x5):((cK x2) Xx)
% 254.05/254.40 Found (x40 x5) as proof of ((cK X6) Xx)
% 254.05/254.40 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 254.05/254.40 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 254.05/254.40 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 254.05/254.40 Found x6:(X6 Xx0)
% 254.05/254.40 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 254.05/254.40 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 254.05/254.40 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 254.05/254.40 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 254.05/254.40 Found x400:=(x40 x5):((cK x2) Xx)
% 254.05/254.40 Found (x40 x5) as proof of ((cK X6) Xx)
% 254.05/254.40 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 254.05/254.40 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 254.05/254.40 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 254.05/254.40 Found x6:(X6 Xx0)
% 254.05/254.40 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 254.05/254.40 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 254.05/254.40 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 254.05/254.40 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 254.05/254.40 Found x400:=(x40 x5):((cK x2) Xx)
% 254.05/254.40 Found (x40 x5) as proof of ((cK X6) Xx)
% 254.05/254.40 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 254.05/254.40 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 254.05/254.40 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 254.05/254.40 Found x6:(X6 Xx0)
% 254.05/254.40 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 254.05/254.40 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 254.05/254.40 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 254.05/254.40 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 254.05/254.40 Found x400:=(x40 x5):((cK x2) Xx)
% 254.05/254.40 Found (x40 x5) as proof of ((cK X6) Xx)
% 254.05/254.40 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 254.05/254.40 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 254.63/254.93 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 254.63/254.93 Found x6:(X6 Xx0)
% 254.63/254.93 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 254.63/254.93 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 254.63/254.93 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 254.63/254.93 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 254.63/254.93 Found x400:=(x40 x5):((cK x2) Xx)
% 254.63/254.93 Found (x40 x5) as proof of ((cK X6) Xx)
% 254.63/254.93 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 254.63/254.93 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 254.63/254.93 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 254.63/254.93 Found x6:(X6 Xx0)
% 254.63/254.93 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 254.63/254.93 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 254.63/254.93 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 254.63/254.93 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 254.63/254.93 Found x400:=(x40 x5):((cK x2) Xx)
% 254.63/254.93 Found (x40 x5) as proof of ((cK X6) Xx)
% 254.63/254.93 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 254.63/254.93 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 254.63/254.93 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 254.63/254.93 Found x6:(X6 Xx0)
% 254.63/254.93 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 254.63/254.93 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 254.63/254.93 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 254.63/254.93 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 254.63/254.93 Found x400:=(x40 x5):((cK x2) Xx)
% 254.63/254.93 Found (x40 x5) as proof of ((cK X6) Xx)
% 254.63/254.93 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 254.63/254.93 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 254.63/254.93 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 254.63/254.93 Found x6:(X6 Xx0)
% 254.63/254.93 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 254.63/254.93 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 254.63/254.93 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 254.63/254.93 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 254.63/254.93 Found x400:=(x40 x5):((cK x2) Xx)
% 254.63/254.93 Found (x40 x5) as proof of ((cK X6) Xx)
% 254.63/254.93 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 254.63/254.93 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 254.63/254.93 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 254.63/254.93 Found x6:(X6 Xx0)
% 254.63/254.93 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 254.63/254.93 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 254.63/254.93 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 254.63/254.93 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 254.63/254.93 Found x400:=(x40 x5):((cK x2) Xx)
% 254.63/254.93 Found (x40 x5) as proof of ((cK X6) Xx)
% 254.63/254.93 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 254.93/255.23 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 254.93/255.23 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 254.93/255.23 Found x6:(X6 Xx0)
% 254.93/255.23 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 254.93/255.23 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 254.93/255.23 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 254.93/255.23 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 254.93/255.23 Found x400:=(x40 x5):((cK x2) Xx)
% 254.93/255.23 Found (x40 x5) as proof of ((cK X6) Xx)
% 254.93/255.23 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 254.93/255.23 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 254.93/255.23 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 254.93/255.23 Found x6:(X6 Xx0)
% 254.93/255.23 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 254.93/255.23 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 254.93/255.23 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 254.93/255.23 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 254.93/255.23 Found x400:=(x40 x5):((cK x2) Xx)
% 254.93/255.23 Found (x40 x5) as proof of ((cK X6) Xx)
% 254.93/255.23 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 254.93/255.23 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 254.93/255.23 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 254.93/255.23 Found x6:(X6 Xx0)
% 254.93/255.23 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 254.93/255.23 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 254.93/255.23 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 254.93/255.23 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 254.93/255.23 Found x400:=(x40 x5):((cK x2) Xx)
% 254.93/255.23 Found (x40 x5) as proof of ((cK X6) Xx)
% 254.93/255.23 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 254.93/255.23 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 254.93/255.23 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 254.93/255.23 Found x6:(X6 Xx0)
% 254.93/255.23 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 254.93/255.23 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 254.93/255.23 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 254.93/255.23 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 254.93/255.23 Found x400:=(x40 x5):((cK x2) Xx)
% 254.93/255.23 Found (x40 x5) as proof of ((cK X6) Xx)
% 254.93/255.23 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 254.93/255.23 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 254.93/255.23 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 254.93/255.23 Found x6:(X6 Xx0)
% 254.93/255.23 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 254.93/255.23 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 254.93/255.23 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 254.93/255.23 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 254.93/255.23 Found x400:=(x40 x5):((cK x2) Xx)
% 254.93/255.23 Found (x40 x5) as proof of ((cK X6) Xx)
% 255.63/255.94 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 255.63/255.94 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 255.63/255.94 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 255.63/255.94 Found x6:(X6 Xx0)
% 255.63/255.94 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 255.63/255.94 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 255.63/255.94 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 255.63/255.94 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 255.63/255.94 Found x400:=(x40 x5):((cK x2) Xx)
% 255.63/255.94 Found (x40 x5) as proof of ((cK X6) Xx)
% 255.63/255.94 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 255.63/255.94 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 255.63/255.94 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 255.63/255.94 Found x6:(X6 Xx0)
% 255.63/255.94 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 255.63/255.94 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 255.63/255.94 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 255.63/255.94 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 255.63/255.94 Found x400:=(x40 x5):((cK x2) Xx)
% 255.63/255.94 Found (x40 x5) as proof of ((cK X6) Xx)
% 255.63/255.94 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 255.63/255.94 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 255.63/255.94 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 255.63/255.94 Found x6:(X6 Xx0)
% 255.63/255.94 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 255.63/255.94 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 255.63/255.94 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 255.63/255.94 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 255.63/255.94 Found x400:=(x40 x5):((cK x2) Xx)
% 255.63/255.94 Found (x40 x5) as proof of ((cK X6) Xx)
% 255.63/255.94 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 255.63/255.94 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 255.63/255.94 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 255.63/255.94 Found x6:(X6 Xx0)
% 255.63/255.94 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 255.63/255.94 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 255.63/255.94 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 255.63/255.94 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 255.63/255.94 Found x400:=(x40 x5):((cK x2) Xx)
% 255.63/255.94 Found (x40 x5) as proof of ((cK X6) Xx)
% 255.63/255.94 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 255.63/255.94 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 255.63/255.94 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 255.63/255.94 Found x6:(X6 Xx0)
% 255.63/255.94 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 255.63/255.94 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 255.63/255.94 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 255.63/255.94 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 255.63/255.94 Found x400:=(x40 x5):((cK x2) Xx)
% 257.62/257.93 Found (x40 x5) as proof of ((cK X6) Xx)
% 257.62/257.93 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 257.62/257.93 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 257.62/257.93 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 257.62/257.93 Found x6:(X6 Xx0)
% 257.62/257.93 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 257.62/257.93 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 257.62/257.93 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 257.62/257.93 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 257.62/257.93 Found x400:=(x40 x5):((cK x2) Xx)
% 257.62/257.93 Found (x40 x5) as proof of ((cK X6) Xx)
% 257.62/257.93 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 257.62/257.93 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 257.62/257.93 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 257.62/257.93 Found x6:(X6 Xx0)
% 257.62/257.93 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 257.62/257.93 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 257.62/257.93 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 257.62/257.93 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 257.62/257.93 Found x400:=(x40 x5):((cK x2) Xx)
% 257.62/257.93 Found (x40 x5) as proof of ((cK X6) Xx)
% 257.62/257.93 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 257.62/257.93 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 257.62/257.93 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 257.62/257.93 Found x6:(X6 Xx0)
% 257.62/257.93 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 257.62/257.93 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 257.62/257.93 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 257.62/257.93 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 257.62/257.93 Found x400:=(x40 x5):((cK x2) Xx)
% 257.62/257.93 Found (x40 x5) as proof of ((cK X6) Xx)
% 257.62/257.93 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 257.62/257.93 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 257.62/257.93 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 257.62/257.93 Found x4:(X6 Xx0)
% 257.62/257.93 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 257.62/257.93 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 257.62/257.93 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 257.62/257.93 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 257.62/257.93 Found x4:(X6 Xx0)
% 257.62/257.93 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 257.62/257.93 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 257.62/257.93 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 257.62/257.93 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 257.62/257.93 Found x4:(X6 Xx0)
% 257.62/257.93 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 257.62/257.93 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 258.10/258.39 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 258.10/258.39 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 258.10/258.39 Found x4:(X6 Xx0)
% 258.10/258.39 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 258.10/258.39 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 258.10/258.39 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 258.10/258.39 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 258.10/258.39 Found x4:(X6 Xx0)
% 258.10/258.39 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 258.10/258.39 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 258.10/258.39 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 258.10/258.39 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 258.10/258.39 Found x4:(X6 Xx0)
% 258.10/258.39 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 258.10/258.39 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 258.10/258.39 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 258.10/258.39 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 258.10/258.39 Found x4:(X6 Xx0)
% 258.10/258.39 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 258.10/258.39 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 258.10/258.39 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 258.10/258.39 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 258.10/258.39 Found x4:(X6 Xx0)
% 258.10/258.39 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 258.10/258.39 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 258.10/258.39 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 258.10/258.39 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 258.10/258.39 Found x4:(X6 Xx0)
% 258.10/258.39 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 258.10/258.39 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 258.10/258.39 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 258.10/258.39 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 258.60/258.94 Found x4:(X6 Xx0)
% 258.60/258.94 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 258.60/258.94 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 258.60/258.94 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 258.60/258.94 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 258.60/258.94 Found x4:(X6 Xx0)
% 258.60/258.94 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 258.60/258.94 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 258.60/258.94 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 258.60/258.94 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 258.60/258.94 Found x4:(X6 Xx0)
% 258.60/258.94 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 258.60/258.94 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 258.60/258.94 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 258.60/258.94 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 258.60/258.94 Found x4:(X6 Xx0)
% 258.60/258.94 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 258.60/258.94 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 258.60/258.94 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 258.60/258.94 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 258.60/258.94 Found x4:(X6 Xx0)
% 258.60/258.94 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 258.60/258.94 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 258.60/258.94 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 258.60/258.94 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 258.60/258.94 Found x4:(X6 Xx0)
% 258.60/258.94 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 258.60/258.94 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 258.60/258.94 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 258.60/258.94 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 258.60/258.94 Found x4:(X6 Xx0)
% 258.60/258.94 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 258.60/258.94 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 258.60/258.94 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 259.32/259.61 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 259.32/259.61 Found x4:(X6 Xx0)
% 259.32/259.61 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 259.32/259.61 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 259.32/259.61 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 259.32/259.61 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 259.32/259.61 Found x4:(X6 Xx0)
% 259.32/259.61 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 259.32/259.61 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 259.32/259.61 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 259.32/259.61 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 259.32/259.61 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 259.32/259.61 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 259.32/259.61 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 259.32/259.61 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 259.32/259.61 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 259.32/259.61 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 259.32/259.61 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 259.32/259.61 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 259.32/259.61 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 259.32/259.61 Found x4:(X6 Xx0)
% 259.32/259.61 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 259.32/259.61 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 259.32/259.61 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 259.32/259.61 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 259.32/259.61 Found x4:(X6 Xx0)
% 259.32/259.61 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 259.32/259.61 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 259.32/259.61 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 259.32/259.61 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 259.32/259.61 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 259.32/259.61 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 259.32/259.61 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 259.52/259.81 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 259.52/259.81 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 259.52/259.81 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 259.52/259.81 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 259.52/259.81 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 259.52/259.81 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 259.52/259.81 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 259.52/259.81 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 259.52/259.81 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 259.52/259.81 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 259.52/259.81 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 259.52/259.81 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 259.52/259.81 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 259.52/259.81 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 259.52/259.81 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 259.52/259.81 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 259.52/259.81 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 259.52/259.81 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 259.52/259.81 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 259.52/259.81 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 259.52/259.81 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 259.52/259.81 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 259.52/259.81 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 259.52/259.81 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 259.52/259.81 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 259.52/259.81 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 259.52/259.81 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 259.52/259.81 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 259.52/259.81 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 259.52/259.81 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 259.52/259.81 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 259.52/259.81 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 259.93/260.30 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 259.93/260.30 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 259.93/260.30 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 259.93/260.30 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 259.93/260.30 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 259.93/260.30 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 259.93/260.30 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 259.93/260.30 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 259.93/260.30 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 259.93/260.30 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 259.93/260.30 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 259.93/260.30 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 259.93/260.30 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 259.93/260.30 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 259.93/260.30 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 259.93/260.30 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 259.93/260.30 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 259.93/260.30 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 259.93/260.30 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 259.93/260.30 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 259.93/260.30 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 259.93/260.30 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 259.93/260.30 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 259.93/260.30 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 259.93/260.30 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 259.93/260.30 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 259.93/260.30 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 259.93/260.30 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 259.93/260.30 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 260.11/260.46 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 260.11/260.46 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 260.11/260.46 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 260.11/260.46 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 260.11/260.46 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 260.11/260.46 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 260.11/260.46 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 260.11/260.46 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 260.11/260.46 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 260.11/260.46 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 260.11/260.46 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 260.11/260.46 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 260.11/260.46 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 260.11/260.46 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 260.11/260.46 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 260.11/260.46 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 260.11/260.46 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 260.11/260.46 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 260.11/260.46 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 260.11/260.46 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 260.11/260.46 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 260.11/260.46 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 260.11/260.46 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 260.11/260.46 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 260.11/260.46 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 260.11/260.46 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 260.11/260.46 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 260.11/260.46 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 260.11/260.46 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 260.11/260.46 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 260.11/260.46 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 260.11/260.46 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 260.11/260.46 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 260.21/260.50 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 260.21/260.50 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 260.21/260.50 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 260.21/260.50 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 260.21/260.50 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 260.21/260.50 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 260.21/260.50 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 260.21/260.50 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 260.21/260.50 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 260.21/260.50 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 260.21/260.50 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 260.21/260.50 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 260.21/260.50 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 260.21/260.50 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 260.21/260.50 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 260.21/260.50 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 260.21/260.50 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 260.21/260.50 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 260.21/260.50 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 260.21/260.50 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 260.21/260.50 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 260.21/260.50 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 260.21/260.50 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 260.21/260.50 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 260.21/260.50 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 260.21/260.50 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 260.21/260.50 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 260.21/260.50 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 260.21/260.50 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 260.33/260.69 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 260.33/260.69 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 260.33/260.69 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 260.33/260.69 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 260.33/260.69 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 260.33/260.69 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 260.33/260.69 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 260.33/260.69 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 260.33/260.69 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 260.33/260.69 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 260.33/260.69 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 260.33/260.69 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 260.33/260.69 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 260.33/260.69 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 260.33/260.69 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 260.33/260.69 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 260.33/260.69 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 260.33/260.69 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 260.33/260.69 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 260.33/260.69 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 260.33/260.69 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 260.33/260.69 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 260.33/260.69 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 260.33/260.69 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 260.33/260.69 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 260.33/260.69 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 260.33/260.69 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 260.33/260.69 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 260.33/260.69 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 260.33/260.69 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 260.33/260.69 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 260.33/260.69 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 260.33/260.69 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 260.33/260.71 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 260.33/260.71 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 260.33/260.71 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 260.33/260.71 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 260.33/260.71 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 260.33/260.71 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 260.33/260.71 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 260.33/260.71 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 260.33/260.71 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 260.33/260.71 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 260.33/260.71 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 260.33/260.71 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 260.33/260.71 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 260.33/260.71 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 260.33/260.71 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 260.33/260.71 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 260.33/260.71 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 260.33/260.71 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 260.33/260.71 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 260.33/260.71 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 260.33/260.71 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 260.33/260.71 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 260.33/260.71 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 260.33/260.71 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 260.33/260.71 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 260.33/260.71 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 260.33/260.71 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 260.33/260.71 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 260.33/260.71 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 260.33/260.71 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 260.52/260.87 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 260.52/260.87 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 260.52/260.87 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 260.52/260.87 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 260.52/260.87 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 260.52/260.87 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 260.52/260.87 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 260.52/260.87 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 260.52/260.87 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 260.52/260.87 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 260.52/260.87 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 260.52/260.87 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 260.52/260.87 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 260.52/260.87 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 260.52/260.87 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 260.52/260.87 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 260.52/260.87 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 260.52/260.87 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 260.52/260.87 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 260.52/260.87 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 260.52/260.87 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 260.52/260.87 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 260.52/260.87 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 260.52/260.87 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 260.52/260.87 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 260.52/260.87 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 260.52/260.87 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 260.52/260.87 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 260.52/260.87 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 260.52/260.87 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 260.52/260.87 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 260.52/260.87 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 260.82/261.11 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 260.82/261.11 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 260.82/261.11 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 260.82/261.11 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 260.82/261.11 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 260.82/261.11 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 260.82/261.11 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 260.82/261.11 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 260.82/261.11 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 260.82/261.11 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 260.82/261.11 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 260.82/261.11 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 260.82/261.11 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 260.82/261.11 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 260.82/261.11 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 260.82/261.11 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 260.82/261.11 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 260.82/261.11 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 260.82/261.11 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 260.82/261.11 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 260.82/261.11 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 260.82/261.11 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 260.82/261.11 Found x4:(X6 Xx0)
% 260.82/261.11 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 260.82/261.11 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 260.82/261.11 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 260.82/261.11 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 260.82/261.11 Found x4:(X6 Xx0)
% 260.82/261.11 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 260.82/261.11 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 260.82/261.11 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 261.42/261.75 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 261.42/261.75 Found x4:(X6 Xx0)
% 261.42/261.75 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 261.42/261.75 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 261.42/261.75 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 261.42/261.75 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 261.42/261.75 Found x4:(X6 Xx0)
% 261.42/261.75 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 261.42/261.75 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 261.42/261.75 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 261.42/261.75 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 261.42/261.75 Found x4:(X6 Xx0)
% 261.42/261.75 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 261.42/261.75 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 261.42/261.75 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 261.42/261.75 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 261.42/261.75 Found x4:(X6 Xx0)
% 261.42/261.75 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 261.42/261.75 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 261.42/261.75 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 261.42/261.75 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 261.42/261.75 Found x4:(X6 Xx0)
% 261.42/261.75 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 261.42/261.75 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 261.42/261.75 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 261.42/261.75 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 261.42/261.75 Found x4:(X6 Xx0)
% 261.42/261.75 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 261.42/261.75 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 261.42/261.75 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 261.42/261.75 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 261.42/261.75 Found x4:(X6 Xx0)
% 261.42/261.75 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 261.95/262.28 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 261.95/262.28 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 261.95/262.28 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 261.95/262.28 Found x4:(X6 Xx0)
% 261.95/262.28 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 261.95/262.28 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 261.95/262.28 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 261.95/262.28 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 261.95/262.28 Found x4:(X6 Xx0)
% 261.95/262.28 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 261.95/262.28 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 261.95/262.28 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 261.95/262.28 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 261.95/262.28 Found x4:(X6 Xx0)
% 261.95/262.28 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 261.95/262.28 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 261.95/262.28 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 261.95/262.28 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 261.95/262.28 Found x4:(X6 Xx0)
% 261.95/262.28 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 261.95/262.28 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 261.95/262.28 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 261.95/262.28 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 261.95/262.28 Found x4:(X6 Xx0)
% 261.95/262.28 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 261.95/262.28 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 261.95/262.28 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 261.95/262.28 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 261.95/262.28 Found x4:(X6 Xx0)
% 261.95/262.28 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 261.95/262.28 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 261.95/262.28 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 262.56/262.90 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 262.56/262.90 Found x4:(X6 Xx0)
% 262.56/262.90 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 262.56/262.90 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 262.56/262.90 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 262.56/262.90 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 262.56/262.90 Found x4:(X6 Xx0)
% 262.56/262.90 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 262.56/262.90 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 262.56/262.90 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 262.56/262.90 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 262.56/262.90 Found x4:(X6 Xx0)
% 262.56/262.90 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 262.56/262.90 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 262.56/262.90 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 262.56/262.90 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 262.56/262.90 Found x4:(X6 Xx0)
% 262.56/262.90 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 262.56/262.90 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 262.56/262.90 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 262.56/262.90 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 262.56/262.90 Found x4:(X6 Xx0)
% 262.56/262.90 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 262.56/262.90 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 262.56/262.90 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 262.56/262.90 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 262.56/262.90 Found x4:(X6 Xx0)
% 262.56/262.90 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 262.56/262.90 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 262.56/262.90 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 262.56/262.90 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 262.56/262.90 Found x6:(X6 Xx0)
% 262.56/262.90 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 262.56/262.90 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 263.24/263.58 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 263.24/263.58 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 263.24/263.58 Found x400:=(x40 x5):((cK x2) Xx)
% 263.24/263.58 Found (x40 x5) as proof of ((cK X6) Xx)
% 263.24/263.58 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 263.24/263.58 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 263.24/263.58 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 263.24/263.58 Found x4:(X6 Xx0)
% 263.24/263.58 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 263.24/263.58 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 263.24/263.58 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 263.24/263.58 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 263.24/263.58 Found x4:(X6 Xx0)
% 263.24/263.58 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 263.24/263.58 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 263.24/263.58 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 263.24/263.58 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 263.24/263.58 Found x4:(X6 Xx0)
% 263.24/263.58 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 263.24/263.58 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 263.24/263.58 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 263.24/263.58 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 263.24/263.58 Found x4:(X6 Xx0)
% 263.24/263.58 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 263.24/263.58 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 263.24/263.58 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 263.24/263.58 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 263.24/263.58 Found x4:(X6 Xx0)
% 263.24/263.58 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 263.24/263.58 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 263.24/263.58 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 263.24/263.58 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 263.24/263.58 Found x6:(X6 Xx0)
% 263.24/263.58 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 263.24/263.58 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 263.24/263.58 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 263.52/263.86 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 263.52/263.86 Found x400:=(x40 x5):((cK x2) Xx)
% 263.52/263.86 Found (x40 x5) as proof of ((cK X6) Xx)
% 263.52/263.86 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 263.52/263.86 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 263.52/263.86 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 263.52/263.86 Found x6:(X6 Xx0)
% 263.52/263.86 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 263.52/263.86 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 263.52/263.86 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 263.52/263.86 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 263.52/263.86 Found x400:=(x40 x5):((cK x2) Xx)
% 263.52/263.86 Found (x40 x5) as proof of ((cK X6) Xx)
% 263.52/263.86 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 263.52/263.86 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 263.52/263.86 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 263.52/263.86 Found x6:(X6 Xx0)
% 263.52/263.86 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 263.52/263.86 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 263.52/263.86 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 263.52/263.86 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 263.52/263.86 Found x400:=(x40 x5):((cK x2) Xx)
% 263.52/263.86 Found (x40 x5) as proof of ((cK X6) Xx)
% 263.52/263.86 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 263.52/263.86 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 263.52/263.86 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 263.52/263.86 Found x6:(X6 Xx0)
% 263.52/263.86 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 263.52/263.86 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 263.52/263.86 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 263.52/263.86 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 263.52/263.86 Found x400:=(x40 x5):((cK x2) Xx)
% 263.52/263.86 Found (x40 x5) as proof of ((cK X6) Xx)
% 263.52/263.86 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 263.52/263.86 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 263.52/263.86 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 263.52/263.86 Found x6:(X6 Xx0)
% 263.52/263.86 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 263.52/263.86 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 263.52/263.86 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 263.52/263.86 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 263.52/263.86 Found x400:=(x40 x5):((cK x2) Xx)
% 263.52/263.86 Found (x40 x5) as proof of ((cK X6) Xx)
% 263.52/263.86 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 263.52/263.86 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 263.52/263.86 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 263.52/263.86 Found x6:(X6 Xx0)
% 263.52/263.86 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 263.52/263.86 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 263.52/263.86 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 263.83/264.18 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 263.83/264.18 Found x400:=(x40 x5):((cK x2) Xx)
% 263.83/264.18 Found (x40 x5) as proof of ((cK X6) Xx)
% 263.83/264.18 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 263.83/264.18 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 263.83/264.18 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 263.83/264.18 Found x6:(X6 Xx0)
% 263.83/264.18 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 263.83/264.18 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 263.83/264.18 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 263.83/264.18 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 263.83/264.18 Found x400:=(x40 x5):((cK x2) Xx)
% 263.83/264.18 Found (x40 x5) as proof of ((cK X6) Xx)
% 263.83/264.18 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 263.83/264.18 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 263.83/264.18 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 263.83/264.18 Found x6:(X6 Xx0)
% 263.83/264.18 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 263.83/264.18 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 263.83/264.18 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 263.83/264.18 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 263.83/264.18 Found x400:=(x40 x5):((cK x2) Xx)
% 263.83/264.18 Found (x40 x5) as proof of ((cK X6) Xx)
% 263.83/264.18 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 263.83/264.18 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 263.83/264.18 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 263.83/264.18 Found x6:(X6 Xx0)
% 263.83/264.18 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 263.83/264.18 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 263.83/264.18 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 263.83/264.18 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 263.83/264.18 Found x400:=(x40 x5):((cK x2) Xx)
% 263.83/264.18 Found (x40 x5) as proof of ((cK X6) Xx)
% 263.83/264.18 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 263.83/264.18 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 263.83/264.18 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 263.83/264.18 Found x6:(X6 Xx0)
% 263.83/264.18 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 263.83/264.18 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 263.83/264.18 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 263.83/264.18 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 263.83/264.18 Found x400:=(x40 x5):((cK x2) Xx)
% 263.83/264.18 Found (x40 x5) as proof of ((cK X6) Xx)
% 263.83/264.18 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 263.83/264.18 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 263.83/264.18 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 263.83/264.18 Found x6:(X6 Xx0)
% 263.83/264.18 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 263.83/264.18 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 263.83/264.18 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 264.11/264.47 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 264.11/264.47 Found x400:=(x40 x5):((cK x2) Xx)
% 264.11/264.47 Found (x40 x5) as proof of ((cK X6) Xx)
% 264.11/264.47 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 264.11/264.47 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 264.11/264.47 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 264.11/264.47 Found x6:(X6 Xx0)
% 264.11/264.47 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 264.11/264.47 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 264.11/264.47 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 264.11/264.47 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 264.11/264.47 Found x400:=(x40 x5):((cK x2) Xx)
% 264.11/264.47 Found (x40 x5) as proof of ((cK X6) Xx)
% 264.11/264.47 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 264.11/264.47 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 264.11/264.47 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 264.11/264.47 Found x6:(X6 Xx0)
% 264.11/264.47 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 264.11/264.47 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 264.11/264.47 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 264.11/264.47 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 264.11/264.47 Found x400:=(x40 x5):((cK x2) Xx)
% 264.11/264.47 Found (x40 x5) as proof of ((cK X6) Xx)
% 264.11/264.47 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 264.11/264.47 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 264.11/264.47 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 264.11/264.47 Found x6:(X6 Xx0)
% 264.11/264.47 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 264.11/264.47 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 264.11/264.47 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 264.11/264.47 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 264.11/264.47 Found x400:=(x40 x5):((cK x2) Xx)
% 264.11/264.47 Found (x40 x5) as proof of ((cK X6) Xx)
% 264.11/264.47 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 264.11/264.47 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 264.11/264.47 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 264.11/264.47 Found x6:(X6 Xx0)
% 264.11/264.47 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 264.11/264.47 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 264.11/264.47 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 264.11/264.47 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 264.11/264.47 Found x400:=(x40 x5):((cK x2) Xx)
% 264.11/264.47 Found (x40 x5) as proof of ((cK X6) Xx)
% 264.11/264.47 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 264.11/264.47 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 264.11/264.47 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 264.11/264.47 Found x6:(X6 Xx0)
% 264.11/264.47 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 264.11/264.47 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 264.41/264.69 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 264.41/264.69 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 264.41/264.69 Found x400:=(x40 x5):((cK x2) Xx)
% 264.41/264.69 Found (x40 x5) as proof of ((cK X6) Xx)
% 264.41/264.69 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 264.41/264.69 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 264.41/264.69 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 264.41/264.69 Found x6:(X6 Xx0)
% 264.41/264.69 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 264.41/264.69 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 264.41/264.69 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 264.41/264.69 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 264.41/264.69 Found x400:=(x40 x5):((cK x2) Xx)
% 264.41/264.69 Found (x40 x5) as proof of ((cK X6) Xx)
% 264.41/264.69 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 264.41/264.69 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 264.41/264.69 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 264.41/264.69 Found x6:(X6 Xx0)
% 264.41/264.69 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 264.41/264.69 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 264.41/264.69 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 264.41/264.69 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 264.41/264.69 Found x400:=(x40 x5):((cK x2) Xx)
% 264.41/264.69 Found (x40 x5) as proof of ((cK X6) Xx)
% 264.41/264.69 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 264.41/264.69 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 264.41/264.69 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 264.41/264.69 Found x6:(X6 Xx0)
% 264.41/264.69 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 264.41/264.69 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 264.41/264.69 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 264.41/264.69 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 264.41/264.69 Found x400:=(x40 x5):((cK x2) Xx)
% 264.41/264.69 Found (x40 x5) as proof of ((cK X6) Xx)
% 264.41/264.69 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 264.41/264.69 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 264.41/264.69 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 264.41/264.69 Found x6:(X6 Xx0)
% 264.41/264.69 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 264.41/264.69 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 264.41/264.69 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 264.41/264.69 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 264.41/264.69 Found x400:=(x40 x5):((cK x2) Xx)
% 264.41/264.69 Found (x40 x5) as proof of ((cK X6) Xx)
% 264.41/264.69 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 264.41/264.69 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 264.41/264.69 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 264.41/264.69 Found x6:(X6 Xx0)
% 264.41/264.69 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 264.41/264.69 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 264.63/264.94 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 264.63/264.94 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 264.63/264.94 Found x400:=(x40 x5):((cK x2) Xx)
% 264.63/264.94 Found (x40 x5) as proof of ((cK X6) Xx)
% 264.63/264.94 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 264.63/264.94 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 264.63/264.94 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 264.63/264.94 Found x6:(X6 Xx0)
% 264.63/264.94 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 264.63/264.94 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 264.63/264.94 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 264.63/264.94 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 264.63/264.94 Found x400:=(x40 x5):((cK x2) Xx)
% 264.63/264.94 Found (x40 x5) as proof of ((cK X6) Xx)
% 264.63/264.94 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 264.63/264.94 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 264.63/264.94 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 264.63/264.94 Found x6:(X6 Xx0)
% 264.63/264.94 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 264.63/264.94 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 264.63/264.94 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 264.63/264.94 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 264.63/264.94 Found x400:=(x40 x5):((cK x2) Xx)
% 264.63/264.94 Found (x40 x5) as proof of ((cK X6) Xx)
% 264.63/264.94 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 264.63/264.94 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 264.63/264.94 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 264.63/264.94 Found x6:(X6 Xx0)
% 264.63/264.94 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 264.63/264.94 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 264.63/264.94 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 264.63/264.94 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 264.63/264.94 Found x400:=(x40 x5):((cK x2) Xx)
% 264.63/264.94 Found (x40 x5) as proof of ((cK X6) Xx)
% 264.63/264.94 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 264.63/264.94 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 264.63/264.94 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 264.63/264.94 Found x6:(X6 Xx0)
% 264.63/264.94 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 264.63/264.94 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 264.63/264.94 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 264.63/264.94 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 264.63/264.94 Found x400:=(x40 x5):((cK x2) Xx)
% 264.63/264.94 Found (x40 x5) as proof of ((cK X6) Xx)
% 264.63/264.94 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 264.63/264.94 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 264.63/264.94 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 264.63/264.94 Found x6:(X6 Xx0)
% 264.63/264.94 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 264.63/264.94 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 265.00/265.37 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 265.00/265.37 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 265.00/265.37 Found x400:=(x40 x5):((cK x2) Xx)
% 265.00/265.37 Found (x40 x5) as proof of ((cK X6) Xx)
% 265.00/265.37 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 265.00/265.37 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 265.00/265.37 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 265.00/265.37 Found x6:(X6 Xx0)
% 265.00/265.37 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 265.00/265.37 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 265.00/265.37 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 265.00/265.37 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 265.00/265.37 Found x400:=(x40 x5):((cK x2) Xx)
% 265.00/265.37 Found (x40 x5) as proof of ((cK X6) Xx)
% 265.00/265.37 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 265.00/265.37 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 265.00/265.37 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 265.00/265.37 Found x6:(X6 Xx0)
% 265.00/265.37 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 265.00/265.37 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 265.00/265.37 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 265.00/265.37 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 265.00/265.37 Found x400:=(x40 x5):((cK x2) Xx)
% 265.00/265.37 Found (x40 x5) as proof of ((cK X6) Xx)
% 265.00/265.37 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 265.00/265.37 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 265.00/265.37 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 265.00/265.37 Found x6:(X6 Xx0)
% 265.00/265.37 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 265.00/265.37 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 265.00/265.37 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 265.00/265.37 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 265.00/265.37 Found x400:=(x40 x5):((cK x2) Xx)
% 265.00/265.37 Found (x40 x5) as proof of ((cK X6) Xx)
% 265.00/265.37 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 265.00/265.37 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 265.00/265.37 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 265.00/265.37 Found x6:(X6 Xx0)
% 265.00/265.37 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 265.00/265.37 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 265.00/265.37 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 265.00/265.37 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 265.00/265.37 Found x400:=(x40 x5):((cK x2) Xx)
% 265.00/265.37 Found (x40 x5) as proof of ((cK X6) Xx)
% 265.00/265.37 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 265.00/265.37 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 265.00/265.37 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 265.00/265.37 Found x6:(X6 Xx0)
% 265.00/265.37 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 265.00/265.37 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 265.75/266.07 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 265.75/266.07 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 265.75/266.07 Found x400:=(x40 x5):((cK x2) Xx)
% 265.75/266.07 Found (x40 x5) as proof of ((cK X6) Xx)
% 265.75/266.07 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 265.75/266.07 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 265.75/266.07 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 265.75/266.07 Found x6:(X6 Xx0)
% 265.75/266.07 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 265.75/266.07 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 265.75/266.07 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 265.75/266.07 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 265.75/266.07 Found x400:=(x40 x5):((cK x2) Xx)
% 265.75/266.07 Found (x40 x5) as proof of ((cK X6) Xx)
% 265.75/266.07 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 265.75/266.07 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 265.75/266.07 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 265.75/266.07 Found x6:(X6 Xx0)
% 265.75/266.07 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 265.75/266.07 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 265.75/266.07 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 265.75/266.07 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 265.75/266.07 Found x400:=(x40 x5):((cK x2) Xx)
% 265.75/266.07 Found (x40 x5) as proof of ((cK X6) Xx)
% 265.75/266.07 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 265.75/266.07 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 265.75/266.07 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 265.75/266.07 Found x6:(X6 Xx0)
% 265.75/266.07 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 265.75/266.07 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 265.75/266.07 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 265.75/266.07 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 265.75/266.07 Found x400:=(x40 x5):((cK x2) Xx)
% 265.75/266.07 Found (x40 x5) as proof of ((cK X6) Xx)
% 265.75/266.07 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 265.75/266.07 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 265.75/266.07 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 265.75/266.07 Found x6:(X6 Xx0)
% 265.75/266.07 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 265.75/266.07 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 265.75/266.07 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 265.75/266.07 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 265.75/266.07 Found x400:=(x40 x5):((cK x2) Xx)
% 265.75/266.07 Found (x40 x5) as proof of ((cK X6) Xx)
% 265.75/266.07 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 265.75/266.07 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 265.75/266.07 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 265.75/266.07 Found x6:(X6 Xx0)
% 265.75/266.07 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 266.00/266.29 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 266.00/266.29 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 266.00/266.29 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 266.00/266.29 Found x400:=(x40 x5):((cK x2) Xx)
% 266.00/266.29 Found (x40 x5) as proof of ((cK X6) Xx)
% 266.00/266.29 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 266.00/266.29 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 266.00/266.29 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 266.00/266.29 Found x6:(X6 Xx0)
% 266.00/266.29 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 266.00/266.29 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 266.00/266.29 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 266.00/266.29 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 266.00/266.29 Found x400:=(x40 x5):((cK x2) Xx)
% 266.00/266.29 Found (x40 x5) as proof of ((cK X6) Xx)
% 266.00/266.29 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 266.00/266.29 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 266.00/266.29 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 266.00/266.29 Found x6:(X6 Xx0)
% 266.00/266.29 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 266.00/266.29 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 266.00/266.29 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 266.00/266.29 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 266.00/266.29 Found x400:=(x40 x5):((cK x2) Xx)
% 266.00/266.29 Found (x40 x5) as proof of ((cK X6) Xx)
% 266.00/266.29 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 266.00/266.29 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 266.00/266.29 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 266.00/266.29 Found x6:(X6 Xx0)
% 266.00/266.29 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 266.00/266.29 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 266.00/266.29 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 266.00/266.29 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 266.00/266.29 Found x400:=(x40 x5):((cK x2) Xx)
% 266.00/266.29 Found (x40 x5) as proof of ((cK X6) Xx)
% 266.00/266.29 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 266.00/266.29 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 266.00/266.29 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 266.00/266.29 Found x6:(X6 Xx0)
% 266.00/266.29 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 266.00/266.29 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 266.00/266.29 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 266.00/266.29 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 266.00/266.29 Found x400:=(x40 x5):((cK x2) Xx)
% 266.00/266.29 Found (x40 x5) as proof of ((cK X6) Xx)
% 266.00/266.29 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 266.00/266.29 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 266.00/266.29 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 266.00/266.29 Found x6:(X6 Xx0)
% 266.00/266.29 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 266.12/266.47 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 266.12/266.47 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 266.12/266.47 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 266.12/266.47 Found x400:=(x40 x5):((cK x2) Xx)
% 266.12/266.47 Found (x40 x5) as proof of ((cK X6) Xx)
% 266.12/266.47 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 266.12/266.47 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 266.12/266.47 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 266.12/266.47 Found x6:(X6 Xx0)
% 266.12/266.47 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 266.12/266.47 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 266.12/266.47 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 266.12/266.47 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 266.12/266.47 Found x400:=(x40 x5):((cK x2) Xx)
% 266.12/266.47 Found (x40 x5) as proof of ((cK X6) Xx)
% 266.12/266.47 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 266.12/266.47 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 266.12/266.47 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 266.12/266.47 Found x6:(X6 Xx0)
% 266.12/266.47 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 266.12/266.47 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 266.12/266.47 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 266.12/266.47 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 266.12/266.47 Found x400:=(x40 x5):((cK x2) Xx)
% 266.12/266.47 Found (x40 x5) as proof of ((cK X6) Xx)
% 266.12/266.47 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 266.12/266.47 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 266.12/266.47 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 266.12/266.47 Found x6:(X6 Xx0)
% 266.12/266.47 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 266.12/266.47 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 266.12/266.47 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 266.12/266.47 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 266.12/266.47 Found x400:=(x40 x5):((cK x2) Xx)
% 266.12/266.47 Found (x40 x5) as proof of ((cK X6) Xx)
% 266.12/266.47 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 266.12/266.47 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 266.12/266.47 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 266.12/266.47 Found x6:(X6 Xx0)
% 266.12/266.47 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 266.12/266.47 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 266.12/266.47 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 266.12/266.47 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 266.12/266.47 Found x400:=(x40 x5):((cK x2) Xx)
% 266.12/266.47 Found (x40 x5) as proof of ((cK X6) Xx)
% 266.12/266.47 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 266.12/266.47 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 266.12/266.47 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 266.12/266.47 Found x6:(X6 Xx0)
% 266.12/266.47 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 268.65/269.02 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 268.65/269.02 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 268.65/269.02 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 268.65/269.02 Found x400:=(x40 x5):((cK x2) Xx)
% 268.65/269.02 Found (x40 x5) as proof of ((cK X6) Xx)
% 268.65/269.02 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 268.65/269.02 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 268.65/269.02 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 268.65/269.02 Found x6:(X6 Xx0)
% 268.65/269.02 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 268.65/269.02 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 268.65/269.02 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 268.65/269.02 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 268.65/269.02 Found x400:=(x40 x5):((cK x2) Xx)
% 268.65/269.02 Found (x40 x5) as proof of ((cK X6) Xx)
% 268.65/269.02 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 268.65/269.02 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 268.65/269.02 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 268.65/269.02 Found x6:(X6 Xx0)
% 268.65/269.02 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 268.65/269.02 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 268.65/269.02 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 268.65/269.02 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 268.65/269.02 Found x400:=(x40 x5):((cK x2) Xx)
% 268.65/269.02 Found (x40 x5) as proof of ((cK X6) Xx)
% 268.65/269.02 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 268.65/269.02 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 268.65/269.02 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 268.65/269.02 Found x6:(X6 Xx0)
% 268.65/269.02 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 268.65/269.02 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 268.65/269.02 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 268.65/269.02 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 268.65/269.02 Found x400:=(x40 x5):((cK x2) Xx)
% 268.65/269.02 Found (x40 x5) as proof of ((cK X6) Xx)
% 268.65/269.02 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 268.65/269.02 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 268.65/269.02 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 268.65/269.02 Found x6:(X6 Xx0)
% 268.65/269.02 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 268.65/269.02 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 268.65/269.02 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 268.65/269.02 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 268.65/269.02 Found x400:=(x40 x5):((cK x2) Xx)
% 268.65/269.02 Found (x40 x5) as proof of ((cK X6) Xx)
% 268.65/269.02 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 268.65/269.02 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 268.65/269.02 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 268.65/269.02 Found x4:(X6 Xx0)
% 268.65/269.02 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 269.25/269.58 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 269.25/269.58 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 269.25/269.58 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 269.25/269.58 Found x4:(X6 Xx0)
% 269.25/269.58 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 269.25/269.58 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 269.25/269.58 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 269.25/269.58 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 269.25/269.58 Found x4:(X6 Xx0)
% 269.25/269.58 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 269.25/269.58 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 269.25/269.58 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 269.25/269.58 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 269.25/269.58 Found x4:(X6 Xx0)
% 269.25/269.58 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 269.25/269.58 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 269.25/269.58 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 269.25/269.58 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 269.25/269.58 Found x4:(X6 Xx0)
% 269.25/269.58 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 269.25/269.58 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 269.25/269.58 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 269.25/269.58 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 269.25/269.58 Found x4:(X6 Xx0)
% 269.25/269.58 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 269.25/269.58 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 269.25/269.58 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 269.25/269.58 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 269.25/269.58 Found x4:(X6 Xx0)
% 269.25/269.58 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 269.25/269.58 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 269.25/269.58 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 269.94/270.25 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 269.94/270.25 Found x4:(X6 Xx0)
% 269.94/270.25 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 269.94/270.25 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 269.94/270.25 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 269.94/270.25 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 269.94/270.25 Found x4:(X6 Xx0)
% 269.94/270.25 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 269.94/270.25 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 269.94/270.25 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 269.94/270.25 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 269.94/270.25 Found x4:(X6 Xx0)
% 269.94/270.25 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 269.94/270.25 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 269.94/270.25 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 269.94/270.25 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 269.94/270.25 Found x4:(X6 Xx0)
% 269.94/270.25 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 269.94/270.25 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 269.94/270.25 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 269.94/270.25 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 269.94/270.25 Found x4:(X6 Xx0)
% 269.94/270.25 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 269.94/270.25 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 269.94/270.25 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 269.94/270.25 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 269.94/270.25 Found x4:(X6 Xx0)
% 269.94/270.25 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 269.94/270.25 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 269.94/270.25 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 269.94/270.25 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 269.94/270.25 Found x4:(X6 Xx0)
% 269.94/270.25 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 269.94/270.25 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 270.42/270.75 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 270.42/270.75 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 270.42/270.75 Found x4:(X6 Xx0)
% 270.42/270.75 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 270.42/270.75 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 270.42/270.75 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 270.42/270.75 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 270.42/270.75 Found x4:(X6 Xx0)
% 270.42/270.75 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 270.42/270.75 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 270.42/270.75 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 270.42/270.75 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 270.42/270.75 Found x4:(X6 Xx0)
% 270.42/270.75 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 270.42/270.75 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 270.42/270.75 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 270.42/270.75 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 270.42/270.75 Found x4:(X6 Xx0)
% 270.42/270.75 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 270.42/270.75 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 270.42/270.75 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 270.42/270.75 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 270.42/270.75 Found x4:(X6 Xx0)
% 270.42/270.75 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 270.42/270.75 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 270.42/270.75 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 270.42/270.75 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 270.42/270.75 Found x4:(X6 Xx0)
% 270.42/270.75 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 270.42/270.75 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 270.42/270.75 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 270.42/270.75 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 270.93/271.29 Found x4:(X6 Xx0)
% 270.93/271.29 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 270.93/271.29 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 270.93/271.29 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 270.93/271.29 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 270.93/271.29 Found x4:(X6 Xx0)
% 270.93/271.29 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 270.93/271.29 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 270.93/271.29 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 270.93/271.29 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 270.93/271.29 Found x4:(X6 Xx0)
% 270.93/271.29 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 270.93/271.29 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 270.93/271.29 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 270.93/271.29 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 270.93/271.29 Found x4:(X6 Xx0)
% 270.93/271.29 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 270.93/271.29 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 270.93/271.29 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 270.93/271.29 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 270.93/271.29 Found x4:(X6 Xx0)
% 270.93/271.29 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 270.93/271.29 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 270.93/271.29 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 270.93/271.29 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 270.93/271.29 Found x4:(X6 Xx0)
% 270.93/271.29 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 270.93/271.29 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 270.93/271.29 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 270.93/271.29 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 270.93/271.29 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 270.93/271.29 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 270.93/271.29 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 270.93/271.29 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 270.93/271.29 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 271.22/271.53 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.22/271.53 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.22/271.53 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.22/271.53 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.22/271.53 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 271.22/271.53 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 271.22/271.53 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 271.22/271.53 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 271.22/271.53 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 271.22/271.53 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.22/271.53 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.22/271.53 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.22/271.53 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.22/271.53 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 271.22/271.53 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 271.22/271.53 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 271.22/271.53 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 271.22/271.53 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 271.22/271.53 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.22/271.53 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.22/271.53 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.22/271.53 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.22/271.53 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 271.22/271.53 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 271.22/271.53 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 271.22/271.53 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 271.22/271.53 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 271.22/271.53 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.22/271.53 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.22/271.53 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.43/271.73 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.43/271.73 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 271.43/271.73 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 271.43/271.73 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 271.43/271.73 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 271.43/271.73 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 271.43/271.73 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.43/271.73 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.43/271.73 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.43/271.73 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.43/271.73 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 271.43/271.73 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 271.43/271.73 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 271.43/271.73 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 271.43/271.73 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 271.43/271.73 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.43/271.73 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.43/271.73 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.43/271.73 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.43/271.73 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 271.43/271.73 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 271.43/271.73 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 271.43/271.73 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 271.43/271.73 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 271.43/271.73 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.43/271.73 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.43/271.73 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.43/271.73 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.43/271.73 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 271.43/271.73 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 271.43/271.73 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 271.43/271.73 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 271.43/271.79 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 271.43/271.79 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.43/271.79 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.43/271.79 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.43/271.79 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.43/271.79 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 271.43/271.79 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 271.43/271.79 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 271.43/271.79 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 271.43/271.79 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 271.43/271.79 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.43/271.79 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.43/271.79 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.43/271.79 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.43/271.79 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 271.43/271.79 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 271.43/271.79 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 271.43/271.79 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 271.43/271.79 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 271.43/271.79 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.43/271.79 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.43/271.79 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.43/271.79 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.43/271.79 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 271.43/271.79 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 271.43/271.79 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 271.43/271.79 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 271.43/271.79 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 271.43/271.79 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.43/271.79 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.43/271.79 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.74/272.09 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.74/272.09 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 271.74/272.09 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 271.74/272.09 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 271.74/272.09 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 271.74/272.09 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 271.74/272.09 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.74/272.09 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.74/272.09 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.74/272.09 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.74/272.09 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 271.74/272.09 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 271.74/272.09 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 271.74/272.09 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 271.74/272.09 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 271.74/272.09 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.74/272.09 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.74/272.09 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.74/272.09 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.74/272.09 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 271.74/272.09 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 271.74/272.09 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 271.74/272.09 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 271.74/272.09 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 271.74/272.09 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.74/272.09 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.74/272.09 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.74/272.09 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.74/272.09 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 271.74/272.09 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 271.74/272.09 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 271.82/272.12 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 271.82/272.12 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 271.82/272.12 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.82/272.12 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.82/272.12 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.82/272.12 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.82/272.12 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 271.82/272.12 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 271.82/272.12 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 271.82/272.12 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 271.82/272.12 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 271.82/272.12 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.82/272.12 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.82/272.12 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.82/272.12 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.82/272.12 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 271.82/272.12 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 271.82/272.12 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 271.82/272.12 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 271.82/272.12 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 271.82/272.12 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.82/272.12 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.82/272.12 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.82/272.12 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.82/272.12 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 271.82/272.12 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 271.82/272.12 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 271.82/272.12 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 271.82/272.12 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 271.82/272.12 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.82/272.12 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.82/272.12 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.90/272.26 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.90/272.26 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 271.90/272.26 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 271.90/272.26 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 271.90/272.26 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 271.90/272.26 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 271.90/272.26 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.90/272.26 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.90/272.26 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.90/272.26 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.90/272.26 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 271.90/272.26 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 271.90/272.26 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 271.90/272.26 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 271.90/272.26 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 271.90/272.26 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.90/272.26 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.90/272.26 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.90/272.26 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.90/272.26 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 271.90/272.26 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 271.90/272.26 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 271.90/272.26 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 271.90/272.26 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 271.90/272.26 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.90/272.26 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.90/272.26 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.90/272.26 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.90/272.26 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 271.99/272.28 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 271.99/272.28 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 271.99/272.28 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 271.99/272.28 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 271.99/272.28 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.99/272.28 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.99/272.28 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.99/272.28 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.99/272.28 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 271.99/272.28 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 271.99/272.28 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 271.99/272.28 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 271.99/272.28 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 271.99/272.28 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.99/272.28 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.99/272.28 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.99/272.28 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.99/272.28 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 271.99/272.28 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 271.99/272.28 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 271.99/272.28 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 271.99/272.28 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 271.99/272.28 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.99/272.28 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.99/272.28 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.99/272.28 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.99/272.28 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 271.99/272.28 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 271.99/272.28 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 271.99/272.28 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 271.99/272.28 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 271.99/272.28 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 271.99/272.28 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.01/272.29 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.01/272.29 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.01/272.29 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 272.01/272.29 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.01/272.29 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.01/272.29 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.01/272.29 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 272.01/272.29 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.01/272.29 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.01/272.29 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.01/272.29 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.01/272.29 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 272.01/272.29 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.01/272.29 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.01/272.29 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.01/272.29 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 272.01/272.29 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.01/272.29 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.01/272.29 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.01/272.29 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.01/272.29 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 272.01/272.29 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.01/272.29 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.01/272.29 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.01/272.29 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 272.01/272.29 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.01/272.29 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.01/272.29 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.01/272.29 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.01/272.30 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 272.01/272.30 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.01/272.30 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.01/272.30 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.01/272.30 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 272.01/272.30 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.01/272.30 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.01/272.30 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.01/272.30 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.01/272.30 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 272.01/272.30 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.01/272.30 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.01/272.30 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.01/272.30 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 272.01/272.30 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.01/272.30 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.01/272.30 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.01/272.30 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.01/272.30 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 272.01/272.30 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.01/272.30 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.01/272.30 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.01/272.30 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 272.01/272.30 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.01/272.30 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.01/272.30 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.01/272.30 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.01/272.30 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 272.01/272.30 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.01/272.30 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.01/272.30 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.01/272.30 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 272.01/272.30 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.04/272.38 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.04/272.38 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.04/272.38 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.04/272.38 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 272.04/272.38 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.04/272.38 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.04/272.38 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.04/272.38 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 272.04/272.38 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.04/272.38 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.04/272.38 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.04/272.38 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.04/272.38 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 272.04/272.38 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.04/272.38 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.04/272.38 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.04/272.38 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 272.04/272.38 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.04/272.38 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.04/272.38 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.04/272.38 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.04/272.38 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 272.04/272.38 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.04/272.38 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.04/272.38 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.04/272.38 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 272.04/272.38 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.04/272.38 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.04/272.38 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.04/272.38 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.20/272.49 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 272.20/272.49 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.20/272.49 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.20/272.49 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.20/272.49 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 272.20/272.49 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.20/272.49 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.20/272.49 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.20/272.49 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.20/272.49 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 272.20/272.49 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.20/272.49 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.20/272.49 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.20/272.49 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 272.20/272.49 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.20/272.49 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.20/272.49 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.20/272.49 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.20/272.49 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 272.20/272.49 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.20/272.49 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.20/272.49 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.20/272.49 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 272.20/272.49 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.20/272.49 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.20/272.49 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.20/272.49 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.20/272.49 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 272.20/272.49 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.20/272.49 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.20/272.49 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.20/272.49 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 272.20/272.57 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.20/272.57 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.20/272.57 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.20/272.57 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.20/272.57 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 272.20/272.57 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.20/272.57 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.20/272.57 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.20/272.57 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 272.20/272.57 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.20/272.57 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.20/272.57 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.20/272.57 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.20/272.57 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 272.20/272.57 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.20/272.57 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.20/272.57 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.20/272.57 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 272.20/272.57 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.20/272.57 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.20/272.57 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.20/272.57 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.20/272.57 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 272.20/272.57 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.20/272.57 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.20/272.57 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.20/272.57 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 272.20/272.57 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.20/272.57 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.20/272.57 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.45/272.77 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.45/272.77 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 272.45/272.77 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.45/272.77 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.45/272.77 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.45/272.77 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 272.45/272.77 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.45/272.77 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.45/272.77 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.45/272.77 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.45/272.77 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 272.45/272.77 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.45/272.77 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.45/272.77 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.45/272.77 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 272.45/272.77 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.45/272.77 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.45/272.77 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.45/272.77 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.45/272.77 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 272.45/272.77 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.45/272.77 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.45/272.77 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.45/272.77 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 272.45/272.77 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.45/272.77 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.45/272.77 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.45/272.77 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.45/272.77 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 272.45/272.77 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.45/272.77 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.45/272.77 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.45/272.77 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 272.51/272.85 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.51/272.85 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.51/272.85 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.51/272.85 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.51/272.85 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 272.51/272.85 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.51/272.85 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.51/272.85 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.51/272.85 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 272.51/272.85 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.51/272.85 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.51/272.85 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.51/272.85 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.51/272.85 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 272.51/272.85 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.51/272.85 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.51/272.85 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.51/272.85 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 272.51/272.85 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.51/272.85 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.51/272.85 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.51/272.85 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.51/272.85 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 272.51/272.85 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.51/272.85 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.51/272.85 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.51/272.85 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 272.51/272.85 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.51/272.85 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.51/272.85 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.58/272.86 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.58/272.86 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 272.58/272.86 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.58/272.86 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.58/272.86 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.58/272.86 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 272.58/272.86 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.58/272.86 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.58/272.86 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.58/272.86 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.58/272.86 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 272.58/272.86 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.58/272.86 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.58/272.86 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.58/272.86 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 272.58/272.86 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.58/272.86 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.58/272.86 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.58/272.86 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.58/272.86 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 272.58/272.86 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.58/272.86 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.58/272.86 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.58/272.86 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 272.58/272.86 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.58/272.86 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.58/272.86 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.58/272.86 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.58/272.86 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 272.58/272.86 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.58/272.86 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.58/272.86 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.62/272.91 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 272.62/272.91 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.62/272.91 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.62/272.91 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.62/272.91 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.62/272.91 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 272.62/272.91 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.62/272.91 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.62/272.91 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.62/272.91 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 272.62/272.91 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.62/272.91 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.62/272.91 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.62/272.91 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.62/272.91 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 272.62/272.91 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.62/272.91 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.62/272.91 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.62/272.91 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 272.62/272.91 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.62/272.91 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.62/272.91 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.62/272.91 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.62/272.91 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 272.62/272.91 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.62/272.91 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.62/272.91 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 272.62/272.91 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 272.62/272.91 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.62/272.91 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 272.62/272.91 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 273.09/273.40 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 273.09/273.40 Found x4:(X6 Xx0)
% 273.09/273.40 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 273.09/273.40 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 273.09/273.40 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 273.09/273.40 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 273.09/273.40 Found x4:(X6 Xx0)
% 273.09/273.40 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 273.09/273.40 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 273.09/273.40 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 273.09/273.40 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 273.09/273.40 Found x4:(X6 Xx0)
% 273.09/273.40 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 273.09/273.40 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 273.09/273.40 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 273.09/273.40 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 273.09/273.40 Found x4:(X6 Xx0)
% 273.09/273.40 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 273.09/273.40 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 273.09/273.40 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 273.09/273.40 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 273.09/273.40 Found x4:(X6 Xx0)
% 273.09/273.40 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 273.09/273.40 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 273.09/273.40 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 273.09/273.40 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 273.09/273.40 Found x4:(X6 Xx0)
% 273.09/273.40 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 273.09/273.40 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 273.09/273.40 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 273.09/273.40 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 273.70/274.06 Found x4:(X6 Xx0)
% 273.70/274.06 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 273.70/274.06 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 273.70/274.06 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 273.70/274.06 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 273.70/274.06 Found x4:(X6 Xx0)
% 273.70/274.06 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 273.70/274.06 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 273.70/274.06 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 273.70/274.06 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 273.70/274.06 Found x4:(X6 Xx0)
% 273.70/274.06 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 273.70/274.06 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 273.70/274.06 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 273.70/274.06 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 273.70/274.06 Found x4:(X6 Xx0)
% 273.70/274.06 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 273.70/274.06 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 273.70/274.06 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 273.70/274.06 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 273.70/274.06 Found x4:(X6 Xx0)
% 273.70/274.06 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 273.70/274.06 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 273.70/274.06 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 273.70/274.06 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 273.70/274.06 Found x4:(X6 Xx0)
% 273.70/274.06 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 273.70/274.06 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 273.70/274.06 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 273.70/274.06 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 273.70/274.06 Found x4:(X6 Xx0)
% 273.70/274.06 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 273.70/274.06 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 274.41/274.71 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 274.41/274.71 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 274.41/274.71 Found x4:(X6 Xx0)
% 274.41/274.71 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 274.41/274.71 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 274.41/274.71 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 274.41/274.71 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 274.41/274.71 Found x4:(X6 Xx0)
% 274.41/274.71 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 274.41/274.71 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 274.41/274.71 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 274.41/274.71 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 274.41/274.71 Found x4:(X6 Xx0)
% 274.41/274.71 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 274.41/274.71 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 274.41/274.71 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 274.41/274.71 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 274.41/274.71 Found x4:(X6 Xx0)
% 274.41/274.71 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 274.41/274.71 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 274.41/274.71 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 274.41/274.71 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 274.41/274.71 Found x4:(X6 Xx0)
% 274.41/274.71 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 274.41/274.71 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 274.41/274.71 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 274.41/274.71 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 274.41/274.71 Found x4:(X6 Xx0)
% 274.41/274.71 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 274.41/274.71 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 274.41/274.71 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 274.41/274.71 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 274.41/274.71 Found x4:(X6 Xx0)
% 274.41/274.71 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 275.80/276.15 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 275.80/276.15 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 275.80/276.15 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 275.80/276.15 Found x4:(X6 Xx0)
% 275.80/276.15 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 275.80/276.15 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 275.80/276.15 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 275.80/276.15 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 275.80/276.15 Found x4:(X6 Xx0)
% 275.80/276.15 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 275.80/276.15 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 275.80/276.15 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 275.80/276.15 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 275.80/276.15 Found x4:(X6 Xx0)
% 275.80/276.15 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 275.80/276.15 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 275.80/276.15 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 275.80/276.15 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 275.80/276.15 Found x4:(X6 Xx0)
% 275.80/276.15 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 275.80/276.15 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 275.80/276.15 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 275.80/276.15 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 275.80/276.15 Found x4:(X6 Xx0)
% 275.80/276.15 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 275.80/276.15 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 275.80/276.15 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 275.80/276.15 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 275.80/276.15 Found x6:(X6 Xx0)
% 275.80/276.15 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 275.80/276.15 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 275.80/276.15 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 276.70/277.05 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 276.70/277.05 Found x400:=(x40 x5):((cK x2) Xx)
% 276.70/277.05 Found (x40 x5) as proof of ((cK X6) Xx)
% 276.70/277.05 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 276.70/277.05 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 276.70/277.05 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 276.70/277.05 Found x6:(X6 Xx0)
% 276.70/277.05 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 276.70/277.05 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 276.70/277.05 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 276.70/277.05 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 276.70/277.05 Found x400:=(x40 x5):((cK x2) Xx)
% 276.70/277.05 Found (x40 x5) as proof of ((cK X6) Xx)
% 276.70/277.05 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 276.70/277.05 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 276.70/277.05 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 276.70/277.05 Found x6:(X6 Xx0)
% 276.70/277.05 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 276.70/277.05 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 276.70/277.05 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 276.70/277.05 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 276.70/277.05 Found x400:=(x40 x5):((cK x2) Xx)
% 276.70/277.05 Found (x40 x5) as proof of ((cK X6) Xx)
% 276.70/277.05 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 276.70/277.05 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 276.70/277.05 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 276.70/277.05 Found x6:(X6 Xx0)
% 276.70/277.05 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 276.70/277.05 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 276.70/277.05 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 276.70/277.05 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 276.70/277.05 Found x400:=(x40 x5):((cK x2) Xx)
% 276.70/277.05 Found (x40 x5) as proof of ((cK X6) Xx)
% 276.70/277.05 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 276.70/277.05 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 276.70/277.05 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 276.70/277.05 Found x6:(X6 Xx0)
% 276.70/277.05 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 276.70/277.05 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 276.70/277.05 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 276.70/277.05 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 276.70/277.05 Found x400:=(x40 x5):((cK x2) Xx)
% 276.70/277.05 Found (x40 x5) as proof of ((cK X6) Xx)
% 276.70/277.05 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 276.70/277.05 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 276.70/277.05 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 276.70/277.05 Found x6:(X6 Xx0)
% 276.70/277.05 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 276.70/277.05 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 276.70/277.05 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 276.99/277.27 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 276.99/277.27 Found x400:=(x40 x5):((cK x2) Xx)
% 276.99/277.27 Found (x40 x5) as proof of ((cK X6) Xx)
% 276.99/277.27 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 276.99/277.27 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 276.99/277.27 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 276.99/277.27 Found x6:(X6 Xx0)
% 276.99/277.27 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 276.99/277.27 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 276.99/277.27 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 276.99/277.27 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 276.99/277.27 Found x400:=(x40 x5):((cK x2) Xx)
% 276.99/277.27 Found (x40 x5) as proof of ((cK X6) Xx)
% 276.99/277.27 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 276.99/277.27 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 276.99/277.27 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 276.99/277.27 Found x6:(X6 Xx0)
% 276.99/277.27 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 276.99/277.27 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 276.99/277.27 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 276.99/277.27 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 276.99/277.27 Found x400:=(x40 x5):((cK x2) Xx)
% 276.99/277.27 Found (x40 x5) as proof of ((cK X6) Xx)
% 276.99/277.27 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 276.99/277.27 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 276.99/277.27 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 276.99/277.27 Found x6:(X6 Xx0)
% 276.99/277.27 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 276.99/277.27 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 276.99/277.27 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 276.99/277.27 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 276.99/277.27 Found x400:=(x40 x5):((cK x2) Xx)
% 276.99/277.27 Found (x40 x5) as proof of ((cK X6) Xx)
% 276.99/277.27 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 276.99/277.27 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 276.99/277.27 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 276.99/277.27 Found x6:(X6 Xx0)
% 276.99/277.27 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 276.99/277.27 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 276.99/277.27 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 276.99/277.27 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 276.99/277.27 Found x400:=(x40 x5):((cK x2) Xx)
% 276.99/277.27 Found (x40 x5) as proof of ((cK X6) Xx)
% 276.99/277.27 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 276.99/277.27 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 276.99/277.27 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 276.99/277.27 Found x6:(X6 Xx0)
% 276.99/277.27 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 276.99/277.27 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 276.99/277.27 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 277.22/277.51 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 277.22/277.51 Found x400:=(x40 x5):((cK x2) Xx)
% 277.22/277.51 Found (x40 x5) as proof of ((cK X6) Xx)
% 277.22/277.51 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 277.22/277.51 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 277.22/277.51 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 277.22/277.51 Found x6:(X6 Xx0)
% 277.22/277.51 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 277.22/277.51 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 277.22/277.51 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 277.22/277.51 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 277.22/277.51 Found x400:=(x40 x5):((cK x2) Xx)
% 277.22/277.51 Found (x40 x5) as proof of ((cK X6) Xx)
% 277.22/277.51 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 277.22/277.51 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 277.22/277.51 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 277.22/277.51 Found x6:(X6 Xx0)
% 277.22/277.51 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 277.22/277.51 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 277.22/277.51 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 277.22/277.51 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 277.22/277.51 Found x400:=(x40 x5):((cK x2) Xx)
% 277.22/277.51 Found (x40 x5) as proof of ((cK X6) Xx)
% 277.22/277.51 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 277.22/277.51 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 277.22/277.51 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 277.22/277.51 Found x6:(X6 Xx0)
% 277.22/277.51 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 277.22/277.51 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 277.22/277.51 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 277.22/277.51 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 277.22/277.51 Found x400:=(x40 x5):((cK x2) Xx)
% 277.22/277.51 Found (x40 x5) as proof of ((cK X6) Xx)
% 277.22/277.51 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 277.22/277.51 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 277.22/277.51 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 277.22/277.51 Found x6:(X6 Xx0)
% 277.22/277.51 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 277.22/277.51 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 277.22/277.51 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 277.22/277.51 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 277.22/277.51 Found x400:=(x40 x5):((cK x2) Xx)
% 277.22/277.51 Found (x40 x5) as proof of ((cK X6) Xx)
% 277.22/277.51 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 277.22/277.51 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 277.22/277.51 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 277.22/277.51 Found x6:(X6 Xx0)
% 277.22/277.51 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 277.22/277.51 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 277.22/277.51 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 277.44/277.80 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 277.44/277.80 Found x400:=(x40 x5):((cK x2) Xx)
% 277.44/277.80 Found (x40 x5) as proof of ((cK X6) Xx)
% 277.44/277.80 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 277.44/277.80 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 277.44/277.80 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 277.44/277.80 Found x6:(X6 Xx0)
% 277.44/277.80 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 277.44/277.80 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 277.44/277.80 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 277.44/277.80 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 277.44/277.80 Found x400:=(x40 x5):((cK x2) Xx)
% 277.44/277.80 Found (x40 x5) as proof of ((cK X6) Xx)
% 277.44/277.80 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 277.44/277.80 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 277.44/277.80 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 277.44/277.80 Found x6:(X6 Xx0)
% 277.44/277.80 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 277.44/277.80 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 277.44/277.80 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 277.44/277.80 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 277.44/277.80 Found x400:=(x40 x5):((cK x2) Xx)
% 277.44/277.80 Found (x40 x5) as proof of ((cK X6) Xx)
% 277.44/277.80 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 277.44/277.80 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 277.44/277.80 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 277.44/277.80 Found x6:(X6 Xx0)
% 277.44/277.80 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 277.44/277.80 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 277.44/277.80 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 277.44/277.80 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 277.44/277.80 Found x400:=(x40 x5):((cK x2) Xx)
% 277.44/277.80 Found (x40 x5) as proof of ((cK X6) Xx)
% 277.44/277.80 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 277.44/277.80 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 277.44/277.80 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 277.44/277.80 Found x6:(X6 Xx0)
% 277.44/277.80 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 277.44/277.80 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 277.44/277.80 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 277.44/277.80 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 277.44/277.80 Found x400:=(x40 x5):((cK x2) Xx)
% 277.44/277.80 Found (x40 x5) as proof of ((cK X6) Xx)
% 277.44/277.80 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 277.44/277.80 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 277.44/277.80 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 277.44/277.80 Found x6:(X6 Xx0)
% 277.44/277.80 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 277.44/277.80 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 277.74/278.02 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 277.74/278.02 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 277.74/278.02 Found x400:=(x40 x5):((cK x2) Xx)
% 277.74/278.02 Found (x40 x5) as proof of ((cK X6) Xx)
% 277.74/278.02 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 277.74/278.02 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 277.74/278.02 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 277.74/278.02 Found x6:(X6 Xx0)
% 277.74/278.02 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 277.74/278.02 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 277.74/278.02 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 277.74/278.02 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 277.74/278.02 Found x400:=(x40 x5):((cK x2) Xx)
% 277.74/278.02 Found (x40 x5) as proof of ((cK X6) Xx)
% 277.74/278.02 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 277.74/278.02 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 277.74/278.02 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 277.74/278.02 Found x6:(X6 Xx0)
% 277.74/278.02 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 277.74/278.02 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 277.74/278.02 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 277.74/278.02 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 277.74/278.02 Found x400:=(x40 x5):((cK x2) Xx)
% 277.74/278.02 Found (x40 x5) as proof of ((cK X6) Xx)
% 277.74/278.02 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 277.74/278.02 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 277.74/278.02 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 277.74/278.02 Found x6:(X6 Xx0)
% 277.74/278.02 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 277.74/278.02 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 277.74/278.02 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 277.74/278.02 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 277.74/278.02 Found x400:=(x40 x5):((cK x2) Xx)
% 277.74/278.02 Found (x40 x5) as proof of ((cK X6) Xx)
% 277.74/278.02 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 277.74/278.02 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 277.74/278.02 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 277.74/278.02 Found x6:(X6 Xx0)
% 277.74/278.02 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 277.74/278.02 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 277.74/278.02 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 277.74/278.02 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 277.74/278.02 Found x400:=(x40 x5):((cK x2) Xx)
% 277.74/278.02 Found (x40 x5) as proof of ((cK X6) Xx)
% 277.74/278.02 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 277.74/278.02 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 277.74/278.02 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 277.74/278.02 Found x6:(X6 Xx0)
% 277.74/278.02 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 277.74/278.02 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 277.93/278.25 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 277.93/278.25 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 277.93/278.25 Found x400:=(x40 x5):((cK x2) Xx)
% 277.93/278.25 Found (x40 x5) as proof of ((cK X6) Xx)
% 277.93/278.25 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 277.93/278.25 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 277.93/278.25 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 277.93/278.25 Found x6:(X6 Xx0)
% 277.93/278.25 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 277.93/278.25 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 277.93/278.25 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 277.93/278.25 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 277.93/278.25 Found x400:=(x40 x5):((cK x2) Xx)
% 277.93/278.25 Found (x40 x5) as proof of ((cK X6) Xx)
% 277.93/278.25 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 277.93/278.25 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 277.93/278.25 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 277.93/278.25 Found x6:(X6 Xx0)
% 277.93/278.25 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 277.93/278.25 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 277.93/278.25 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 277.93/278.25 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 277.93/278.25 Found x400:=(x40 x5):((cK x2) Xx)
% 277.93/278.25 Found (x40 x5) as proof of ((cK X6) Xx)
% 277.93/278.25 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 277.93/278.25 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 277.93/278.25 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 277.93/278.25 Found x6:(X6 Xx0)
% 277.93/278.25 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 277.93/278.25 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 277.93/278.25 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 277.93/278.25 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 277.93/278.25 Found x400:=(x40 x5):((cK x2) Xx)
% 277.93/278.25 Found (x40 x5) as proof of ((cK X6) Xx)
% 277.93/278.25 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 277.93/278.25 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 277.93/278.25 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 277.93/278.25 Found x6:(X6 Xx0)
% 277.93/278.25 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 277.93/278.25 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 277.93/278.25 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 277.93/278.25 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 277.93/278.25 Found x400:=(x40 x5):((cK x2) Xx)
% 277.93/278.25 Found (x40 x5) as proof of ((cK X6) Xx)
% 277.93/278.25 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 277.93/278.25 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 277.93/278.25 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 277.93/278.25 Found x6:(X6 Xx0)
% 277.93/278.25 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 277.93/278.25 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 279.13/279.42 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 279.13/279.42 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 279.13/279.42 Found x400:=(x40 x5):((cK x2) Xx)
% 279.13/279.42 Found (x40 x5) as proof of ((cK X6) Xx)
% 279.13/279.42 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 279.13/279.42 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 279.13/279.42 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 279.13/279.42 Found x6:(X6 Xx0)
% 279.13/279.42 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 279.13/279.42 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 279.13/279.42 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 279.13/279.42 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 279.13/279.42 Found x400:=(x40 x5):((cK x2) Xx)
% 279.13/279.42 Found (x40 x5) as proof of ((cK X6) Xx)
% 279.13/279.42 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 279.13/279.42 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 279.13/279.42 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 279.13/279.42 Found x6:(X6 Xx0)
% 279.13/279.42 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 279.13/279.42 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 279.13/279.42 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 279.13/279.42 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 279.13/279.42 Found x400:=(x40 x5):((cK x2) Xx)
% 279.13/279.42 Found (x40 x5) as proof of ((cK X6) Xx)
% 279.13/279.42 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 279.13/279.42 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 279.13/279.42 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 279.13/279.42 Found x6:(X6 Xx0)
% 279.13/279.42 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 279.13/279.42 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 279.13/279.42 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 279.13/279.42 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 279.13/279.42 Found x400:=(x40 x5):((cK x2) Xx)
% 279.13/279.42 Found (x40 x5) as proof of ((cK X6) Xx)
% 279.13/279.42 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 279.13/279.42 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 279.13/279.42 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 279.13/279.42 Found x6:(X6 Xx0)
% 279.13/279.42 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 279.13/279.42 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 279.13/279.42 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 279.13/279.42 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 279.13/279.42 Found x400:=(x40 x5):((cK x2) Xx)
% 279.13/279.42 Found (x40 x5) as proof of ((cK X6) Xx)
% 279.13/279.42 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 279.13/279.42 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 279.13/279.42 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 279.13/279.42 Found x6:(X6 Xx0)
% 279.13/279.42 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 279.13/279.42 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 280.45/280.79 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 280.45/280.79 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 280.45/280.79 Found x400:=(x40 x5):((cK x2) Xx)
% 280.45/280.79 Found (x40 x5) as proof of ((cK X6) Xx)
% 280.45/280.79 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 280.45/280.79 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 280.45/280.79 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 280.45/280.79 Found x6:(X6 Xx0)
% 280.45/280.79 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 280.45/280.79 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 280.45/280.79 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 280.45/280.79 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 280.45/280.79 Found x400:=(x40 x5):((cK x2) Xx)
% 280.45/280.79 Found (x40 x5) as proof of ((cK X6) Xx)
% 280.45/280.79 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 280.45/280.79 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 280.45/280.79 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 280.45/280.79 Found x6:(X6 Xx0)
% 280.45/280.79 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 280.45/280.79 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 280.45/280.79 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 280.45/280.79 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 280.45/280.79 Found x400:=(x40 x5):((cK x2) Xx)
% 280.45/280.79 Found (x40 x5) as proof of ((cK X6) Xx)
% 280.45/280.79 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 280.45/280.79 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 280.45/280.79 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 280.45/280.79 Found x6:(X6 Xx0)
% 280.45/280.79 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 280.45/280.79 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 280.45/280.79 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 280.45/280.79 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 280.45/280.79 Found x400:=(x40 x5):((cK x2) Xx)
% 280.45/280.79 Found (x40 x5) as proof of ((cK X6) Xx)
% 280.45/280.79 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 280.45/280.79 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 280.45/280.79 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 280.45/280.79 Found x6:(X6 Xx0)
% 280.45/280.79 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 280.45/280.79 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 280.45/280.79 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 280.45/280.79 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 280.45/280.79 Found x400:=(x40 x5):((cK x2) Xx)
% 280.45/280.79 Found (x40 x5) as proof of ((cK X6) Xx)
% 280.45/280.79 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 280.45/280.79 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 280.45/280.79 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 280.45/280.79 Found x6:(X6 Xx0)
% 280.45/280.79 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 281.44/281.75 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 281.44/281.75 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 281.44/281.75 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 281.44/281.75 Found x400:=(x40 x5):((cK x2) Xx)
% 281.44/281.75 Found (x40 x5) as proof of ((cK X6) Xx)
% 281.44/281.75 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 281.44/281.75 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 281.44/281.75 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 281.44/281.75 Found x4:(X6 Xx0)
% 281.44/281.75 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 281.44/281.75 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 281.44/281.75 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 281.44/281.75 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 281.44/281.75 Found x4:(X6 Xx0)
% 281.44/281.75 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 281.44/281.75 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 281.44/281.75 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 281.44/281.75 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 281.44/281.75 Found x4:(X6 Xx0)
% 281.44/281.75 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 281.44/281.75 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 281.44/281.75 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 281.44/281.75 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 281.44/281.75 Found x4:(X6 Xx0)
% 281.44/281.75 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 281.44/281.75 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 281.44/281.75 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 281.44/281.75 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 281.44/281.75 Found x4:(X6 Xx0)
% 281.44/281.75 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 281.44/281.75 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 281.44/281.75 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 281.44/281.75 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 281.44/281.75 Found x4:(X6 Xx0)
% 281.44/281.75 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 281.44/281.75 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 281.44/281.75 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 282.02/282.31 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 282.02/282.31 Found x4:(X6 Xx0)
% 282.02/282.31 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 282.02/282.31 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 282.02/282.31 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 282.02/282.31 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 282.02/282.31 Found x4:(X6 Xx0)
% 282.02/282.31 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 282.02/282.31 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 282.02/282.31 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 282.02/282.31 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 282.02/282.31 Found x4:(X6 Xx0)
% 282.02/282.31 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 282.02/282.31 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 282.02/282.31 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 282.02/282.31 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 282.02/282.31 Found x4:(X6 Xx0)
% 282.02/282.31 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 282.02/282.31 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 282.02/282.31 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 282.02/282.31 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 282.02/282.31 Found x4:(X6 Xx0)
% 282.02/282.31 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 282.02/282.31 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 282.02/282.31 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 282.02/282.31 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 282.02/282.31 Found x4:(X6 Xx0)
% 282.02/282.31 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 282.02/282.31 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 282.02/282.31 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 282.02/282.31 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 282.02/282.31 Found x4:(X6 Xx0)
% 282.02/282.31 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 282.71/283.03 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 282.71/283.03 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 282.71/283.03 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 282.71/283.03 Found x4:(X6 Xx0)
% 282.71/283.03 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 282.71/283.03 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 282.71/283.03 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 282.71/283.03 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 282.71/283.03 Found x4:(X6 Xx0)
% 282.71/283.03 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 282.71/283.03 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 282.71/283.03 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 282.71/283.03 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 282.71/283.03 Found x4:(X6 Xx0)
% 282.71/283.03 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 282.71/283.03 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 282.71/283.03 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 282.71/283.03 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 282.71/283.03 Found x4:(X6 Xx0)
% 282.71/283.03 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 282.71/283.03 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 282.71/283.03 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 282.71/283.03 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 282.71/283.03 Found x4:(X6 Xx0)
% 282.71/283.03 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 282.71/283.03 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 282.71/283.03 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 282.71/283.03 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 282.71/283.03 Found x4:(X6 Xx0)
% 282.71/283.03 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 282.71/283.03 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 282.71/283.03 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 283.72/284.04 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 283.72/284.04 Found x4:(X6 Xx0)
% 283.72/284.04 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 283.72/284.04 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 283.72/284.04 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 283.72/284.04 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 283.72/284.04 Found x4:(X6 Xx0)
% 283.72/284.04 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 283.72/284.04 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 283.72/284.04 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 283.72/284.04 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 283.72/284.04 Found x4:(X6 Xx0)
% 283.72/284.04 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 283.72/284.04 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 283.72/284.04 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 283.72/284.04 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 283.72/284.04 Found x4:(X6 Xx0)
% 283.72/284.04 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 283.72/284.04 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 283.72/284.04 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 283.72/284.04 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 283.72/284.04 Found x4:(X6 Xx0)
% 283.72/284.04 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 283.72/284.04 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 283.72/284.04 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 283.72/284.04 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 283.72/284.04 Found x4:(X6 Xx0)
% 283.72/284.04 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 283.72/284.04 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 283.72/284.04 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 283.72/284.04 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 283.72/284.04 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 283.72/284.04 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 283.72/284.04 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 283.72/284.04 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 283.94/284.25 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 283.94/284.25 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 283.94/284.25 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 283.94/284.25 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 283.94/284.25 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 283.94/284.25 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 283.94/284.25 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 283.94/284.25 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 283.94/284.25 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 283.94/284.25 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 283.94/284.25 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 283.94/284.25 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 283.94/284.25 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 283.94/284.25 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 283.94/284.25 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 283.94/284.25 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 283.94/284.25 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 283.94/284.25 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 283.94/284.25 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 283.94/284.25 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 283.94/284.25 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 283.94/284.25 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 283.94/284.25 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 283.94/284.25 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 283.94/284.25 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 283.94/284.25 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 283.94/284.25 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 283.94/284.25 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 283.94/284.25 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 283.94/284.25 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 283.94/284.25 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 284.03/284.32 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 284.03/284.32 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 284.03/284.32 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 284.03/284.32 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 284.03/284.32 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 284.03/284.32 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 284.03/284.32 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 284.03/284.32 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 284.03/284.32 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 284.03/284.32 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 284.03/284.32 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 284.03/284.32 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 284.03/284.32 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 284.03/284.32 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 284.03/284.32 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 284.03/284.32 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 284.03/284.32 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 284.03/284.32 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 284.03/284.32 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 284.03/284.32 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 284.03/284.32 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 284.03/284.32 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 284.03/284.32 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 284.03/284.32 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 284.03/284.32 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 284.03/284.32 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 284.03/284.32 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 284.03/284.32 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 284.03/284.32 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 284.03/284.32 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 284.03/284.32 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 284.18/284.48 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 284.18/284.48 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 284.18/284.48 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 284.18/284.48 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 284.18/284.48 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 284.18/284.48 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 284.18/284.48 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 284.18/284.48 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 284.18/284.48 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 284.18/284.48 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 284.18/284.48 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 284.18/284.48 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 284.18/284.48 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 284.18/284.48 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 284.18/284.48 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 284.18/284.48 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 284.18/284.48 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 284.18/284.48 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 284.18/284.48 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 284.18/284.48 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 284.18/284.48 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 284.18/284.48 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 284.18/284.48 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 284.18/284.48 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 284.18/284.48 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 284.18/284.48 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 284.18/284.48 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 284.18/284.48 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 284.18/284.48 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 284.18/284.48 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 284.18/284.48 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 284.18/284.48 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 284.24/284.56 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 284.24/284.56 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 284.24/284.56 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 284.24/284.56 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 284.24/284.56 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 284.24/284.56 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 284.24/284.56 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 284.24/284.56 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 284.24/284.56 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 284.24/284.56 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 284.24/284.56 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 284.24/284.56 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 284.24/284.56 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 284.24/284.56 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 284.24/284.56 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 284.24/284.56 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 284.24/284.56 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 284.24/284.56 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 284.24/284.56 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 284.24/284.56 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 284.24/284.56 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 284.24/284.56 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 284.24/284.56 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 284.24/284.56 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 284.24/284.56 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 284.24/284.56 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 284.24/284.56 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 284.24/284.56 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 284.24/284.56 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 284.39/284.73 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 284.39/284.73 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 284.39/284.73 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 284.39/284.73 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 284.39/284.73 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 284.39/284.73 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 284.39/284.73 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 284.39/284.73 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 284.39/284.73 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 284.39/284.73 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 284.39/284.73 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 284.39/284.73 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 284.39/284.73 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 284.39/284.73 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 284.39/284.73 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 284.39/284.73 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 284.39/284.73 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 284.39/284.73 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 284.39/284.73 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 284.39/284.73 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 284.39/284.73 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 284.39/284.73 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 284.39/284.73 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 284.39/284.73 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 284.39/284.73 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 284.39/284.73 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 284.39/284.73 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 284.39/284.73 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 284.39/284.73 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 284.39/284.73 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 284.39/284.73 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 284.39/284.73 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 284.39/284.73 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 284.39/284.74 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 284.39/284.74 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 284.39/284.74 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 284.39/284.74 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 284.39/284.74 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 284.39/284.74 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 284.39/284.74 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 284.39/284.74 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 284.39/284.74 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 284.39/284.74 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 284.39/284.74 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 284.39/284.74 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 284.39/284.74 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 284.39/284.74 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 284.39/284.74 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 284.39/284.74 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 284.39/284.74 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 284.39/284.74 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 284.39/284.74 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 284.39/284.74 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 284.39/284.74 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 284.39/284.74 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 284.39/284.74 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 284.39/284.74 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 284.39/284.74 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 284.39/284.74 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 284.39/284.74 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 284.39/284.74 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 284.39/284.74 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 284.49/284.79 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 284.49/284.79 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 284.49/284.79 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 284.49/284.79 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 284.49/284.79 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 284.49/284.79 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 284.49/284.79 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 284.49/284.79 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 284.49/284.79 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 284.49/284.79 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 284.49/284.79 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 284.49/284.79 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 284.49/284.79 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 284.49/284.79 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 284.49/284.79 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 284.49/284.79 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 284.49/284.79 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 284.49/284.79 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 284.49/284.79 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 284.49/284.79 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 284.49/284.79 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 284.49/284.79 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 284.49/284.79 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 284.49/284.79 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 284.49/284.79 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 284.49/284.79 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 284.49/284.79 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 284.49/284.79 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 284.49/284.79 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 284.49/284.79 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 284.49/284.79 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 284.49/284.79 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 284.49/284.79 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 285.81/286.11 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 285.81/286.11 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 285.81/286.11 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 285.81/286.11 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 285.81/286.11 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 285.81/286.11 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 285.81/286.11 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 285.81/286.11 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 285.81/286.11 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 285.81/286.11 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 285.81/286.11 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 285.81/286.11 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 285.81/286.11 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 285.81/286.11 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 285.81/286.11 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 285.81/286.11 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 285.81/286.11 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 285.81/286.11 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 285.81/286.11 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 285.81/286.11 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 285.81/286.11 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 285.81/286.11 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 285.81/286.11 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 285.81/286.11 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 285.81/286.11 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 285.81/286.11 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 285.81/286.11 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 285.81/286.11 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 285.81/286.11 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 285.81/286.11 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 286.21/286.50 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 286.21/286.50 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 286.21/286.50 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 286.21/286.50 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 286.21/286.50 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 286.21/286.50 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 286.21/286.50 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 286.21/286.50 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 286.21/286.50 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 286.21/286.50 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 286.21/286.50 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 286.21/286.50 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 286.21/286.50 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 286.21/286.50 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 286.21/286.50 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 286.21/286.50 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 286.21/286.50 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 286.21/286.50 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 286.21/286.50 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 286.21/286.50 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 286.21/286.50 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 286.21/286.50 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 286.21/286.50 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 286.21/286.50 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 286.21/286.50 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 286.21/286.50 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 286.21/286.50 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 286.21/286.50 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 286.21/286.50 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 286.21/286.50 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 286.21/286.50 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 286.21/286.50 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 286.31/286.68 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 286.31/286.68 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 286.31/286.68 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 286.31/286.68 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 286.31/286.68 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 286.31/286.68 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 286.31/286.68 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 286.31/286.68 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 286.31/286.68 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 286.31/286.68 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 286.31/286.68 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 286.31/286.68 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 286.31/286.68 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 286.31/286.68 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 286.31/286.68 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 286.31/286.68 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 286.31/286.68 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 286.31/286.68 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 286.31/286.68 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 286.31/286.68 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 286.31/286.68 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 286.31/286.68 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 286.31/286.68 Found x4:(X6 Xx0)
% 286.31/286.68 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 286.31/286.68 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 286.31/286.68 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 286.31/286.68 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 286.31/286.68 Found x4:(X6 Xx0)
% 286.31/286.68 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 286.31/286.68 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 287.02/287.36 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 287.02/287.36 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 287.02/287.36 Found x4:(X6 Xx0)
% 287.02/287.36 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 287.02/287.36 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 287.02/287.36 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 287.02/287.36 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 287.02/287.36 Found x4:(X6 Xx0)
% 287.02/287.36 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 287.02/287.36 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 287.02/287.36 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 287.02/287.36 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 287.02/287.36 Found x4:(X6 Xx0)
% 287.02/287.36 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 287.02/287.36 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 287.02/287.36 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 287.02/287.36 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 287.02/287.36 Found x4:(X6 Xx0)
% 287.02/287.36 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 287.02/287.36 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 287.02/287.36 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 287.02/287.36 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 287.02/287.36 Found x4:(X6 Xx0)
% 287.02/287.36 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 287.02/287.36 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 287.02/287.36 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 287.02/287.36 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 287.02/287.36 Found x4:(X6 Xx0)
% 287.02/287.36 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 287.02/287.36 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 287.02/287.36 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 287.02/287.36 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 287.02/287.36 Found x4:(X6 Xx0)
% 287.02/287.36 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 287.50/287.84 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 287.50/287.84 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 287.50/287.84 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 287.50/287.84 Found x4:(X6 Xx0)
% 287.50/287.84 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 287.50/287.84 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 287.50/287.84 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 287.50/287.84 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 287.50/287.84 Found x4:(X6 Xx0)
% 287.50/287.84 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 287.50/287.84 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 287.50/287.84 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 287.50/287.84 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 287.50/287.84 Found x4:(X6 Xx0)
% 287.50/287.84 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 287.50/287.84 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 287.50/287.84 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 287.50/287.84 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 287.50/287.84 Found x4:(X6 Xx0)
% 287.50/287.84 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 287.50/287.84 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 287.50/287.84 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 287.50/287.84 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 287.50/287.84 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 287.50/287.84 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 287.50/287.84 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 287.50/287.84 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 287.50/287.84 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 287.50/287.84 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 287.50/287.84 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 287.50/287.84 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 287.50/287.84 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 287.74/288.08 Found x4:(X6 Xx0)
% 287.74/288.08 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 287.74/288.08 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 287.74/288.08 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 287.74/288.08 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 287.74/288.08 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 287.74/288.08 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 287.74/288.08 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 287.74/288.08 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 287.74/288.08 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 287.74/288.08 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 287.74/288.08 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 287.74/288.08 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 287.74/288.08 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 287.74/288.08 Found x4:(X6 Xx0)
% 287.74/288.08 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 287.74/288.08 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 287.74/288.08 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 287.74/288.08 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 287.74/288.08 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 287.74/288.08 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 287.74/288.08 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 287.74/288.08 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 287.74/288.08 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 287.74/288.08 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 287.74/288.08 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 287.74/288.08 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 287.74/288.08 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 287.74/288.08 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 287.74/288.08 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 287.74/288.08 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 287.74/288.08 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 287.74/288.08 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 287.82/288.15 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 287.82/288.15 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 287.82/288.15 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 287.82/288.15 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 287.82/288.15 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 287.82/288.15 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 287.82/288.15 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 287.82/288.15 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 287.82/288.15 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 287.82/288.15 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 287.82/288.15 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 287.82/288.15 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 287.82/288.15 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 287.82/288.15 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 287.82/288.15 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 287.82/288.15 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 287.82/288.15 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 287.82/288.15 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 287.82/288.15 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 287.82/288.15 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 287.82/288.15 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 287.82/288.15 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 287.82/288.15 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 287.82/288.15 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 287.82/288.15 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 287.82/288.15 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 287.82/288.15 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 287.82/288.15 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 287.82/288.15 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 287.82/288.15 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 287.89/288.21 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 287.89/288.21 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 287.89/288.21 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 287.89/288.21 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 287.89/288.21 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 287.89/288.21 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 287.89/288.21 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 287.89/288.21 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 287.89/288.21 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 287.89/288.21 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 287.89/288.21 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 287.89/288.21 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 287.89/288.21 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 287.89/288.21 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 287.89/288.21 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 287.89/288.21 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 287.89/288.21 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 287.89/288.21 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 287.89/288.21 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 287.89/288.21 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 287.89/288.21 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 287.89/288.21 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 287.89/288.21 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 287.89/288.21 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 287.89/288.21 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 287.89/288.21 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 287.89/288.21 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 287.89/288.21 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 287.89/288.21 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 287.89/288.21 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 287.89/288.21 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 287.89/288.21 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 287.89/288.22 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 287.89/288.22 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 287.89/288.22 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 287.89/288.22 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 287.89/288.22 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 287.89/288.22 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 287.89/288.22 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 287.89/288.22 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 287.89/288.22 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 287.89/288.22 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 287.89/288.22 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 287.89/288.22 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 287.89/288.22 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 287.89/288.22 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 287.89/288.22 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 287.89/288.22 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 287.89/288.22 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 287.89/288.22 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 287.89/288.22 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 287.89/288.22 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 287.89/288.22 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 287.89/288.22 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 287.89/288.22 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 287.89/288.22 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 287.89/288.22 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 287.89/288.22 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 287.89/288.22 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 287.89/288.22 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 287.89/288.22 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 287.89/288.22 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 287.89/288.22 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 288.04/288.39 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 288.04/288.39 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 288.04/288.39 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 288.04/288.39 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 288.04/288.39 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 288.04/288.39 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 288.04/288.39 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 288.04/288.39 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 288.04/288.39 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 288.04/288.39 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 288.04/288.39 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 288.04/288.39 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 288.04/288.39 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 288.04/288.39 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 288.04/288.39 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 288.04/288.39 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 288.04/288.39 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 288.04/288.39 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 288.04/288.39 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 288.04/288.39 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 288.04/288.39 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 288.04/288.39 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 288.04/288.39 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 288.04/288.39 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 288.04/288.39 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 288.04/288.39 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 288.04/288.39 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 288.04/288.39 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 288.04/288.39 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 288.04/288.39 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 288.04/288.39 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 288.04/288.39 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 288.13/288.43 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 288.13/288.43 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 288.13/288.43 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 288.13/288.43 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 288.13/288.43 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 288.13/288.43 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 288.13/288.43 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 288.13/288.43 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 288.13/288.43 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 288.13/288.43 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 288.13/288.43 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 288.13/288.43 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 288.13/288.43 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 288.13/288.43 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 288.13/288.43 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 288.13/288.43 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 288.13/288.43 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 288.13/288.43 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 288.13/288.43 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 288.13/288.43 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 288.13/288.43 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 288.13/288.43 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 288.13/288.43 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 288.13/288.43 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 288.13/288.43 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 288.13/288.43 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 288.13/288.43 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 288.13/288.43 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 288.13/288.43 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 288.13/288.43 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 288.13/288.43 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 288.13/288.47 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 288.13/288.47 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 288.13/288.47 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 288.13/288.47 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 288.13/288.47 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 288.13/288.47 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 288.13/288.47 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 288.13/288.47 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 288.13/288.47 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 288.13/288.47 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 288.13/288.47 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 288.13/288.47 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 288.13/288.47 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 288.13/288.47 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 288.13/288.47 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 288.13/288.47 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 288.13/288.47 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 288.13/288.47 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 288.13/288.47 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 288.13/288.47 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 288.13/288.47 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 288.13/288.47 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 288.13/288.47 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 288.13/288.47 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 288.13/288.47 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 288.13/288.47 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 288.13/288.47 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 288.13/288.47 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 288.13/288.47 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 288.13/288.47 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 288.34/288.63 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 288.34/288.63 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 288.34/288.63 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 288.34/288.63 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 288.34/288.63 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 288.34/288.63 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 288.34/288.63 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 288.34/288.63 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 288.34/288.63 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 288.34/288.63 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 288.34/288.63 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 288.34/288.63 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 288.34/288.63 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 288.34/288.63 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 288.34/288.63 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 288.34/288.63 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 288.34/288.63 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 288.34/288.63 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 288.34/288.63 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 288.34/288.63 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 288.34/288.63 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 288.34/288.63 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 288.34/288.63 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 288.34/288.63 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 288.34/288.63 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 288.34/288.63 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 288.34/288.63 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 288.34/288.63 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 288.34/288.63 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 288.34/288.63 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 288.34/288.63 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 288.34/288.63 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 288.34/288.67 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 288.34/288.67 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 288.34/288.67 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 288.34/288.67 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 288.34/288.67 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 288.34/288.67 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 288.34/288.67 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 288.34/288.67 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 288.34/288.67 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 288.34/288.67 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 288.34/288.67 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 288.34/288.67 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 288.34/288.67 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 288.34/288.67 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 288.34/288.67 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 288.34/288.67 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 288.34/288.67 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 288.34/288.67 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 288.34/288.67 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 288.34/288.67 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 288.34/288.67 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 288.34/288.67 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 288.34/288.67 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 288.34/288.67 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 288.34/288.67 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 288.34/288.67 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 288.34/288.67 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 288.34/288.67 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 288.34/288.67 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 288.41/288.72 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 288.41/288.72 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 288.41/288.72 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 288.41/288.72 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 288.41/288.72 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 288.41/288.72 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 288.41/288.72 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 288.41/288.72 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 288.41/288.72 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 288.41/288.72 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 288.41/288.72 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 288.41/288.72 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 288.41/288.72 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 288.41/288.72 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 288.41/288.72 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 288.41/288.72 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 288.41/288.72 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 288.41/288.72 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 288.41/288.72 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 288.41/288.72 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 288.41/288.72 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 288.41/288.72 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 288.41/288.72 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 288.41/288.72 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 288.41/288.72 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 288.41/288.72 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 288.41/288.72 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 288.41/288.72 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 288.41/288.72 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 288.41/288.72 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 288.41/288.72 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 288.41/288.72 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 288.41/288.72 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 290.01/290.35 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 290.01/290.35 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 290.01/290.35 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 290.01/290.35 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 290.01/290.35 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 290.01/290.35 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 290.01/290.35 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 290.01/290.35 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 290.01/290.35 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 290.01/290.35 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 290.01/290.35 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 290.01/290.35 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 290.01/290.35 Found x4:(X6 Xx0)
% 290.01/290.35 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 290.01/290.35 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 290.01/290.35 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 290.01/290.35 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 290.01/290.35 Found x6:(X6 Xx0)
% 290.01/290.35 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 290.01/290.35 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 290.01/290.35 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 290.01/290.35 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 290.01/290.35 Found x400:=(x40 x5):((cK x2) Xx)
% 290.01/290.35 Found (x40 x5) as proof of ((cK X6) Xx)
% 290.01/290.35 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 290.01/290.35 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 290.01/290.35 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 290.01/290.35 Found x6:(X6 Xx0)
% 290.01/290.35 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 290.01/290.35 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 290.01/290.35 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 290.01/290.35 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 290.01/290.35 Found x400:=(x40 x5):((cK x2) Xx)
% 290.01/290.35 Found (x40 x5) as proof of ((cK X6) Xx)
% 290.01/290.35 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 290.01/290.35 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 290.40/290.76 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 290.40/290.76 Found x6:(X6 Xx0)
% 290.40/290.76 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 290.40/290.76 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 290.40/290.76 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 290.40/290.76 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 290.40/290.76 Found x400:=(x40 x5):((cK x2) Xx)
% 290.40/290.76 Found (x40 x5) as proof of ((cK X6) Xx)
% 290.40/290.76 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 290.40/290.76 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 290.40/290.76 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 290.40/290.76 Found x6:(X6 Xx0)
% 290.40/290.76 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 290.40/290.76 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 290.40/290.76 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 290.40/290.76 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 290.40/290.76 Found x400:=(x40 x5):((cK x2) Xx)
% 290.40/290.76 Found (x40 x5) as proof of ((cK X6) Xx)
% 290.40/290.76 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 290.40/290.76 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 290.40/290.76 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 290.40/290.76 Found x6:(X6 Xx0)
% 290.40/290.76 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 290.40/290.76 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 290.40/290.76 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 290.40/290.76 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 290.40/290.76 Found x400:=(x40 x5):((cK x2) Xx)
% 290.40/290.76 Found (x40 x5) as proof of ((cK X6) Xx)
% 290.40/290.76 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 290.40/290.76 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 290.40/290.76 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 290.40/290.76 Found x6:(X6 Xx0)
% 290.40/290.76 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 290.40/290.76 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 290.40/290.76 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 290.40/290.76 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 290.40/290.76 Found x400:=(x40 x5):((cK x2) Xx)
% 290.40/290.76 Found (x40 x5) as proof of ((cK X6) Xx)
% 290.40/290.76 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 290.40/290.76 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 290.40/290.76 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 290.40/290.76 Found x6:(X6 Xx0)
% 290.40/290.76 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 290.40/290.76 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 290.40/290.76 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 290.40/290.76 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 290.40/290.76 Found x400:=(x40 x5):((cK x2) Xx)
% 290.40/290.76 Found (x40 x5) as proof of ((cK X6) Xx)
% 290.40/290.76 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 290.40/290.76 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 290.72/291.07 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 290.72/291.07 Found x6:(X6 Xx0)
% 290.72/291.07 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 290.72/291.07 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 290.72/291.07 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 290.72/291.07 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 290.72/291.07 Found x400:=(x40 x5):((cK x2) Xx)
% 290.72/291.07 Found (x40 x5) as proof of ((cK X6) Xx)
% 290.72/291.07 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 290.72/291.07 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 290.72/291.07 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 290.72/291.07 Found x6:(X6 Xx0)
% 290.72/291.07 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 290.72/291.07 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 290.72/291.07 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 290.72/291.07 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 290.72/291.07 Found x400:=(x40 x5):((cK x2) Xx)
% 290.72/291.07 Found (x40 x5) as proof of ((cK X6) Xx)
% 290.72/291.07 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 290.72/291.07 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 290.72/291.07 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 290.72/291.07 Found x6:(X6 Xx0)
% 290.72/291.07 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 290.72/291.07 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 290.72/291.07 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 290.72/291.07 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 290.72/291.07 Found x400:=(x40 x5):((cK x2) Xx)
% 290.72/291.07 Found (x40 x5) as proof of ((cK X6) Xx)
% 290.72/291.07 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 290.72/291.07 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 290.72/291.07 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 290.72/291.07 Found x6:(X6 Xx0)
% 290.72/291.07 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 290.72/291.07 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 290.72/291.07 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 290.72/291.07 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 290.72/291.07 Found x400:=(x40 x5):((cK x2) Xx)
% 290.72/291.07 Found (x40 x5) as proof of ((cK X6) Xx)
% 290.72/291.07 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 290.72/291.07 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 290.72/291.07 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 290.72/291.07 Found x6:(X6 Xx0)
% 290.72/291.07 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 290.72/291.07 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 290.72/291.07 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 290.72/291.07 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 290.72/291.07 Found x400:=(x40 x5):((cK x2) Xx)
% 290.72/291.07 Found (x40 x5) as proof of ((cK X6) Xx)
% 290.72/291.07 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 291.08/291.38 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 291.08/291.38 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 291.08/291.38 Found x6:(X6 Xx0)
% 291.08/291.38 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 291.08/291.38 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 291.08/291.38 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 291.08/291.38 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 291.08/291.38 Found x400:=(x40 x5):((cK x2) Xx)
% 291.08/291.38 Found (x40 x5) as proof of ((cK X6) Xx)
% 291.08/291.38 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 291.08/291.38 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 291.08/291.38 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 291.08/291.38 Found x6:(X6 Xx0)
% 291.08/291.38 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 291.08/291.38 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 291.08/291.38 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 291.08/291.38 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 291.08/291.38 Found x400:=(x40 x5):((cK x2) Xx)
% 291.08/291.38 Found (x40 x5) as proof of ((cK X6) Xx)
% 291.08/291.38 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 291.08/291.38 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 291.08/291.38 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 291.08/291.38 Found x6:(X6 Xx0)
% 291.08/291.38 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 291.08/291.38 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 291.08/291.38 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 291.08/291.38 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 291.08/291.38 Found x400:=(x40 x5):((cK x2) Xx)
% 291.08/291.38 Found (x40 x5) as proof of ((cK X6) Xx)
% 291.08/291.38 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 291.08/291.38 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 291.08/291.38 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 291.08/291.38 Found x6:(X6 Xx0)
% 291.08/291.38 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 291.08/291.38 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 291.08/291.38 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 291.08/291.38 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 291.08/291.38 Found x400:=(x40 x5):((cK x2) Xx)
% 291.08/291.38 Found (x40 x5) as proof of ((cK X6) Xx)
% 291.08/291.38 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 291.08/291.38 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 291.08/291.38 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 291.08/291.38 Found x6:(X6 Xx0)
% 291.08/291.38 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 291.08/291.38 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 291.08/291.38 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 291.08/291.38 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 291.08/291.38 Found x400:=(x40 x5):((cK x2) Xx)
% 291.08/291.38 Found (x40 x5) as proof of ((cK X6) Xx)
% 293.62/293.93 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 293.62/293.93 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 293.62/293.93 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 293.62/293.93 Found x6:(X6 Xx0)
% 293.62/293.93 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 293.62/293.93 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 293.62/293.93 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 293.62/293.93 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 293.62/293.93 Found x400:=(x40 x5):((cK x2) Xx)
% 293.62/293.93 Found (x40 x5) as proof of ((cK X6) Xx)
% 293.62/293.93 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 293.62/293.93 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 293.62/293.93 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 293.62/293.93 Found x6:(X6 Xx0)
% 293.62/293.93 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 293.62/293.93 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 293.62/293.93 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 293.62/293.93 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 293.62/293.93 Found x400:=(x40 x5):((cK x2) Xx)
% 293.62/293.93 Found (x40 x5) as proof of ((cK X6) Xx)
% 293.62/293.93 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 293.62/293.93 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 293.62/293.93 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 293.62/293.93 Found x6:(X6 Xx0)
% 293.62/293.93 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 293.62/293.93 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 293.62/293.93 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 293.62/293.93 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 293.62/293.93 Found x400:=(x40 x5):((cK x2) Xx)
% 293.62/293.93 Found (x40 x5) as proof of ((cK X6) Xx)
% 293.62/293.93 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 293.62/293.93 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 293.62/293.93 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 293.62/293.93 Found x6:(X6 Xx0)
% 293.62/293.93 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 293.62/293.93 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 293.62/293.93 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 293.62/293.93 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 293.62/293.93 Found x400:=(x40 x5):((cK x2) Xx)
% 293.62/293.93 Found (x40 x5) as proof of ((cK X6) Xx)
% 293.62/293.93 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 293.62/293.93 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 293.62/293.93 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 293.62/293.93 Found x4:(X6 Xx0)
% 293.62/293.93 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 293.62/293.93 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 293.62/293.93 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 293.62/293.93 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 293.62/293.93 Found x4:(X6 Xx0)
% 293.62/293.93 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 294.00/294.39 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 294.00/294.39 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 294.00/294.39 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 294.00/294.39 Found x4:(X6 Xx0)
% 294.00/294.39 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 294.00/294.39 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 294.00/294.39 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 294.00/294.39 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 294.00/294.39 Found x4:(X6 Xx0)
% 294.00/294.39 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 294.00/294.39 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 294.00/294.39 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 294.00/294.39 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 294.00/294.39 Found x4:(X6 Xx0)
% 294.00/294.39 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 294.00/294.39 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 294.00/294.39 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 294.00/294.39 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 294.00/294.39 Found x4:(X6 Xx0)
% 294.00/294.39 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 294.00/294.39 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 294.00/294.39 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 294.00/294.39 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 294.00/294.39 Found x4:(X6 Xx0)
% 294.00/294.39 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 294.00/294.39 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 294.00/294.39 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 294.00/294.39 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 294.00/294.39 Found x4:(X6 Xx0)
% 294.00/294.39 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 294.00/294.39 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 294.00/294.39 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 294.59/294.91 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 294.59/294.91 Found x4:(X6 Xx0)
% 294.59/294.91 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 294.59/294.91 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 294.59/294.91 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 294.59/294.91 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 294.59/294.91 Found x4:(X6 Xx0)
% 294.59/294.91 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 294.59/294.91 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 294.59/294.91 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 294.59/294.91 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 294.59/294.91 Found x4:(X6 Xx0)
% 294.59/294.91 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 294.59/294.91 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 294.59/294.91 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 294.59/294.91 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 294.59/294.91 Found x4:(X6 Xx0)
% 294.59/294.91 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 294.59/294.91 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 294.59/294.91 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 294.59/294.91 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 294.59/294.91 Found x4:(X6 Xx0)
% 294.59/294.91 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 294.59/294.91 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 294.59/294.91 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 294.59/294.91 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 294.59/294.91 Found x4:(X6 Xx0)
% 294.59/294.91 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 294.59/294.91 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 294.59/294.91 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 294.59/294.91 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 294.59/294.91 Found x4:(X6 Xx0)
% 294.59/294.91 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 294.59/294.91 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 296.42/296.77 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 296.42/296.77 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 296.42/296.77 Found x6:(X6 Xx0)
% 296.42/296.77 Found x6 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 296.42/296.77 Found (fun (x6:(X6 Xx0))=> x6) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 296.42/296.77 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 296.42/296.77 Found (fun (Xx0:a) (x6:(X6 Xx0))=> x6) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 296.42/296.77 Found x400:=(x40 x5):((cK x2) Xx)
% 296.42/296.77 Found (x40 x5) as proof of ((cK X6) Xx)
% 296.42/296.77 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 296.42/296.77 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 296.42/296.77 Found ((x4 Xx) x5) as proof of ((cK X6) Xx)
% 296.42/296.77 Found x4:(X6 Xx0)
% 296.42/296.77 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 296.42/296.77 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 296.42/296.77 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 296.42/296.77 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 296.42/296.77 Found x4:(X6 Xx0)
% 296.42/296.77 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 296.42/296.77 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 296.42/296.77 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 296.42/296.77 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 296.42/296.77 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 296.42/296.77 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 296.42/296.77 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 296.42/296.77 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 296.42/296.77 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 296.42/296.77 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 296.42/296.77 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 296.42/296.77 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 296.42/296.77 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 296.42/296.77 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 296.42/296.77 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 296.42/296.77 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 296.42/296.77 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 296.42/296.77 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 296.60/296.90 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 296.60/296.90 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 296.60/296.90 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 296.60/296.90 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 296.60/296.90 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 296.60/296.90 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 296.60/296.90 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 296.60/296.90 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 296.60/296.91 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 296.60/296.91 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 296.60/296.91 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 296.60/296.91 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 296.60/296.91 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 296.60/296.91 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 296.60/296.91 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 296.60/296.91 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 296.60/296.91 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 296.60/296.91 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 296.60/296.91 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 296.60/296.91 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 296.60/296.91 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 296.60/296.91 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 296.60/296.91 Found x4:(X6 Xx0)
% 296.60/296.91 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 296.60/296.91 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 296.60/296.91 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 296.60/296.91 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 296.60/296.91 Found x4:(X6 Xx0)
% 296.60/296.91 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 296.60/296.91 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 296.60/296.91 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 297.01/297.38 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 297.01/297.38 Found x4:(X6 Xx0)
% 297.01/297.38 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 297.01/297.38 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 297.01/297.38 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 297.01/297.38 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 297.01/297.38 Found x4:(X6 Xx0)
% 297.01/297.38 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 297.01/297.38 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 297.01/297.38 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 297.01/297.38 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 297.01/297.38 Found x4:(X6 Xx0)
% 297.01/297.38 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 297.01/297.38 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 297.01/297.38 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 297.01/297.38 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 297.01/297.38 Found x4:(X6 Xx0)
% 297.01/297.38 Found x4 as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 297.01/297.38 Found (fun (x4:(X6 Xx0))=> x4) as proof of ((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0))))
% 297.01/297.38 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of ((X6 Xx0)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx00:a), ((S Xx00)->((cK S) Xx00)))) (S Xx0)))))
% 297.01/297.38 Found (fun (Xx0:a) (x4:(X6 Xx0))=> x4) as proof of (forall (Xx:a), ((X6 Xx)->((ex (a->Prop)) (fun (S:(a->Prop))=> ((and (forall (Xx0:a), ((S Xx0)->((cK S) Xx0)))) (S Xx))))))
% 297.01/297.38 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 297.01/297.38 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.01/297.38 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.01/297.38 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.01/297.38 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 297.01/297.38 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.01/297.38 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.01/297.38 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.01/297.38 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.01/297.38 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 297.01/297.38 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.01/297.38 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.11/297.42 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.11/297.42 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 297.11/297.42 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.11/297.42 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.11/297.42 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.11/297.42 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.11/297.42 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 297.11/297.42 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.11/297.42 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.11/297.42 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.11/297.42 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 297.11/297.42 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.11/297.42 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.11/297.42 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.11/297.42 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.11/297.42 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 297.11/297.42 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.11/297.42 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.11/297.42 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.11/297.42 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 297.11/297.42 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.11/297.42 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.11/297.42 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.11/297.42 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.11/297.42 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 297.11/297.42 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.11/297.42 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.11/297.42 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.11/297.42 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 297.11/297.42 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.11/297.42 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.11/297.42 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.11/297.44 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.11/297.44 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 297.11/297.44 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.11/297.44 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.11/297.44 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.11/297.44 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 297.11/297.44 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.11/297.44 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.11/297.44 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.11/297.44 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.11/297.44 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 297.11/297.44 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.11/297.44 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.11/297.44 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.11/297.44 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 297.11/297.44 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.11/297.44 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.11/297.44 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.11/297.44 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.11/297.44 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 297.11/297.44 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.11/297.44 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.11/297.44 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.11/297.44 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 297.11/297.44 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.11/297.44 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.11/297.44 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.11/297.44 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.11/297.44 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 297.20/297.51 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.20/297.51 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.20/297.51 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.20/297.51 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 297.20/297.51 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.20/297.51 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.20/297.51 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.20/297.51 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.20/297.51 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 297.20/297.51 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.20/297.51 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.20/297.51 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.20/297.51 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 297.20/297.51 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.20/297.51 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.20/297.51 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.20/297.51 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.20/297.51 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 297.20/297.51 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.20/297.51 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.20/297.51 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.20/297.51 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 297.20/297.51 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.20/297.51 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.20/297.51 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.20/297.51 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.20/297.51 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 297.20/297.51 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.20/297.51 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.20/297.51 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.20/297.51 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 297.20/297.51 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.20/297.51 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.20/297.55 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.20/297.55 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.20/297.55 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 297.20/297.55 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.20/297.55 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.20/297.55 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.20/297.55 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 297.20/297.55 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.20/297.55 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.20/297.55 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.20/297.55 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.20/297.55 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 297.20/297.55 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.20/297.55 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.20/297.55 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.20/297.55 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 297.20/297.55 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.20/297.55 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.20/297.55 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.20/297.55 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.20/297.55 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 297.20/297.55 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.20/297.55 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.20/297.55 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.20/297.55 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 297.20/297.55 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.20/297.55 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.20/297.55 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.20/297.55 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.72/298.05 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 297.72/298.05 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.72/298.05 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.72/298.05 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.72/298.05 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 297.72/298.05 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.72/298.05 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.72/298.05 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.72/298.05 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.72/298.05 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 297.72/298.05 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.72/298.05 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.72/298.05 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.72/298.05 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 297.72/298.05 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.72/298.05 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.72/298.05 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.72/298.05 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.72/298.05 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 297.72/298.05 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.72/298.05 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.72/298.05 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.72/298.05 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 297.72/298.05 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.72/298.05 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.72/298.05 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.72/298.05 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.72/298.05 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 297.72/298.05 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.72/298.05 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.72/298.05 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.72/298.05 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 297.72/298.05 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.72/298.06 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.72/298.06 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.72/298.06 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.72/298.06 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 297.72/298.06 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.72/298.06 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.72/298.06 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.72/298.06 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 297.72/298.06 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.72/298.06 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.72/298.06 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.72/298.06 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.72/298.06 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 297.72/298.06 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.72/298.06 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.72/298.06 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.72/298.06 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 297.72/298.06 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.72/298.06 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.72/298.06 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.72/298.06 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.72/298.06 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 297.72/298.06 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.72/298.06 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.72/298.06 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.72/298.06 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 297.72/298.06 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.72/298.06 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.72/298.06 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.72/298.06 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.72/298.07 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 297.72/298.07 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.72/298.07 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.72/298.07 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.72/298.07 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 297.72/298.07 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.72/298.07 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.72/298.07 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.72/298.07 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.72/298.07 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 297.72/298.07 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.72/298.07 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.72/298.07 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.72/298.07 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 297.72/298.07 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.72/298.07 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.72/298.07 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.72/298.07 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.72/298.07 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 297.72/298.07 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.72/298.07 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.72/298.07 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.72/298.07 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 297.72/298.07 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.72/298.07 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.72/298.07 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.72/298.07 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.72/298.07 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 297.72/298.07 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.72/298.07 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.72/298.07 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.72/298.07 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 297.72/298.10 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.72/298.10 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.72/298.10 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.72/298.10 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.72/298.10 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 297.72/298.10 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.72/298.10 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.72/298.10 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.72/298.10 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 297.72/298.10 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.72/298.10 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.72/298.10 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.72/298.10 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.72/298.10 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 297.72/298.10 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.72/298.10 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.72/298.10 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.72/298.10 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 297.72/298.10 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.72/298.10 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.72/298.10 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.72/298.10 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.72/298.10 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 297.72/298.10 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.72/298.10 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.72/298.10 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.72/298.10 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 297.72/298.10 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.72/298.10 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.72/298.10 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.72/298.10 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.82/298.12 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 297.82/298.12 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.82/298.12 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.82/298.12 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.82/298.12 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 297.82/298.12 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.82/298.12 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.82/298.12 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.82/298.12 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.82/298.12 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 297.82/298.12 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.82/298.12 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.82/298.12 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.82/298.12 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 297.82/298.12 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.82/298.12 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.82/298.12 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.82/298.12 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.82/298.12 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 297.82/298.12 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.82/298.12 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.82/298.12 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.82/298.12 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 297.82/298.12 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.82/298.12 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.82/298.12 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.82/298.12 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.82/298.12 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 297.82/298.12 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.82/298.12 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.82/298.12 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.82/298.12 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 297.82/298.13 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.82/298.13 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.82/298.13 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.82/298.13 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.82/298.13 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 297.82/298.13 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.82/298.13 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.82/298.13 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.82/298.13 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 297.82/298.13 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.82/298.13 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.82/298.13 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.82/298.13 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.82/298.13 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 297.82/298.13 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.82/298.13 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.82/298.13 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.82/298.13 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 297.82/298.13 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.82/298.13 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.82/298.13 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.82/298.13 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.82/298.13 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 297.82/298.13 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.82/298.13 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.82/298.13 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 297.82/298.13 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 297.82/298.13 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.82/298.13 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 297.82/298.13 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 298.11/298.44 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 298.11/298.44 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 298.11/298.44 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 298.11/298.44 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 298.11/298.44 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 298.11/298.44 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 298.11/298.44 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 298.11/298.44 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 298.11/298.44 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 298.11/298.44 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 298.11/298.44 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 298.11/298.44 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 298.11/298.44 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 298.11/298.44 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 298.11/298.44 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 298.11/298.44 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 298.11/298.44 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 298.11/298.44 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 298.11/298.44 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 298.11/298.44 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 298.11/298.44 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 298.11/298.44 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 298.11/298.44 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 298.11/298.44 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 298.11/298.44 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 298.11/298.44 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 298.11/298.44 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 298.11/298.44 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 298.11/298.44 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 298.11/298.44 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 298.11/298.44 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 298.11/298.44 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 298.31/298.62 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 298.31/298.62 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 298.31/298.62 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 298.31/298.62 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 298.31/298.62 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 298.31/298.62 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 298.31/298.62 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 298.31/298.62 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 298.31/298.62 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 298.31/298.62 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 298.31/298.62 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 298.31/298.62 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 298.31/298.62 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 298.31/298.62 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 298.31/298.62 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 298.31/298.62 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 298.31/298.62 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 298.31/298.62 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 298.31/298.62 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 298.31/298.62 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 298.31/298.62 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 298.31/298.62 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 298.31/298.62 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 298.31/298.62 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 298.31/298.62 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 298.31/298.62 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 298.31/298.62 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 298.31/298.62 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 298.31/298.62 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 298.31/298.62 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 298.31/298.62 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 298.33/298.66 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 298.33/298.66 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 298.33/298.66 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 298.33/298.66 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 298.33/298.66 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 298.33/298.66 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 298.33/298.66 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 298.33/298.66 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 298.33/298.66 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 298.33/298.66 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 298.33/298.66 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 298.33/298.66 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 298.33/298.66 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 298.33/298.66 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 298.33/298.66 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 298.33/298.66 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 298.33/298.66 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 298.33/298.66 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 298.33/298.66 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 298.33/298.66 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 298.33/298.66 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 298.33/298.66 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 298.33/298.66 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 298.33/298.66 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 298.33/298.66 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 298.33/298.66 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 298.33/298.66 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 298.33/298.66 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 298.33/298.66 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 298.33/298.66 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 298.33/298.67 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 298.33/298.67 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 298.33/298.67 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 298.33/298.67 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 298.33/298.67 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 298.33/298.67 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 298.33/298.67 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 298.33/298.67 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 298.33/298.67 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 298.33/298.67 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 298.33/298.67 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 298.33/298.67 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 298.33/298.67 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 298.33/298.67 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 298.33/298.67 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 298.33/298.67 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 298.33/298.67 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 298.33/298.67 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 298.33/298.67 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 298.33/298.67 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 298.33/298.67 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 298.33/298.67 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 298.33/298.67 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 298.33/298.67 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 298.33/298.67 Found (((fun (P:Type) (x4:((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->P)))=> (((((and_rect (forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))) (x2 Xx)) P) x4) x3)) ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 298.33/298.67 Found x40:=(x4 Xx):((x2 Xx)->((cK x2) Xx))
% 298.33/298.67 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 298.33/298.67 Found (x4 Xx) as proof of ((x2 Xx)->((cK X6) Xx))
% 298.33/298.67 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((x2 Xx)->((cK X6) Xx))
% 298.33/298.67 Found (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx)) as proof of ((forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0)))->((x2 Xx)->((cK X6) Xx)))
% 298.33/298.67 Found (and_rect00 (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X6) Xx)
% 298.33/298.67 Found ((and_rect0 ((cK X6) Xx)) (fun (x4:(forall (Xx0:a), ((x2 Xx0)->((cK x2) Xx0))))=> (x4 Xx))) as proof of ((cK X
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